Chapter 6: Lgic Based Testing LOGIC BASED TESTING: This unit gives an indepth verview f lgic based testing and its implementatin. At the end f this unit, the student will be able t: Understand the cncept f Lgic based testing. Learn abut Decisin Tables and their applicatin Understand the use f decisin tables in test-case design and knw their limitatins. Understand and interpret KV Charts and knw their limitatins. Learn hw t transfrm specificatins int sentences and map them int KV charts. Understand the imprtance f dnt-care cnditins. OVERVIEW OF LOGIC BASED TESTING: INTRODUCTION: The functinal requirements f many prgrams can be specified by decisin tables, which prvide a useful basis fr prgram and test design. Cnsistency and cmpleteness can be analyzed by using blean algebra, which can als be used as a basis fr test design. Blean algebra is trivialized by using Karnaugh-Veitch charts. "Lgic" is ne f the mst ften used wrds in prgrammers' vcabularies but ne f their least used techniques. Blean algebra is t lgic as arithmetic is t mathematics. Withut it, the tester r prgrammer is cut ff frm many test and design techniques and tls that incrprate thse techniques. Lgic has been, fr several decades, the primary tl f hardware lgic designers. Many test methds develped fr hardware lgic can be adapted t sftware lgic testing. Because hardware testing autmatin is 10 t 15 years ahead f sftware testing autmatin, hardware testing methds and its assciated thery is a fertile grund fr sftware testing methds. As prgramming and test techniques have imprved, the bugs have shifted clser t the prcess frnt end, t requirements and their specificatins. These bugs range frm 8% t 30% f the ttal and because they're first-in and last-ut, they're the cstliest f all. The truble with specificatins is that they're hard t express. Blean algebra (als knwn as the sentential calculus) is the mst basic f all lgic systems. Higher-rder lgic systems are needed and used fr frmal specificatins. Much f lgical analysis can be and is embedded in tls. But these tls incrprate methds t simplify, transfrm, and check specificatins, and the methds are t a large extent based n blean algebra. KWLEDGE BASED SYSTEM: The knwledge-based system (als expert system r artificial intelligence system has becme the prgramming cnstruct f chice fr many applicatins that were nce cnsidered very difficult. Knwledge-based systems incrprate knwledge frm a knwledge dmain such as medicine, law, r civil engineering int a database. The Chapter 6 Page 1

Chapter 6: Lgic Based Testing data can then be queried and interacted with t prvide slutins t prblems in that dmain. One implementatin f knwledge-based systems is t incrprate the expert's knwledge int a set f rules. The user can then prvide data and ask questins based n that data. The user's data is prcessed thrugh the rule base t yield cnclusins (tentative r definite) and requests fr mre data. The prcessing is dne by a prgram called the inference engine. Understanding knwledge-based systems and their validatin prblems requires an understanding f frmal lgic. Decisin tables are extensively used in business data prcessing; Decisin-table preprcessrs as extensins t COBOL are in cmmn use; blean algebra is embedded in the implementatin f these prcessrs. Althugh prgrammed tls are nice t have, mst f the benefits f blean algebra can be reaped by whlly manual means if yu have the right cnceptual tl: the Karnaugh-Veitch diagram is that cnceptual tl. DECISION TABLES: Figure 6.1 is a limited - entry decisin table. It cnsists f fur areas called the cnditin stub, the cnditin entry, the actin stub, and the actin entry. Each clumn f the table is a rule that specifies the cnditins under which the actins named in the actin stub will take place. The cnditin stub is a list f names f cnditins. Figure 6.1: Examples f Decisin Table. A mre general decisin table can be as belw: Chapter 6 Page 2

