1. Process Algebra (2IF45) Dr. Suzana Andova

2. 1 Process Algebra (2IF45) Practical issues Lecturer - Suzana Andova - Group: Software Engineering and Technology group - Section: Model Driven Software Engineering My coordinates: office HG 5.36 email s.andova@tue.nls.andova@tue.nl phone: 5089

3. 2 Process Algebra (2IF45) Organization Course information - http://www.win.tue.nl/~andova/education/2IF45/201112/201112.html Course material book: −Jos C.M. Baeten, T. Basten, M.A. Reniers “Process Algebra: Equational Theories of Communicating Processes” lecture notes “Probabilistic Process Algebra” available at http://www.win.tue.nl/~andova/education/2IF45/lnpa.pdf distributed papers slides

4. 3 Process Algebra (2IF45) Organization Lectures Quarter 3 (06-02-2012 – 02-04-2012): laplace-gebouw -1.19 Quarter 4 (23-04-2012 – 18-06-2012): HG 6.09 Course activities group assignments −3 assignments = 40% of the final grade exam = 60% of the final grade home works − not compulsory but useful active participation, discussion few questionnaires – evaluation

5. 4 Process Algebra (2IF45) Content of the course Equational theories and Operational semantics Equational theory of communication processes Equational theories for probabilistic processes Learning objectives: be able to develop extensions of a process algebraic language, axiomatically and semantically be able to establish and analyze relations and discover "inconsistencies" between a given equational theory and its operational semantics be able to decide the most suitable construct(s) to specify particular system behavior be able to specify and analyze probabilistic process specifications

6. 5 Process Algebra (2IF45) Questions for you Where did you do your bachelor: TU/e (CS, ES, WIN) TU/e (Mechanical eng., Electrical eng. ) HBO Manipal other university? Who knows what formal methods are about? Who is familiar with labeled transition systems ? Who is familiar with (any level) mCRL2, Chi? Who has knowledge (any level) on model checking? Who has knowledge on bisimulation relations ? Who is acquainted with probability theory?

7. 6 Process Algebra (2IF45) Questions for me?

8. Process Algebra (2IF45) Introduction Dr. Suzana Andova

9. 8 Foundations (Example) Natural numbers N = {0, 1, 2, …} Operations: + and The Peano axioms define the arithmetical properties of natural numbers “ingredients” to build the set of natural numbers N − 0 constant and −s unary operator (successor function) Axiom If n is a natural number then s(n) is natural number, n  N  s(n)  N Process Algebra (2IF45)

10. 9 Foundations (Example - cont.) Addition of natural numbers “addition” a: N x N → N is axiomatized as −a(x,0) = x −a(x,s(y)) = s(a(x,y)) Multiplication of natural numbers “multiplication” m: N x N → N is axiomatized as −m(x,0) = 0 −m(x,s(y)) = a(m(x,y),x) Process Algebra (2IF45)

11. 10 Foundations (Example - cont.) Derivation of other equalities use the axioms derive more equalities using the following rules: −reflexivity x = x −symmetry x= y  y = x −transitivity x = y  y = z  x = z Example of a theorem: s(s(0)) = m(s(s(0)), s(0)) Process Algebra (2IF45)

12. 11 Foundations (Example – recap ) The Peano axioms define the arithmetical properties of natural numbers −0 constant and −S unary operator −“addition” a: N x N → N binary function −“multiplication” m: N x N → N binary function −Terms: s(s(0)), a(s(0),m(s(0),s(s(s(0))))), 0, −n  N  s(n)  N −a(x,0) = x −a(x,s(y)) = s(a(x,y)) −m(x,0) = 0 −m(x,s(y)) = a(m(x,y),x) −reflexivity x = x −symmetry x= y  y = x −transitivity x = y  y = z  x = z Process Algebra (2IF45) Signature Axioms Relation (derivation rules)

13. 12 Foundation Axiom is any mathematical statement that serves as a starting point from which other statements are logically derived “absolute truth” Derivation rules are also part of the theory used to form new “truths” from the old once. Theorems are mathematical statements that can be derived from the axioms by derivation. Interpretation and models of an equational theory Process Algebra (2IF45)

14. 13 Alternative Representation of numbers: unary semantics Process Algebra (2IF45) If we would like to represent numbers as s(s(0)) s(0) 0 1 1

15. 14 Alternative Representation of numbers: unary semantics 00 1 1 y  y’ a(x,y)  a( x, y’) s(x)  x 1 1 1 x  x’, y  a(x,y)  x’ x , y  a(x,y)      1 a( s(s(0)), s(s(s(0))) )a( s(s(0)), s(s(0)) ) 1 a( s(s(0)), s(0) )  1 a( s(s(0)), 0 )  s(0)  1 0 1   

