PES INSTITUTE OF TECHNOLOGY- BANGALORE SOUTH CAMPUS

Size: px
Start display at page:

Download "PES INSTITUTE OF TECHNOLOGY- BANGALORE SOUTH CAMPUS"

Transcription

1 Sixth Semester B.E. IA Test I, Feb, 2015 USN 1 P E I S PES INSTITUTE OF TECHNOLOGY- BANGALORE SOUTH CAMPUS (Hosur Road, Electronic City, Bangalore ) Date & Time: , 8:30 AM - 11:00 AM Max Marks: 50 Subject & Code: Software Testing & 10IS65 Time: 90 Minutes Branch: Information Science & Engineering Semester: VI A & B Name of Faculty: Mr. Animesh Giri Solution Schema 1. a) Explain Structural testing (White Box) with diagram & list out the advantages and drawbacks of Functional (Black Box) testing approach (6 Marks) Answer: White box/structural/clear box testing: White box testing (also known as clear box testing, glass box testing, and transparent box testing and structural testing) is a method of testing software that tests internal structures or workings of an application, as opposed to its functionality. Some structural testing methods are Path testing and dataflow testing. Fig: White box testing Functional testing have two distinct advantages: 1) They are independent of how the software is implemented, so if the implementation changes the test cases are still useful. 2) Test case development can occur in parallel with the implementation, there by reducing the overall project development interval.

2 Drawbacks of functional testing approach: 1) Significant redundancies may exist among test cases, compounded by the possibility of gaps of untested software. 2) Because functional testing are based on the specified behavior, it is hard to imagine these methods identifying behaviors that are not on the specified behavior b) What are the motivation behind usage of Equivalence Class testing & how does it addresses the problem observed in Boundary Value Analysis testing. (4 Marks) Answer: The use of equivalence classes as the basis for functional testing has two motivations: a. To have a sense of complete testing and b. To avoid redundancy The problems faced in BVA method are: The test cases generated by BVA method emphasize more on the extreme values of input variables. Hence, in BVA method serious gaps exist between test cases which does not results in a satisfactory testing. Moreover, it has an assumption that the input variables are truly independent, and when this assumption is not warranted, the method generates unsatisfactory test cases. The BVA test cases are obtained by holding the values of all but one variable at their nominal values, and letting that variable assume its extreme values. This results in redundant test cases at nominal values of variables. Both the problems faced in BVA test cases are overcome by Equivalence class test cases: Equivalence classes form partitions of an input set, where partitions refer to a collection of mutually disjoint subsets, the union of which is the entire set. This has two implications for testing: the fact that the entire set is represented provides a form of completeness, and The disjointedness ensures a form of non redundancy. 2. Explain in detail the Worst-Case Boundary Value Analysis (WC-BVA) testing with appropriate diagram to generate test cases for a function of two variables, Also, List all the generated WC-BVA Test Cases. Finally tabulate 10 Unique Test Cases along with the expected output for Triangle Problem (10 Marks) Answer: Worst Case Testing:

3 Worst Case testing considers the five element set that contains the min, min+, nom, max- and max values for each variable. Cartesian product of these sets is taken to generate test cases. Worst case testing does not consider the single fault assumption of reliability theory. Worst case testing is clearly more thorough in the sense that boundary value analysis test cases are proper subset of worst case test cases. Worst case test cases for a function of n variables generate 5 n test cases. Worst case test cases for a function of two variables is shown in Figure 2.4 x 2 d c a b x 1 Case a b c Expected Output Isosceles Isosceles Equilateral Isosceles Not A Triangle Isosceles Isosceles 3. Tabulate 10 each unique Test Case along with the expected output by applying Robust BVA & Worst BVA approach. Mention the boundary for each variables used for the below mentioned examples. i) NextDate Function ii) Commission Problem (10 Marks)

4 Answer: Next Date Function: NextDate is a function of three variables: month,day, and year. It returns the date if the day after the input date. The month, day, and year variables have integer values subject to these conditions: c1. 1<=month<=12 c2. 1<= day<=31 c <=year<=2012 NextDate function Boundary Value Analysis Test Cases Case month day year Expected Output june 16, june 16, june 16, june 16, june 16, june 2, june 3,1912 Commission Problem Output Boundary Value Analysis Test Cases: Case Locks Stocks Barrels Sales Commission Comment Output minimum Output minimum Output minimum Output minimum Midpoint Border Point Border Point-

5 4. Explain in detail the Equivalence Class testing technique for a function of two variables generating all possible test cases considering i) Weak Normal Equivalence Class Testing ii) Strong Robust Equivalence Class Testing Mention all possible Valid & Invalid Equivalence Classes for generating test cases for Next Date Function. Finally tabulate 10 Unique Test Cases along with the expected output by applying Weak Normal & Strong Robust Equivalence Class Testing approach (10 Marks) Answer:. Weak Normal Equivalence Class Testing: It identifies equivalence classes of valid values. Faults due to valid values of a single variable is detected (Single fault assumption). Weak normal class testing is accomplished by using one variable from each equivalence class (interval) in a test case. It is suitable for regression testing. Weak normal equivalence class test cases: where, a<=x1<=d, with intervals [a,b), [b,c), [c,d]; e<=x2<=g, with intervals [e,f), [f,g] are valid classes ii). Strong robust Equivalence Class Testing: In Strong robust Equivalence Class testing, the robust part comes from consideration of invalid values, and the strong part refers to the multiple fault assumption. we obtain test cases from each element of the cartesian product of all the equivalence classes, as shown:

6 where, a<=x1<=d, with intervals [a,b), [b,c), [c,d]; e<=x2<=g, with intervals [e,f), [f,g] x1<a, x1>d and x1<e, x2>g are valid classes and are invalid classes Problem Statement: NextDate is a function of three variables: month, day, and year. It returns the date if the day after the input date. The month, day, and year variables have integer values subject to these conditions: c1. 1<=month<=12 c2. 1<= day<=31 c <=year<=2012 Responses are defined for invalid values of the input variables for the day, month, and year and invalid combination of inputs. If any of the conditions c1, c2 and c3 fails, NextDate produces an output indicating the corresponding variable has an out of range value. The NextDate function illustrates very well the craft of choosing the underlying equivalence relation. NextDate is a function of three variables month, day, and year and these have intervals of valid values defined as follows: M1 = {month : 1 month 12} D1 = {day : 1 day 31} Y1 = {year : 1812 year 2012} The invalid equivalence classes are: M2 = {month : month < 1} M3 = {month : month > 12} D2 = day : day < 1} D3 = {day : day>31} Y2 = {year : year < 1812} Y3 = {year : year >2012}

7 Because the number of valid classes equals the number of independent variables, onl one weak normal equivalence class test case occurs, and it is identical to the strong normal equivalence class test case: Case ID Month Day Year Expected Output WN1, SN /16/1912 Here is the full set of weak robust test cases: Case ID Month Day Year Expected Output WR /16/1912 WR Value of month not in range 1 12 WR Value of month not in range 1 12 WR Value of day not in range 1 31 WR Value of day not in range 1 31 WR Value of year not in range WR Value of year not in range Here is one corner of the cube in 3 space of the additional strong robust equivalence class test cases: Case ID Month Day Year Expected Output SR Value of month not in range 1 12 SR Value of day not in range 1 31 SR Value of year not in range SR Value of day not in range 1 31 Value of month not in range 1 12 SR Value of day not in range 1 31 Value of year not in range SR Value of year not in range Value of month not in range 1 12 SR Value of month not in range 1 12 Value of day not in the range 1 31

8 Value of year not in range If we carefully choose the equivalence relation, the resulting equivalence classes will be more useful. We next reduce the granularity by focusing on more specific treatment. What must be done to an input date? If it is the last day of a month, the NextDate function will simple increment the day value. At the end of a month, the next day is 1 and the month is incremented. At the end of a year, both the day and month are reset to 1, and the year is incremented. Finally, the problem of leap year makes determining the last day of a month interesting. With all this in mind, we might postulate the following equivalence classes: M1 = {month : month has 30 days} M2 = {month : month has 31 days} M3 = {month : month is February} D1 = {day : 1 day 28} D2 = {day : day = 29} D3 = {day : day = 30} D4 = {day : day = 31} Y1 = {year : year = 2000} Y2 = {year : year is a non century leap year} Y3 = {year : year is a common year} By choosing separate classes for 30 and 31 day months, we simplify the question of the last day of a month. By taking February as a separate class, we can give more attention to leap year questions. We also give special attention to day values: days in D1 are (nearly) always incremented, while days in D4 only have meaning for months in M2. Finally, we have three classes of years: the special case of the year 2000, leap years, and non leap years. This is not a perfect set of equivalence classes, but its use will reveal many potential errors Equivalence Class Test Cases: Weak Normal Equivalence class test cases for the revised classes are: Case ID Month Day Year Expected Output WN /15/1912 WN /30/1996

9 WN Invalid input date WN Invalid input date Strong Normal Equivalence class test cases for the revised classes are: Case ID Month Day Year Expected Output SN /15/2000 SN /15/1996 SN /15/2002 SN /30/2000 SN /30/1996 SN /30/2002 SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date SN /15/2000 SN /15/1996 SN /15/2002 SN /30/2000 SN /30/1996 SN /30/2002 SN /31/2000 SN /31/1996 SN /31/2002 SN /1/2000 SN /1/1996 SN /1/2002 SN /15/2000 SN /15/1996 SN /15/2002 SN Invalid input date SN /1/1996 SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date SN Invalid input date

10 The move from weak to strong, whether with normal or robust classes, always makes the presumption of independence, and this is reflected in the crossproduct of the equivalence classes. 3 month classes 4 day classes 3 year classes = 36 strong normal equivalence test cases. 5. a) Illustrate the scenario with the help of sample decision table where the decision table is Redundant and Inconsistent (i.e. Nondeterministic). (4 Marks) Answer: Decision table be concluded as redundant - if it has two identical rules i.e same action entries in two or more rules for different or identical condition entries as shown: In the table shown above action entries in rule 9 is identical to rule 1 to 4. Decision table be concluded as inconsistent - if actions in redundant rule are not identical (different) to the corresponding part of decision table as shown: In the table shown above, if a transaction in which c1 is true and both c2 and c3 are false then both rules 4 and 9 apply. Two observations can be made: - rules 4 and 9 are inconsistent. - the decision table is nondeterministic.

11 b) Explain in detail the concept of Rule Count considering Refined Decision Table for Triangle Program to indicate irrelevant don t care entries present in the decision table. (6 Marks) Answer: For limited entry decision tables, if n conditions exists, there must be 2^n rules. When don t care entries really indicate that the condition is irrelevant, we can develop a rule count as follows: rules in which no don t care entries occur count as one rule, and each don t care entry in a rule doubles the count of that rule as shown below: The sum of the rule count= 2^6= Identify and mention the set boundaries and draw equivalence partitions based upon output range for the below mentioned problem statements. Justify your answer. Problem Statement -1 (Store Management System) A store in city offers different discounts depending on the purchases made by the individual. In order to test the software that calculates the discounts, we can identify the ranges of purchase values that earn the different discounts. For example, if a purchase is in the range of $1 up to $50 has no discounts, a purchase over $50 and up to $200 has a 5% discount, and purchases of $201 and up to $500 have a 10% discounts, and purchases of $501 and above have a 15% discounts. Problem Statement -2 (Travelers Reservation System) Suppose an application collects some data about a traveler using the dialog box shown in the diagram 1. When the OK button is pressed the component calculates a fare from the current location using the input values. There is a standard fare to each destination. Our travel service offers discounts to travelers based on their age as in the following discount table.

