13.1 DECISION ANALYSIS WITH DECISION TREES AND TABLES (CONDITION-ACTION ANALYSIS)

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1 Obligatory Reading Fakultät Informatik, Institut für Software- und Multimediatechnik, Lehrstuhl für Softwaretechnologie alzert, Kapitel über Entscheidungstabellen Ghezzi 6.3 Decision-table based testing Pfleeger 4.4, 5.6 3) (ondition-action and Event-ondition-Action Analysis) Prof. Dr. U. Aßmann Technische Universität Dresden Institut für Software- und Multimediatechnik Gruppe Softwaretechnologie Version -.2, Structured decisions: decision diagrams and decision tables) 2. inary decision diagrams (DD) And Ordered DD 3. Event-ondition Action Design 4. Model hecking 2 Goal Event-condition-action- (EA-)based design relies on condition analysis Understand how to describe the control-flow of methods and procedures by decision analysis Understand that several views on a decision tree exist (tables, DD, ODD) Understand that model checking is a technology with future ondition-action-analysis can also be employed for requirements analysis 3. DEISION ANALYSIS WITH DEISION TREES AND TALES (ONDITION-ATION ANALYSIS) 3 4

2 A House-Selling Expert System (ondition-action Analysis) Ok, I do not like bungalows, but my wife does not like that the car stands in free space in winter. Hmm... I rather would like to have the half double house... ut we need anyway 2 floors, because I need this space for my hobbies. My wife also would like a garden. Is necessary when complex, intertwined decisions should be made that should result in actions Decision trees and tables collect actions based on conditions A simple form of event-condition-action (EA) rules However, without events, only conditions How does the system analyze the customers requirements and derive appropriate proposals? Which conditions provoke which actions? 5 6 Decision Trees Decision Trees with ode Actions Decisions can be analyzed with a decision tree A trie (Präfixbaum) is a tree which has an edge marking Every path in the trie assembles a word from a language of the marking A trie on l = {,} is called decision tree Paths denote sequences of decisions (a set of vectors over l). A path corresponds to a vector over l A set of actions, each for one sequence of decisions Sequences of decisions can be represented in a path in the decision tree A A2 A3 A4 A5 The action may be code The inner nodes of same tree layer correspond to a condition E[i] Then, a Trie is isomorphic to an If-then- cascade if (E) then // case E === true if (E) then if(e2) then A5 A4 // case E === false if (E) then if(e2) then if (E3) then A3 A2 A A A2 A3 A4 A5 E E E2 E3 7 8

3 Decision Tables How to onstruct A Decision Table onditions and actions can be entered in a table ) Elaborate decisions oolean cross product 2) Elaborate actions 3) Enter into table 4) onstruct a cross boolean product as upper right quadrant (set of boolean vectors) Multiple choice quadrant 5) onstruct a multiple choice quadrant (lower right) by associating actions to boolean vectors 6) onsolidate E E oalesce yes/no to doesn t matter Introduce Else rule A A2 A A2 9 What Students Should Do to Professors After Exams ommon olumns an e Folded 2

4 Or Abbreviated to Else Action (onsolidated Decision Table) Applications of Decision Tables and Trees Deciding (decision management) omplex case distinctions (more than 2 decisions) ASE tools can generate code automatically Requirements analysis Describing the behavior of methods Describing business rules efore programming if-cascades, better make first a nice decision tree or table onfiguration management Decisions correspond here to configuration variants Processor=i486? System=linux? Same application as #ifdefs in preprocessor Formal design methods 3 4 Truth Tables oolean decision tables are truth tables ondition E Yes Yes No No ondition E Yes No Yes No Value of F = X X Value of F = X X 3.2 NORMALIZING ONTROL FLOW WITH NORMALIZED DD E E F Yes Yes Yes No No Yes No No 5 6

5 DDs (inary Decision Diagrams) DDs (inary Decision Diagrams) Are dags that result by merging the same subtrees into one (common subtree elimination) If the action is just a boolean value boolean functions f: l n --> l can be represented The decisions E[i] are regarded as boolean variables E E E2 E3 E E E2 E3 A A2 A3 7 8 ODDs (Ordered inary Decision Diagrams) omplex DD Problem: for one boolean function there are many DD Idea: introduce a standardized order for the variables Result: orderd binary decision diagrams In all ODD holds for all children u of parents v ord(u) > ord(v). For one order of variables there is one normal form ODD (canonical ODD) Leads to efficient comparison algorithm of boolean functions: compareooleanfunction() = { Fix variable order for two DD Transform both DD into ODD ompare both ODD syntactically } 9 2

6 If-cascades, DD and ODD if A then if then if then true false if then false true if then if then false true if then true false A A A A Variable order is [A,,] 2 22 Normalizing Wild Procedures: Normalized If-Structures with ODD There is only one canonical ODD for one order Develop normalized and factorized if-structures with it:. Elaborate arbitrary decision tree 2. hoose a variable order 3. Transform to ODD 4. Transform to If structure 5. Factor out common subtrees by subprograms Reengineering Structuring of legacy procedures onfiguration management Development of canonical versions of preprocessor nestings Help to master large systems Applications 23 24

7 Event-ondition-Action Design Decision analysis is invoked when events occur Event-condition-action (EA) rules Which conditions provoke which actions, given some events? 3.3 EVENT-ONDITION- ATION ASED DESIGN (EA) EA An event-condition-action (EA) system listens on channel(s) for events, analyses a condition, and executes an action Statecharts, EA rules, Tür Petri Nets ondition analysis can be done by DD Verification by model checking öffnen() schließen() verriegeln() entriegeln() entriegeln(), schließen()/ beep() öffnen(), verriegeln(), entriegeln()/ - öffnen()/ - geschlosse n offen <<Steuerungsmachine>> verriegel n/ amp.rote slichtan () entriegel n/ amp.grün eslichta n() schließe n/ amp.gelb eslichta n() abgesperrt öffnen, schließen, verriegeln / MODEL HEKING LARGE STATE SPAES 27 28

8 Representation of Mathematical Structures in DD and ODD Model hecking on DD Several mathematical data types can be represented with DD/ ODD: Sets, partial orders and lattices (e.g., in Z, VDM, SETL) Represent subsets of a set in the powerset lattice of the set Map the powerset lattice to a boolean algebra (theorem of Stone) Use a DD to encode the sets Uniform efficient representation in space and time Functions over finite domains of size n Associate to every element a vector from l k, where k = ld n ode sets with sets of such vectors Map again to boolean algebra Relations and graphs (also state machines) Interprete the elements of the relation (the edges) as sets of ordered k- tuples Represent as in the case of sets DD and ODD are very compact representation for state machines, boolean functions, and predicate logic (modal logic) uild a basis for checking state transition systems with modal logic (model checking) System is modeled as a state transition system and encoded as ODD Features of the system (predicates, logic formulas) are encoded as ODD, too Then, a model checker compares the ODDs and checks whether a feature holds in a state Effectively, the model checker only compares normalized representations of boolean functions, the ODD 29 3 The Use of Model hecking The End: What Have We Learned State spaces up to 2**2 can be handled Model checking checks whether features hold in states of large state spaces Used in hardware verification Proving circuits correct Software verification Safety-critical systems Minimization of boolean circuits Very important technique for verification of safety-critical hard- and software Decision analysis (ondition-action analysis) is an important analysis to describe requirements, to describe complex behavior of a procedure The control-flow of a procedure can be normalized with a DD and ODD onditions in large state spaces can be encoded in ODD and efficiently checked oolean functions, decision trees, relations, graphs, automata can be encoded in ODD 3 32