Chapter 6: Lgic Based Testing Figure 6.2: Anther Examples f Decisin Table. A rule specifies whether a cnditin shuld r shuld nt be met fr the rule t be satisfied. "" means that the cnditin must be met, "" means that the cnditin must nt be met, and "I" means that the cnditin plays n part in the rule, r it is immaterial t that rule. The actin stub names the actins the rutine will take r initiate if the rule is satisfied. If the actin entry is "", the actin will take place; if "", the actin will nt take place. The table in Figure 6.1 can be translated as fllws: Actin 1 will take place if cnditins 1 and 2 are met and if cnditins 3 and 4 are nt met (rule 1) r if cnditins 1, 3, and 4 are met (rule 2). "Cnditin" is anther wrd fr predicate. Decisin-table uses "cnditin" and "satisfied" r "met". Let us use "predicate" and TRUE / FALSE. Nw the abve translatins becme: 1. Actin 1 will be taken if predicates 1 and 2 are true and if predicates 3 and 4 are false (rule 1), r if predicates 1, 3, and 4 are true (rule 2). 2. Actin 2 will be taken if the predicates are all false, (rule 3). 3. Actin 3 will take place if predicate 1 is false and predicate 4 is true (rule 4). In additin t the stated rules, we als need a Default Rule that specifies the default actin t be taken when all ther rules fail. The default rules fr Table in Figure 6.1 is shwn in Figure 6.3 Chapter 6 Page 3

Chapter 6: Lgic Based Testing Figure 6.3: The default rules f Table in Figure 6.1 DECISION-TABLE PROCESSORS: Decisin tables can be autmatically translated int cde and, as such, are a higher-rder language If the rule is satisfied, the crrespnding actin takes place Otherwise, rule 2 is tried. This prcess cntinues until either a satisfied rule results in an actin r n rule is satisfied and the default actin is taken Decisin tables have becme a useful tl in the prgrammers kit, in business data prcessing. DECISION-TABLES AS BASIS FOR TEST CASE DESIGN: 0. The specificatin is given as a decisin table r can be easily cnverted int ne. 1. The rder in which the predicates are evaluated des nt affect interpretatin f the rules r the resulting actin - i.e., an arbitrary permutatin f the predicate rder will nt, r shuld nt, affect which actin takes place. 2. The rder in which the rules are evaluated des nt affect the resulting actin - i.e., an arbitrary permutatin f rules will nt, r shuld nt, affect which actin takes place. 3. Once a rule is satisfied and an actin selected, n ther rule need be examined. 4. If several actins can result frm satisfying a rule, the rder in which the actins are executed desn't matter DECISION-TABLES AND STRUCTURE: Decisin tables can als be used t examine a prgram's structure. Figure 6.4 shws a prgram segment that cnsists f a decisin tree. These decisins, in varius cmbinatins, can lead t actins 1, 2, r 3. Chapter 6 Page 4

Chapter 6: Lgic Based Testing Figure 6.4 : A Sample Prgram If the decisin appears n a path, put in a r as apprpriate. If the decisin des nt appear n the path, put in an I, Rule 1 des nt cntain decisin C, therefre its entries are:,, I,. The crrespnding decisin table is shwn in Table 6.1 CONDITION A CONDITION B CONDITION C CONDITION D ACTION 1 ACTION 2 ACTION 3 RULE 1 RULE 2 RULE 3 RULE 4 RULE 5 RULE 6 I I I I I I I I Table 6.1 : Decisin Table crrespnding t Figure 6.4 As an example, expanding the immaterial cases results as belw: Similalrly, If we expand the immaterial cases fr the abve Table 6.1, it results in Table 6.2 as belw: Chapter 6 Page 5