12 The Discount Table Age Discount 0-4 years 100% 5-15 years 50% years 0% 64 years and older 25% Diagram 1: Traveler Details (10 Marks) 7. Create a decision table for NextDate Function by identifying appropriate Equivalence classes as conditions and determine actions for generating all possible test cases by considering decision table with 22 Rules. Finally tabulate all 22 test cases for NextDate Function (10 Marks) Answer: M1= {month : month has 30 days} M2= {month : month has 31 days} M3= {month : month is february} M4:{month:month is December} D1= {day : 1<=day<=28} D2= {day : day=29} D3= {day : day=30} D4= {day : day=31} Y1= {year : year=2000} Y2= {year : year is a non-century leap year}

13 Y3= {year : year is a common year

PESIT Bangalore South Campus

PESIT Bangalore South Campus USN 1 P E PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Information Science & Engineering INTERNAL ASSESSMENT TEST 1 Date : 23/02/2016 Max Marks: 50

More information

EECS 4313 Software Engineering Testing. Topic 05: Equivalence Class Testing Zhen Ming (Jack) Jiang

EECS 4313 Software Engineering Testing. Topic 05: Equivalence Class Testing Zhen Ming (Jack) Jiang EECS 4313 Software Engineering Testing Topic 05: Equivalence Class Testing Zhen Ming (Jack) Jiang Relevant Readings [Jorgensen] chapter 6 Introduction Boundary Value Testing derives test cases with Massive

More information

Functional Testing (Black Box Testing)

Functional Testing (Black Box Testing) Functional Testing (Black Box Testing) In black box testing, program is treated as a black box. Implementation details do not matter. Takes a user point of view. Functional testing verifies that each function

More information

Quality Assurance in Software Development

Quality Assurance in Software Development Quality Assurance in Software Development Qualitätssicherung in der Softwareentwicklung A.o.Univ.-Prof. Dipl.-Ing. Dr. Bernhard Aichernig Graz University of Technology Austria Summer Term 2017 1 / 47 Agenda

More information

Software Testing. 1. Testing is the process of demonstrating that errors are not present.

Software Testing. 1. Testing is the process of demonstrating that errors are not present. What is Testing? Software Testing Many people understand many definitions of testing :. Testing is the process of demonstrating that errors are not present.. The purpose of testing is to show that a program

More information

Mainline Functional Testing Techniques

Mainline Functional Testing Techniques Mainline Functional Testing Techniques (4 flavors) Equivalence Partitions (another 4 flavors) Special Value Testing Output Domain (Range) Checking Decision Table Based Testing (aka Cause and Effect Graphs

More information

Software Testing: A Craftsman s Approach, 4 th Edition. Chapter 5 Boundary Value Testing

Software Testing: A Craftsman s Approach, 4 th Edition. Chapter 5 Boundary Value Testing Chapter 5 Boundary Value Testing Functional Testing The rationale for referring to specification-based testing as functional testing is likely due to the abstraction that any program can be viewed as a

More information

Question Bank. Unit 1: Perspective on Testing, Examples. Chapter 1 & 2 from Dr. Paul C. Jorgensen

Question Bank. Unit 1: Perspective on Testing, Examples. Chapter 1 & 2 from Dr. Paul C. Jorgensen Unit 1: Perspective on Testing, Examples Chapter 1 & 2 from Dr. Paul C. Jorgensen Sl no Question Description 1. Make a Venn Diagram that reflects a part of the following statement: we have left undone

More information

UNIT-4 Black Box & White Box Testing

UNIT-4 Black Box & White Box Testing Black Box & White Box Testing Black Box Testing (Functional testing) o Equivalence Partitioning o Boundary Value Analysis o Cause Effect Graphing White Box Testing (Structural testing) o Coverage Testing

More information

UNIT-4 Black Box & White Box Testing

UNIT-4 Black Box & White Box Testing Black Box & White Box Testing Black Box Testing (Functional testing) o Equivalence Partitioning o Boundary Value Analysis o Cause Effect Graphing White Box Testing (Structural testing) o Coverage Testing

More information

Specification-based test design

Specification-based test design Software and Systems Verification (VIMIMA01) Specification-based test design Zoltan Micskei, Istvan Majzik Budapest University of Technology and Economics Fault Tolerant Systems Research Group Budapest

More information

Software technology 7. Testing (2) BSc Course Dr. Katalin Balla

Software technology 7. Testing (2) BSc Course Dr. Katalin Balla Software technology 7. Testing (2) BSc Course Dr. Katalin Balla Contents Testing techniques Static testing techniques Dynamic testing Black box testing White-box testing Testing in the agile environment

More information

CS 4387/5387 SOFTWARE V&V LECTURE 4 BLACK-BOX TESTING

CS 4387/5387 SOFTWARE V&V LECTURE 4 BLACK-BOX TESTING 1 CS 4387/5387 SOFTWARE V&V LECTURE 4 BLACK-BOX TESTING Outline 2 Quiz Black-Box Testing Equivalence Class Testing (Equivalence Partitioning) Boundary value analysis Decision Table Testing 1 3 Quiz - 1

More information

PESIT Bangalore South Campus SOLUTION

PESIT Bangalore South Campus SOLUTION USN 1 P E PESIT Bangalore South Campus Hosur road, 1km before Electronic City, Bengaluru -100 Department of Information Science & Engineering INTERNAL ASSESSMENT TEST 2 Date : 02/04/2018 Max Marks: 40

More information

No Source Code. EEC 521: Software Engineering. Specification-Based Testing. Advantages

No Source Code. EEC 521: Software Engineering. Specification-Based Testing. Advantages No Source Code : Software Testing Black-Box Testing Test-Driven Development No access to source code So test cases don t worry about structure Emphasis is only on ensuring that the contract is met Specification-Based

More information

Equivalence Class Partitioning and Boundary Value Analysis -Black Box Testing Techniques

Equivalence Class Partitioning and Boundary Value Analysis -Black Box Testing Techniques Equivalence Class Partitioning and Boundary Value Analysis -Black Box Testing Techniques In this tutorial, we will discuss the approach to design the test cases and also how to apply the boundary value

