1 Towards formal manipulations of scenarios represented by High-level Message Sequence Charts Loïc Hélouet Claude Jard Benoît Caillaud IRISA/PAMPA (INRIA/CNRS/Univ. Rennes) Campus de Beaulieu, F RENNES, France.

2 Motivations n Formal methods and tools to improve the development process of (distributed) software n Need to instrument at early stages of the development n Interest of graphical scenario languages like Message Sequence Charts in the SDL framework or Sequence Diagrams of the popular Unified Modelling Language n Problems with their formal semantics n Problems with their declarative (high-level) nature : Normal forms ? State-finiteness ? Executability ?

3 Contributions n Partial-order semantics of the High-level Message Sequence Charts (HMSC is the ITU/Z.120 standard) n Effective notion of equivalence based on event- structures and graph-grammars n Normal form of HMSCs n Towards new efficient methods : to decide divergence, to simulate and to check properties

4 Outline n MSC et HMSC n Event structures n Partial order semantics of HMSC n Covering graphs of event structures n Graph grammars n Regularity of graph grammars n Equivalence n Applications n Conclusion and perspectives

5 Basic Message Sequence Charts (BMSC) n Instances, events and messages n Ordering of events : due to sequentiality of instances due to message causality Partial order M= ( E,<, ,A,I ) E : events < : causal ordering  : labelling of events  : E -> A x I A : action names I : instance names

6 High-level Message Sequence Charts (HMSC) n Hierarchical graph of MSCs n Sequence, choice and loop operators n Non-deterministic choice n Sequence is communication-closed but without synchronization

7 Sequencing Instance by instance, maximal events of the first HMSC are linked to the minimal events of the second HMSC

8 Choice : union of scenarios

9 Recursion (unfolding)

10 Specifications which are not implementable Non-local choices Divergence

11 Infinite family of partial orders n Paths of the HMSC graph form (generally) an infinite family of partial orders n This family can be uniquely represented by an event structure (communication closed assumption)

12 Event structures n Compact representation of partial order families. Used in concurrency theory ES = (E, <, #, , A, I ) E : events < : partial order (causality) # : conflict relation (symmetric, inherited by causality)  : labelling

13 Reduction to minimal conflicts

14 From HMSCs to event structures n Sequencing : as for partial orders; conflicts are inherited n Choice : creates new conflicts n Recursion : unfolding

15 HMSC partial order semantics n HMSC Semantics = the corresponding event structure n Strong notion of equivalence given by isomorphism of event structures n Isomorphism of (infinite) graphs can be computed using graph grammars [Caucal 92] such that : the graph is regular the graph is finitely branching n Based on the computation of normal forms of the grammars

16 Non regular specifications

17 Irregular graphs Cannot be represented by a graph grammar

18 Covering graphs with conflict inheritance edges

19 Transformation into a regular graph

20 Graph grammar n Hyperarc : s 1....s n n Hypergraph : Graph + hyperarcs n Rule : (Hyperarc, Hypergraph) n Graph grammar = G = (Axiom,Rules)

21 Graph rewriting

22 From HMSCs to graph grammars (ends)

23 From HMSCs to graph grammars (sequence)

24 From HMSCs to graph grammars (choice)

25 From HMSCs to graph grammars (recursion)

26 From HMSCs to graph grammars (conflict inheritance arcs) Context management

27 Example (HMSC)

28 Example (graph grammar)

29 Example (graph grammar)

30 Properties of covering graphs n Covering graphs with inheritance edges are regular (can be finitely described by graph grammars) n Branching of conflicts is finite n Branching of causality is generally infinite n But ignoring them preserves the isomorphism of the event structures (the infinite branching can be reconstructed from the simplified graph)

31 Decision of equivalence n Let us consider two HMSCs H1 and H2 ¬ Compute their graph grammars G1 and G2 ­ Replace the inheritance edges that are not made from choice to choice by the corresponding conflicts (minimization of basic event structures) ® Compute grammars G’1 and G’2 by eliminating redundancies (to avoid global optimization) ¯ Compute FBG1 and FBG2 by eliminating infinite branchings within G’1 and G’2 ° Compute FNG1 and FNG2, the normal forms of FBG1 and FBG2 n If FBG1 and FBG2 have the same normal forms up to a renaming, then H1 and H2 are equivalent

32 Normal forms n Global transformation to ensure a certain distance between the hyperarcs n Polynomial A rule which is not normalized

33 Example of two equivalent HMSCs

34 Their covering graph

35 Decision of divergence An HMSC is not divergent iff the communication graph of each simple loop is symmetric Can be computed on the graph grammar by finite rewriting

36 Summary n Towards formal manipulations of scenario languages n Partial order semantics of the HMSC standard n Equivalence defined as a structure isomorphism n Use of graph grammars and of recent decision algorithms ftp://ftp.inria.fr/INRIA/publication/RR/RR-3499.ps.gz

37 Perspectives n Short term : Implementation Weaker notions of equivalence Animation (using normal forms) n Middle term : HMSCs with values Parallel composition Integration in the UML meta-model n Long term : Decision of properties Quantitative analysis using Max + techniques Generation of squeletons, protocol synthesis