16. 15 Alternative Representation of numbers: unary semantics 1 a( s(s(0)), s(s(s(0))) )a( s(0), s(s(s(0))) ) 1 a( 0, s(s(s(0))) )  1 a(0, s(s(0)) )  a(0, s(0) ) 1 a(0,0) 1     1 a( s(s(0)), s(s(0)) )a( s(0), s(s(0)) ) 1  1  1  1  1  1 a( s(s(0)), s(0) )a( s(0), s(0) ) 1   1 a( s(s(0)), 0 )a( s(0), 0 ) 1  1 1   

17. Process Algebra (2IF45) Representation of Reactive systems Dr. Suzana Andova

18. 17 Process Algebra (2IF45) Reactive systems Reactive systems execute by reacting to stimuli from its environment Many of them are control crucial and/or safety critical These systems are large and usually consist of a number of components which interact with each other Modeling reactive systems abstract model of the system unambiguous description methods and tools for model analysis (verification of qualitative properties, performance analysis)

19. 18 Process Algebra (2IF45) Representation as Labeled transition systems x:= 1; y:= x+1; out(y). in(x); y:= x+1; while (true) { out(y); }. ?x y:=x+1 !y ?x y:=x+1 !y out(x); in(y). !x ?y

20. 19 Process Algebra (2IF45) Representation as Labeled transition systems !tea ?coin !coffee ?return !tea !coffee ?coin ?return !tea !coffee error VM1VM2VM3 ?coin User !coin ?coffee

21. 20 Process Algebra (2IF45) Representation as Labeled transition systems !tea ?coin !coffee VM1 User !coin ?coffee composition VM1 and User coin coffee ?coin !coffee !tea

22. 21 Process Algebra (2IF45) Representation as Labeled transition systems !coin ?return !tea !coffee VM2’ User ?coin !coffee ?coffee ?tea ?coffee ?return !tea !coffee VM2 ?coin

23. 22 Process Algebra (2IF45) Representation as Labeled transition systems !tea !coffee VM1’ ?coin !tea !coffee VM1’’ ?coin Using VM1’ coin coffee Using VM1’’ coffee coin

24. 23 Process Algebra (2IF45) Questions When modeling a system, is an LTS a model to start with or is it something to be obtained as a final or side product? What entities do we need to have predefined, to be able to produce an LTS? What is a state? What is a transition? How do we know drawing a transition from a state s to a state s’ is right? How do we know which label to assign to it? How do we combine LTSs?

25. 24 Process Algebra (2IF45) Use of LTS representations In (model checking) tools manipulating the state space (LTSs): UPPAAL, Prism, MRMC manipulating the specification (language): mCRL2, Chi, CADP, FDR, PEPA, MRMC +IMC components’ specifications the whole system specification the state space verification model checking reduction on specification reduction on specification reduction on LTSs composition by axiom SSpace generation property specification Yes! No! …

26. 25 Process Algebra (2IF45) components’ specifications Equational theory in place In (model checking) tools manipulating the state space (LTSs): UPPAAL, Prism, MRMC manipulating the specification (language): mCRL2, Chi, CADP, FDR, PEPA, MRMC updated IMC the whole system specification the state space verification model checking reduction on specification reduction on specification reduction on LTSs composition by axiom SS generation by the SOS rules property specification Yes! No! … equiational theory (axioms) Semantic rules

27. 26 Process Algebra (2IF45) components’ specifications Equational theory in place In (model checking) tools manipulating the state space (LTSs): UPPAAL, Prism, MRMC manipulating the specification (language): mCRL2, Chi, CADP, FDR, PEPA, MRMC updated IMC the whole system specification the state space verification model checking reduction on specification reduction on specification reduction on LTSs composition by axiom SS generation by the SOS rules property specification Yes! No! … equiational theory (axioms) Operational semantics (SOS) reduction to basic forms reduction by equations reduction by equivalence relations (bisimulation) consistent

28. 27 Process Algebra (2IF45) components’ specifications Equational theory in place In (model checking) tools manipulating the state space (LTSs): UPPAAL, Prism, MRMC manipulating the specification (language): mCRL2, Chi, CADP, FDR, PEPA, MRMC updated IMC the whole system specification the state space verification model checking reduction on specification reduction on specification reduction on LTSs composition by axiom SS generation by the SOS rules property specification Yes! No! … equiational theory (axioms) Operational semantics (SOS) reduction to basic forms reduction by equations reduction by equivalence relations (bisimulation) consistent In this course we will learn HOW to build a consistent Process Algebra = specification language + axioms + SOS rules + reduction equivalence relations so that the initial specification and the model checked LTS, they both describe the same system!