More information

Black Box Testing. EEC 521: Software Engineering. Specification-Based Testing. No Source Code. Software Testing

Black Box Testing. EEC 521: Software Engineering. Specification-Based Testing. No Source Code. Software Testing Black Box Testing EEC 521: Software Engineering Software Testing Black-Box Testing Test-Driven Development Also known as specification-based testing Tester has access only to running code and the specification

More information

Introduction. Easy to get started, based on description of the inputs

Introduction. Easy to get started, based on description of the inputs Introduction Testing is about choosing elements from input domain. The input domain of a program consists of all possible inputs that could be taken by the program. Easy to get started, based on description

More information

4B Summary of some Key SW Testing Concepts 1

4B Summary of some Key SW Testing Concepts 1 4B Summary of some Key SW Testing Concepts 1 Note: Section 4A presented a particular, specific method for developing (system or requirements level) tests cases from UML use cases. Section 4B provides a

More information

Software Quality Assurance. David Janzen

Software Quality Assurance. David Janzen Software Quality Assurance David Janzen What is quality? Crosby: Conformance to requirements Issues: who establishes requirements? implicit requirements Juran: Fitness for intended use Issues: Who defines

More information

Chapter 3: Dynamic Testing Techniques

Chapter 3: Dynamic Testing Techniques Chapter 3: Dynamic Testing Techniques " The system was not fully tested to a satisfactory level of quality and resilience before full implementation on 26 October 1992." Extract from the main conclusions

More information

Chapter 20. A Closer Look at All Pairs Testing. Software Testing: A Craftsman s Approach, 4 th Edition. Chapter 20 All Pairs Testing

Chapter 20. A Closer Look at All Pairs Testing. Software Testing: A Craftsman s Approach, 4 th Edition. Chapter 20 All Pairs Testing Chapter 20 A Closer Look at All Pairs Testing Overview What is it? Why are people excited about it? Should we be excited about it? James Bach s summary Assumptions Appropriate choices Examples (and counter-examples)

More information

Software Quality Assurance Dynamic Test

Software Quality Assurance Dynamic Test Software Quality Assurance Dynamic Test Contents Properties and goals Structural testing Control flow testing Data flow testing Functional test Diversified test 2 Properties and Goals Properties of dynamic

More information

Input Space Partitioning

Input Space Partitioning Input Space Partitioning Instructor : Ali Sharifara CSE 5321/4321 Summer 2017 CSE 5321/4321, Ali Sharifara, UTA 1 Input Space Partitioning Introduction Equivalence Partitioning Boundary-Value Analysis

More information

Graph Theory Questions from Past Papers

Graph Theory Questions from Past Papers Graph Theory Questions from Past Papers Bilkent University, Laurence Barker, 19 October 2017 Do not forget to justify your answers in terms which could be understood by people who know the background theory

More information

CHAPTER 8. Copyright Cengage Learning. All rights reserved.

CHAPTER 8. Copyright Cengage Learning. All rights reserved. CHAPTER 8 RELATIONS Copyright Cengage Learning. All rights reserved. SECTION 8.3 Equivalence Relations Copyright Cengage Learning. All rights reserved. The Relation Induced by a Partition 3 The Relation

More information

EXERCISES (Software Engineering)

EXERCISES (Software Engineering) Chapter 1 1. What is Software Engineering? 2. What is Requirement Engineering? EXERCISES (Software Engineering) 3. What are the Different types of Architectures in Software Engineering? 4. How many subdisciplines

More information

SOFTWARE TESTING LABORATORY. I.AMarks:20 Hours/Week: 03 ExamHours: 3 Total Hours: 40 Exam Marks: 80 Number of Lecture Hours/Week: 01I + 02P

SOFTWARE TESTING LABORATORY. I.AMarks:20 Hours/Week: 03 ExamHours: 3 Total Hours: 40 Exam Marks: 80 Number of Lecture Hours/Week: 01I + 02P SOFTWARE TESTING LABORATORY Subject Code: 15ISL67 I.AMarks:20 Hours/Week: 03 ExamHours: 3 Total Hours: 40 Exam Marks: 80 Number of Lecture Hours/Week: 01I + 02P 1. Design and develop a program in a language

More information

SOFTWARE TESTING LABORATORY

SOFTWARE TESTING LABORATORY oratory M.I.T VI ISE SOFTWARE TESTING LABORATORY Subject Code: 10ISL68 I.A. Marks : 25 Hours/Week : 03 Exam Hours: 03 Total Hours : 42 Exam Marks: 50 1. Design and develop a program in a language of your

More information

Software Testing. Software Testing. Theory, Practise and Reality IBM Corporation

Software Testing. Software Testing. Theory, Practise and Reality IBM Corporation Software Testing Software Testing Theory, Practise and Reality Who am I? David Vines (dvines@uk.ibm.com) Degree in Computer Science and Operational Research Joined IBM in 1984 Been involved in product

More information

9.5 Equivalence Relations

9.5 Equivalence Relations 9.5 Equivalence Relations You know from your early study of fractions that each fraction has many equivalent forms. For example, 2, 2 4, 3 6, 2, 3 6, 5 30,... are all different ways to represent the same

More information

SOFTWARE TESTING LABORATORY. Subject Code: 10ISL68 I.A. Marks: 25 Hours/Week: 03 Exam Hours: 03 Total Hours: 42 Exam Marks: 50

SOFTWARE TESTING LABORATORY. Subject Code: 10ISL68 I.A. Marks: 25 Hours/Week: 03 Exam Hours: 03 Total Hours: 42 Exam Marks: 50 SOFTWARE TESTING LABORATORY Subject Code: 10ISL68 I.A. Marks: 25 Hours/Week: 03 Exam Hours: 03 Total Hours: 42 Exam Marks: 50 1. Design and develop a program in a language of your choice to solve the Triangle