Chapter 6: Lgic Based Testing CONDITION A CONDITION B CONDITION C CONDITION D R 1 RULE 2 R 3 RULE 4 R 5 R 6 YY YY YN YY YYYY NNNN NNYY YNNY YY YY YN NN NNNN YYNN YYYY NYYN NN NY NN YY NN YN NN NN Table 6.2 : Expansin f Table 6.1 Sixteen cases are represented in Table 6.1, and n case appears twice. Cnsequently, the flwgraph appears t be cmplete and cnsistent. As a first check, befre yu lk fr all sixteen cmbinatins, cunt the number f Y's and N's in each rw. They shuld be equal. We can find the bug that way. ATHER EXAMPLE - A TROUBLE SOME PROGRAM: Cnsider the fllwing specificatin whse putative flwgraph is shwn in Figure 6.5: 1. If cnditin A is met, d prcess A1 n matter what ther actins are taken r what ther cnditins are met. 2. If cnditin B is met, d prcess A2 n matter what ther actins are taken r what ther cnditins are met. 3. If cnditin C is met, d prcess A3 n matter what ther actins are taken r what ther cnditins are met. 4. If nne f the cnditins is met, then d prcesses A1, A2, and A3. 5. When mre than ne prcess is dne, prcess A1 must be dne first, then A2, and then A3. The nly permissible cases are: (A1), (A2), (A3), (A1,A3), (A2,A3) and (A1,A2,A3). Figure 6.5 shws a sample prgram with a bug. Figure 6.5: A Trublesme Prgram Chapter 6 Page 6

Chapter 6: Lgic Based Testing The prgrammer tried t frce all three prcesses t be executed fr the cases but frgt that the B and C predicates wuld be dne again, thereby bypassing prcesses A2 and A3. Table 6.3 shws the cnversin f this flwgraph int a decisin table after expansin. Table 6.3: Decisin Table fr Figure 6.5 PATH EXPRESSIONS: GENERAL: Lgic-based testing is structural testing when it's applied t structure (e.g., cntrl flwgraph f an implementatin); it's functinal testing when it's applied t a specificatin. In lgic-based testing we fcus n the truth values f cntrl flw predicates. A predicate is implemented as a prcess whse utcme is a truth-functinal value. Fr ur purpse, lgic-based testing is restricted t binary predicates. We start by generating path expressins by path tracing as in Unit V, but this time, ur purpse is t cnvert the path expressins int blean algebra, using the predicates' truth values (e.g., A and ) as weights. BOOLEAN ALGEBRA: STEPS: 1. Label each decisin with an uppercase letter that represents the truth value f the predicate. The r TRUE branch is labeled with a letter (say A) and the r FALSE branch with the same letter verscred (say ). 2. The truth value f a path is the prduct f the individual labels. Cncatenatin r prducts mean "AND". Fr example, the straightthrugh path f Figure 6.5, which ges via ndes 3, 6, 7, 8, 10, 11, 12, and 2, has a truth value f ABC. The path via ndes 3, 6, 7, 9 and 2 has a value f. 3. If tw r mre paths merge at a nde, the fact is expressed by use f a plus sign (+) which means "OR". Chapter 6 Page 7

Chapter 6: Lgic Based Testing Figure 6.5 : A Trublesme Prgram Using this cnventin, the truth-functinal values fr several f the ndes can be expressed in terms f segments frm previus ndes. Use the nde name t identify the pint. There are nly tw numbers in blean algebra: zer (0) and ne (1). One means "always true" and zer means "always false". RULES OF BOOLEAN ALGEBRA: Blean algebra has three peratrs: X (AND), + (OR) and (T) X : meaning AND. Als called multiplicatin. A statement such as AB (A X B) means "A and B are bth true". This symbl is usually left ut as in rdinary algebra. + : meaning OR. "A + B" means "either A is true r B is true r bth". meaning T. Als negatin r cmplementatin. This is read as either "nt A" r "A bar". The entire expressin under the bar is negated. The fllwing are the laws f blean algebra: Chapter 6 Page 8

Chapter 6: Lgic Based Testing In all f the abve, a letter can represent a single sentence r an entire blean algebra expressin. Individual letters in a blean algebra expressin are called Literals (e.g. A,B) The prduct f several literals is called a prduct term (e.g., ABC, DE). An arbitrary blean expressin that has been multiplied ut s that it cnsists f the sum f prducts (e.g., ABC + DEF + GH) is said t be in sum-f-prducts frm. The result f simplificatins (using the rules abve) is again in the sum f prduct frm and each prduct term in such a simplified versin is called a prime implicant. Fr example, ABC + AB + DEF reduces by rule 20 t AB + DEF; that is, AB and DEF are prime implicants. The path expressins f Figure 6.5 can nw be simplified by applying the rules. The fllwing are the laws f blean algebra: Chapter 6 Page 9