More information

MATH 115: Review for Chapter 1

MATH 115: Review for Chapter 1 MATH 115: Review for Chapter 1 Can you use the Distance Formula to find the distance between two points? (1) Find the distance d P, P between the points P and 1 1, 6 P 10,9. () Find the length of the line

More information

Lecture 17: Testing Strategies. Developer Testing

Lecture 17: Testing Strategies. Developer Testing Lecture 17: Testing Strategies Structural Coverage Strategies (White box testing): Statement Coverage Branch Coverage Condition Coverage Data Path Coverage Function Coverage Strategies (Black box testing):

More information

Darshan Institute of Engineering & Technology Unit : 9

Darshan Institute of Engineering & Technology Unit : 9 1) Explain software testing strategy for conventional software architecture. Draw the spiral diagram showing testing strategies with phases of software development. Software Testing: Once source code has

More information

MAT 145: PROBLEM SET 4

MAT 145: PROBLEM SET 4 MAT 145: PROBLEM SET 4 DUE TO FRIDAY FEB 22 Abstract. This problem set corresponds to the sixth week of the Combinatorics Course in the Winter Quarter 2019. It was posted online on Friday Feb 15 and is

More information

18-642: Unit Testing 1/31/ Philip Koopman

18-642: Unit Testing 1/31/ Philip Koopman 18-642: Unit Testing 1/31/2018 2017-2018 Philip Koopman YOU ARE HERE Product Requirements SPECIFY PRODUCT SPECIFY SOFTWARE Software Requirements TRACEABILITY & VALIDATION Test Plan & Test Results Test

More information

7th Bay Area Mathematical Olympiad

7th Bay Area Mathematical Olympiad 7th Bay Area Mathematical Olympiad February 22, 2005 Problems and Solutions 1 An integer is called formidable if it can be written as a sum of distinct powers of 4, and successful if it can be written

More information

6th Bay Area Mathematical Olympiad

6th Bay Area Mathematical Olympiad 6th Bay Area Mathematical Olympiad February 4, 004 Problems and Solutions 1 A tiling of the plane with polygons consists of placing the polygons in the plane so that interiors of polygons do not overlap,

More information

60th ANNUAL HIGH SCHOOL HONORS MATHEMATICS CONTEST

60th ANNUAL HIGH SCHOOL HONORS MATHEMATICS CONTEST 60th ANNUAL HIGH SCHOOL HONORS MATHEMATICS CONTEST April, 017 on the campus of the University of California, San Diego PART I 5 Questions Welcome to the contest! Please do not open the exam until told

More information

Multidimensional Divide and Conquer 2 Spatial Joins

Multidimensional Divide and Conquer 2 Spatial Joins Multidimensional Divide and Conque Spatial Joins Yufei Tao ITEE University of Queensland Today we will continue our discussion of the divide and conquer method in computational geometry. This lecture will

More information

Verification and Validation

Verification and Validation Chapter 5 Verification and Validation Chapter Revision History Revision 0 Revision 1 Revision 2 Revision 3 Revision 4 original 94/03/23 by Fred Popowich modified 94/11/09 by Fred Popowich reorganization

More information

CS 451 Software Engineering Winter 2009

CS 451 Software Engineering Winter 2009 CS 451 Software Engineering Winter 2009 Yuanfang Cai Room 104, University Crossings 215.895.0298 yfcai@cs.drexel.edu 1 Software Testing Techniques FUNDAMENTALS The goal of testing is to find errors. A

More information

THE THIRD JTST FOR JBMO - Saudi Arabia, 2017

THE THIRD JTST FOR JBMO - Saudi Arabia, 2017 THE THIRD JTST FOR JBMO - Saudi Arabia, 017 Problem 1. Let a, b, c be positive real numbers such that a + b + c = 3. Prove the inequality a(a b ) + b(b c ) + c(c a ) 0. a + b b + c c + a Problem. Find

More information

As your databases continue to evolve, you will need to incorporate advanced queries and reports. This chapter addresses how to create and use action

As your databases continue to evolve, you will need to incorporate advanced queries and reports. This chapter addresses how to create and use action As your databases continue to evolve, you will need to incorporate advanced queries and reports. This chapter addresses how to create and use action queries and how to create queries that perform more

More information

International Journal of Computer Engineering and Applications, Volume XII, Special Issue, September 18, ISSN SOFTWARE TESTING

International Journal of Computer Engineering and Applications, Volume XII, Special Issue, September 18,   ISSN SOFTWARE TESTING International Journal of Computer Engineering and Applications, Volume XII, Special Issue, September 18, www.ijcea.com ISSN 2321-3469 SOFTWARE TESTING Rajat Galav 1, Shivank Lavania 2, Brijesh Kumar Singh

More information

2386 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 6, JUNE 2006

2386 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 6, JUNE 2006 2386 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 6, JUNE 2006 The Encoding Complexity of Network Coding Michael Langberg, Member, IEEE, Alexander Sprintson, Member, IEEE, and Jehoshua Bruck,

More information

1. A statement is a set of words and/or symbols that collectively make a claim that can be classified as true or false.

1. A statement is a set of words and/or symbols that collectively make a claim that can be classified as true or false. Chapter 1 Line and Angle Relationships 1.1 Sets, Statements and Reasoning Definitions 1. A statement is a set of words and/or symbols that collectively make a claim that can be classified as true or false.

More information

GENERALISED GEOMETRY

GENERALISED GEOMETRY GENERALISED GEOMETRY INTRODUCTION Generalised Geometry, which we will discuss in the chapters that follow, is a «New Geometry» that emerged from the need to broaden certain parts of Euclidean Geometry,

More information

Matching Theory. Figure 1: Is this graph bipartite?

Matching Theory. Figure 1: Is this graph bipartite? Matching Theory 1 Introduction A matching M of a graph is a subset of E such that no two edges in M share a vertex; edges which have this property are called independent edges. A matching M is said to

More information

PAIRED-DOMINATION. S. Fitzpatrick. Dalhousie University, Halifax, Canada, B3H 3J5. and B. Hartnell. Saint Mary s University, Halifax, Canada, B3H 3C3

PAIRED-DOMINATION. S. Fitzpatrick. Dalhousie University, Halifax, Canada, B3H 3J5. and B. Hartnell. Saint Mary s University, Halifax, Canada, B3H 3C3 Discussiones Mathematicae Graph Theory 18 (1998 ) 63 72 PAIRED-DOMINATION S. Fitzpatrick Dalhousie University, Halifax, Canada, B3H 3J5 and B. Hartnell Saint Mary s University, Halifax, Canada, B3H 3C3

More information

Chapter 2 QUIZ. Section 2.1 The Parallel Postulate and Special Angles

Chapter 2 QUIZ. Section 2.1 The Parallel Postulate and Special Angles Chapter 2 QUIZ Section 2.1 The Parallel Postulate and Special Angles (1.) How many lines can be drawn through point P that are parallel to line? (2.) Lines and m are cut by transversal t. Which angle corresponds

More information

The Encoding Complexity of Network Coding

The Encoding Complexity of Network Coding The Encoding Complexity of Network Coding Michael Langberg Alexander Sprintson Jehoshua Bruck California Institute of Technology Email: mikel,spalex,bruck @caltech.edu Abstract In the multicast network

More information

Black-Box, Functional Testing

Black-Box, Functional Testing Black-Box, Functional Testing 1 Introduction Based on the definition of what a program s specification, as opposed to its structure Does the implementation correctly implement the functionality as per

More information

Modern Methods in Software Engineering. Testing.

Modern Methods in Software Engineering. Testing. Modern Methods in Software Engineering Testing www.imit.kth.se/courses/2g1522 Literature used Text book Chapter 11 Introduction Content Terminology Types of errors Dealing with errors Component Testing

More information

[Ch 6] Set Theory. 1. Basic Concepts and Definitions. 400 lecture note #4. 1) Basics

[Ch 6] Set Theory. 1. Basic Concepts and Definitions. 400 lecture note #4. 1) Basics 400 lecture note #4 [Ch 6] Set Theory 1. Basic Concepts and Definitions 1) Basics Element: ; A is a set consisting of elements x which is in a/another set S such that P(x) is true. Empty set: notated {

More information

PESIT Bangalore South Campus

PESIT Bangalore South Campus Fourth Semester B.E. IA Test-1, 2015 USN 1 P E I S PESIT Bangalore South Campus (Hosur Road, 1KM before Electronic City, Bangalore-560 100) Department of Information Science & Engineering Section: 4 th

More information

PESIT Bangalore South Campus

PESIT Bangalore South Campus Fifth Semester B.E. IA Test-I, 2014 USN 1 P E I S PESIT Bangalore South Campus (Hosur Road, 1KM before Electronic City, Bangalore-560 100) Department of Information Science & Engineering Section: 5 ISE

More information

All numbered readings are from Stillwell s The four pillars of geometry.

All numbered readings are from Stillwell s The four pillars of geometry. MATH 350. Assigned readings and homework All numbered readings are from Stillwell s The four pillars of geometry. Reading Jan 30, Feb 1: Chapters 1.1 1.4 Feb 6, 8: Chapters 1.5 2.2 Feb 13, 15: Chapters

More information

Math 302 Introduction to Proofs via Number Theory. Robert Jewett (with small modifications by B. Ćurgus)

Math 302 Introduction to Proofs via Number Theory. Robert Jewett (with small modifications by B. Ćurgus) Math 30 Introduction to Proofs via Number Theory Robert Jewett (with small modifications by B. Ćurgus) March 30, 009 Contents 1 The Integers 3 1.1 Axioms of Z...................................... 3 1.

More information

International Journal of Computer Engineering and Applications, Volume XII, Special Issue, April- ICITDA 18,

International Journal of Computer Engineering and Applications, Volume XII, Special Issue, April- ICITDA 18, International Journal of Computer Engineering and Applications, Volume XII, Special Issue, April- ICITDA 18, www.ijcea.com ISSN 2321-3469 SOFTWARE TESTING Rajat Galav, Shivank Lavania Student, Department

More information

a. The following method would allow an object of the static type List<String> to be passed to it as an argument.

a. The following method would allow an object of the static type List<String> to be passed to it as an argument. On the final exam you will be provided UML diagrams for design patterns (as in the midterm) and also JavaDoc description of methods in the Reflection API. 1. True/False (if false, explain why) a. The following

More information

18-642: Unit Testing 9/18/ Philip Koopman

18-642: Unit Testing 9/18/ Philip Koopman 18-642: Unit Testing 9/18/2017 2017 Philip Koopman Unit Testing Anti-Patterns: Only system testing Testing only happy paths Forgetting to test missing code Unit testing Test a single subroutine/procedure/method

More information

Basic Counting Principles: The Product Rule

Basic Counting Principles: The Product Rule Section 6.1 Basic Counting Principles: The Product Rule The Product Rule: A procedure can be broken down into a sequence of two tasks. There are n 1 ways to do the first task and n 2 ways to do the second

More information

Computational Systems COMP1209

Computational Systems COMP1209 Computational Systems COMP1209 Testing Yvonne Howard ymh@ecs.soton.ac.uk A Problem A café wants to build an automated system to provide breakfasts. The robot waiter greets people before taking their order

More information

Matching and Planarity

Matching and Planarity Matching and Planarity Po-Shen Loh June 010 1 Warm-up 1. (Bondy 1.5.9.) There are n points in the plane such that every pair of points has distance 1. Show that there are at most n (unordered) pairs of

More information

3. Data Preprocessing. 3.1 Introduction

3. Data Preprocessing. 3.1 Introduction 3. Data Preprocessing Contents of this Chapter 3.1 Introduction 3.2 Data cleaning 3.3 Data integration 3.4 Data transformation 3.5 Data reduction SFU, CMPT 740, 03-3, Martin Ester 84 3.1 Introduction Motivation