Chapter 6: Lgic Based Testing Similarly, The deviatin frm the specificatin is nw clear. The functins shuld have been: Lps cmplicate things because we may have t slve a blean equatin t determine what predicate-value cmbinatins lead t where. KV CHARTS: INTRODUCTION: If yu had t deal with expressins in fur, five, r six variables, yu culd get bgged dwn in the algebra and make as many errrs in designing test cases as there are bugs in the rutine yu're testing. Chapter 6 Page 10

Chapter 6: Lgic Based Testing Karnaugh-Veitch chart reduces blean algebraic manipulatins t graphical trivia. Beynd six variables these diagrams get cumbersme and may nt be effective. SINGLE VARIABLE: Figure 6.6 shws all the blean functins f a single variable and their equivalent representatin as a KV chart. Figure 6.6 : KV Charts fr Functins f a Single Variable. The charts shw all pssible truth values that the variable A can have. A "1" means the variable s value is "1" r TRUE. A "0" means that the variable's value is 0 r FALSE. The entry in the bx (0 r 1) specifies whether the functin that the chart represents is true r false fr that value f the variable. We usually d nt explicitly put in 0 entries but specify nly the cnditins under which the functin is true. TWO VARIABLES: Figure 6.7 shws eight f the sixteen pssible functins f tw variables. Chapter 6 Page 11

Chapter 6: Lgic Based Testing Figure 6.7: KV Charts fr Functins f Tw Variables. Each bx crrespnds t the cmbinatin f values f the variables fr the rw and clumn f that bx. A pair may be adjacent either hrizntally r vertically but nt diagnally. Any variable that changes in either the hrizntal r vertical directin des nt appear in the expressin. In the fifth chart, the B variable changes frm 0 t 1 ging dwn the clumn, and because the A variable's value fr the clumn is 1, the chart is equivalent t a simple A. Figure 6.8 shws the remaining eight functins f tw variables. Chapter 6 Page 12

Chapter 6: Lgic Based Testing Figure 6.8: Mre Functins f Tw Variables. The first chart has tw 1's in it, but because they are nt adjacent, each must be taken separately. They are written using a plus sign. It is clear nw why there are sixteen functins f tw variables. Each bx in the KV chart crrespnds t a cmbinatin f the variables' values. That cmbinatin might r might nt be in the functin (i.e., the bx crrespnding t that cmbinatin might have a 1 r 0 entry). Since n variables lead t 2 n cmbinatins f 0 and 1 fr the variables, and each such cmbinatin (bx) can be filled r nt filled, leading t 2 2n ways f ding this. Chapter 6 Page 13

Chapter 6: Lgic Based Testing Cnsequently fr ne variable there are 2 21 = 4 functins, 16 functins f 2 variables, 256 functins f 3 variables, 16,384 functins f 4 variables, and s n. Given tw charts ver the same variables, arranged the same way, their prduct is the term by term prduct, their sum is the term by term sum, and the negatin f a chart is gtten by reversing all the 0 and 1 entries in the chart. THREE VARIABLES: KV charts fr three variables are shwn belw. As befre, each bx represents an elementary term f three variables with a bar appearing r nt appearing accrding t whether the rw-clumn heading fr that bx is 0 r 1. A three-variable chart can have grupings f 1, 2, 4, and 8 bxes. A few examples will illustrate the principles: OR Chapter 6 Page 14

Chapter 6: Lgic Based Testing Chapter 6 Page 15

Chapter 6: Lgic Based Testing Figure 6.8: KV Charts fr Functins f Three Variables. Chapter 6 Page 16