More information

CLASSIFICATION OF SURFACES

CLASSIFICATION OF SURFACES CLASSIFICATION OF SURFACES JUSTIN HUANG Abstract. We will classify compact, connected surfaces into three classes: the sphere, the connected sum of tori, and the connected sum of projective planes. Contents

More information

Midpoint and Distance Formulas

Midpoint and Distance Formulas CP1 Math Unit 5: Coordinate Geometry: Day Name Midpoint Formula: Midpoint and Distance Formulas The midpoint of the line segment between any two points (x!, y! ) to (x!, y! ) is given by: In your groups,

More information

Honors 213. Third Hour Exam. Name

Honors 213. Third Hour Exam. Name Honors 213 Third Hour Exam Name Monday, March 27, 2000 100 points Page 1 Please note: Because of multiple exams given Monday, this exam will be returned by Thursday, March 30. 1. (5 pts.) Define what it

More information

2. Data Preprocessing

2. Data Preprocessing 2. Data Preprocessing Contents of this Chapter 2.1 Introduction 2.2 Data cleaning 2.3 Data integration 2.4 Data transformation 2.5 Data reduction Reference: [Han and Kamber 2006, Chapter 2] SFU, CMPT 459

More information

Tiling of Sphere by Congruent Pentagons

Tiling of Sphere by Congruent Pentagons Tiling of Sphere by Congruent Pentagons Min Yan September 9, 2017 webpage for further reading: http://www.math.ust.hk/ mamyan/research/urop.shtml We consider tilings of the sphere by congruent pentagons.

More information

This Lecture. We will first introduce some basic set theory before we do counting. Basic Definitions. Operations on Sets.

This Lecture. We will first introduce some basic set theory before we do counting. Basic Definitions. Operations on Sets. Sets A B C This Lecture We will first introduce some basic set theory before we do counting. Basic Definitions Operations on Sets Set Identities Defining Sets Definition: A set is an unordered collection

More information

Non-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, Politecnico di Milano, February 3, 2017, Lesson 1

Non-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, Politecnico di Milano, February 3, 2017, Lesson 1 Non-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, attilio.frangi@polimi.it Politecnico di Milano, February 3, 2017, Lesson 1 1 Politecnico di Milano, February 3, 2017, Lesson 1 2 Outline

More information

A graph is finite if its vertex set and edge set are finite. We call a graph with just one vertex trivial and all other graphs nontrivial.

A graph is finite if its vertex set and edge set are finite. We call a graph with just one vertex trivial and all other graphs nontrivial. 2301-670 Graph theory 1.1 What is a graph? 1 st semester 2550 1 1.1. What is a graph? 1.1.2. Definition. A graph G is a triple (V(G), E(G), ψ G ) consisting of V(G) of vertices, a set E(G), disjoint from

More information

CSE 215: Foundations of Computer Science Recitation Exercises Set #9 Stony Brook University. Name: ID#: Section #: Score: / 4

CSE 215: Foundations of Computer Science Recitation Exercises Set #9 Stony Brook University. Name: ID#: Section #: Score: / 4 CSE 215: Foundations of Computer Science Recitation Exercises Set #9 Stony Brook University Name: ID#: Section #: Score: / 4 Unit 14: Set Theory: Definitions and Properties 1. Let C = {n Z n = 6r 5 for

More information

2.1 Angles, Lines and Parallels & 2.2 Congruent Triangles and Pasch s Axiom

2.1 Angles, Lines and Parallels & 2.2 Congruent Triangles and Pasch s Axiom 2 Euclidean Geometry In the previous section we gave a sketch overview of the early parts of Euclid s Elements. While the Elements set the standard for the modern axiomatic approach to mathematics, it

More information

Black Box Testing (revisited) Csci 565 Spring 2007

Black Box Testing (revisited) Csci 565 Spring 2007 Black Box Testing (revisited) Csci 565 Spring 2007 Objectives Cause-Effect Graphs in Functional testing Input validation and Syntax-driven Testing Decision Table-Based Testing State transition testing

More information

Integrating the classification tree method with combinatorial testing: test selection strategy

Integrating the classification tree method with combinatorial testing: test selection strategy Integrating the classification tree method with combinatorial testing: test selection strategy Eduardo Miranda, PhD. CMU/MSE MSE/NIST Seminar June 7th, 2011 Pittsburgh, PA The Classification Tree Method

More information

Software Testing. Software Testing. in the textbook. Chapter 8. Verification and Validation. Verification Techniques

Software Testing. Software Testing. in the textbook. Chapter 8. Verification and Validation. Verification Techniques Software Testing in the textbook Software Testing Chapter 8 Introduction (Verification and Validation) 8.1 Development testing 8.2 Test-driven development 8.3 Release testing 8.4 User testing 1 2 Verification

More information

Pebble Sets in Convex Polygons

Pebble Sets in Convex Polygons 2 1 Pebble Sets in Convex Polygons Kevin Iga, Randall Maddox June 15, 2005 Abstract Lukács and András posed the problem of showing the existence of a set of n 2 points in the interior of a convex n-gon

More information

Assignments in Mathematics Class IX (Term I) 5. InTroduCTIon To EuClId s GEoMETry. l Euclid s five postulates are : ANIL TUTORIALS

Assignments in Mathematics Class IX (Term I) 5. InTroduCTIon To EuClId s GEoMETry. l Euclid s five postulates are : ANIL TUTORIALS Assignments in Mathematics Class IX (Term I) 5. InTroduCTIon To EuClId s GEoMETry IMporTAnT TErMs, definitions And results l In geometry, we take a point, a line and a plane as undefined terms. l An axiom

More information

Why testing and analysis. Software Testing. A framework for software testing. Outline. Software Qualities. Dependability Properties

Why testing and analysis. Software Testing. A framework for software testing. Outline. Software Qualities. Dependability Properties Why testing and analysis Software Testing Adapted from FSE 98 Tutorial by Michal Young and Mauro Pezze Software is never correct no matter what developing testing technique is used All software must be

More information

Solutions to the Test. Problem 1. 1) Who is the author of the first comprehensive text on geometry? When and where was it written?

Solutions to the Test. Problem 1. 1) Who is the author of the first comprehensive text on geometry? When and where was it written? Solutions to the Test Problem 1. 1) Who is the author of the first comprehensive text on geometry? When and where was it written? Answer: The first comprehensive text on geometry is called The Elements

More information

Solutions to In-Class Problems Week 4, Fri

Solutions to In-Class Problems Week 4, Fri Massachusetts Institute of Technology 6.042J/18.062J, Fall 02: Mathematics for Computer Science Professor Albert Meyer and Dr. Radhika Nagpal Solutions to In-Class Problems Week 4, Fri Definition: The

More information

13 th Annual Johns Hopkins Math Tournament Saturday, February 19, 2011 Automata Theory EUR solutions

13 th Annual Johns Hopkins Math Tournament Saturday, February 19, 2011 Automata Theory EUR solutions 13 th Annual Johns Hopkins Math Tournament Saturday, February 19, 011 Automata Theory EUR solutions Problem 1 (5 points). Prove that any surjective map between finite sets of the same cardinality is a

More information

Software Testing Prof. Rajib Mall Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Software Testing Prof. Rajib Mall Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Software Testing Prof. Rajib Mall Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture - 07 Special Value Testing Welcome to this session. So far we had looked

More information

The strong chromatic number of a graph

The strong chromatic number of a graph The strong chromatic number of a graph Noga Alon Abstract It is shown that there is an absolute constant c with the following property: For any two graphs G 1 = (V, E 1 ) and G 2 = (V, E 2 ) on the same

More information

Decision Tables - Wikipedia Decision Table-Based Testing

Decision Tables - Wikipedia Decision Table-Based Testing Decision ables Wikipedia Decision ablebased esting Chapter A precise yet compact way to model complicated logic Associate conditions with actions to perform Can associate many independent conditions with

More information

Aerospace Software Engineering

Aerospace Software Engineering 16.35 Aerospace Software Engineering Verification & Validation Prof. Kristina Lundqvist Dept. of Aero/Astro, MIT Would You...... trust a completely-automated nuclear power plant?... trust a completely-automated

More information

Theory of Computing. Lecture 10 MAS 714 Hartmut Klauck

Theory of Computing. Lecture 10 MAS 714 Hartmut Klauck Theory of Computing Lecture 10 MAS 714 Hartmut Klauck Seven Bridges of Königsberg Can one take a walk that crosses each bridge exactly once? Seven Bridges of Königsberg Model as a graph Is there a path

More information

Data Mining. Part 2. Data Understanding and Preparation. 2.4 Data Transformation. Spring Instructor: Dr. Masoud Yaghini. Data Transformation

Data Mining. Part 2. Data Understanding and Preparation. 2.4 Data Transformation. Spring Instructor: Dr. Masoud Yaghini. Data Transformation Data Mining Part 2. Data Understanding and Preparation 2.4 Spring 2010 Instructor: Dr. Masoud Yaghini Outline Introduction Normalization Attribute Construction Aggregation Attribute Subset Selection Discretization

More information

7.0 Test Design Techniques & Dynamic Testing

7.0 Test Design Techniques & Dynamic Testing 7.0 Test Design Techniques & Dynamic Testing Test Design Techniques 7.1 The Test Development Process 7.2 Categories of Test Design Techniques 7.3 Specification based or Black Box Techniques 7.4 Structure

More information

no triangle can have more than one right angle or obtuse angle.

no triangle can have more than one right angle or obtuse angle. Congruence Theorems in Action Isosceles Triangle Theorems.3 Learning Goals In this lesson, you will: Prove the Isosceles Triangle Base Theorem. Prove the Isosceles Triangle Vertex Angle Theorem. Prove

More information

Acute Triangulations of Polygons

Acute Triangulations of Polygons Europ. J. Combinatorics (2002) 23, 45 55 doi:10.1006/eujc.2001.0531 Available online at http://www.idealibrary.com on Acute Triangulations of Polygons H. MAEHARA We prove that every n-gon can be triangulated

More information

Warm-Up. Find the domain and range:

Warm-Up. Find the domain and range: Warm-Up Find the domain and range: Geometry Vocabulary & Notation Point Name: Use only the capital letter, without any symbol. Line Name: Use any two points on the line with a line symbol above. AB Line

More information

Unifying industrial and academic approaches to domain testing

Unifying industrial and academic approaches to domain testing Unifying industrial and academic approaches to domain testing CAST Grand Rapids August 3, 2010 Cem Kaner Sowmya Padmanabhan 1 Abstract The most widely used technique in software testing is called Equivalence

More information

Effective Information Management and Governance: Building the Business Case for Taxonomy

Effective Information Management and Governance: Building the Business Case for Taxonomy Effective Information Management and Governance: Building the Business Case for Taxonomy May 16, 2017 A WAND, Inc. White Paper By Mark Leher, COO, WAND, Inc. Executive Summary Companies are often reluctant

More information

Dynamic Programming Homework Problems

Dynamic Programming Homework Problems CS 1510 Dynamic Programming Homework Problems 1. Consider the recurrence relation T(0) = T(1) = 2 and for n > 1 n 1 T(n) = T(i)T(i 1) i=1 We consider the problem of computing T(n) from n. (a) Show that

More information

Software Engineering: Theory and Practice. Verification by Testing. Test Case Design. Tom Verhoeff

Software Engineering: Theory and Practice. Verification by Testing. Test Case Design. Tom Verhoeff Software Engineering: Theory and Practice Verification by Testing Test Case Design Tom Verhoeff Eindhoven University of Technology Department of Mathematics & Computer Science Software Engineering & Technology

More information