Abstract
In this paper we describe a method for the obtention of the minimal transition system, representing a communicating system given by a set of parallel processes, avoiding the complexity of the non minimal transition system. We consider minimization with respect to observational equivalence, but the method may be adapted to any other equivalence.
An interesting method to achieve this goal is to proceed by stepwise composition and minimization of the components of the system. However, if no precautions are taken, the intermediate state graphs generated by this method may contain a lot of transitions which are impossible in the whole context. We give here a variant of this method which allows to avoid these impossible transitions by taking into account at each composition step a guess of the interface behaviour of the context. This “interface specification” must be provided by the user. The method is based on a reduction operator for the composition of a subsystem with its interface specification, which is similar to the parallel operator but introduces undefinedness predicates whereever the interface “cuts off” a transition. The parallel operator is defined in a way that these undefinedness predicates disappear again in the full context if and only if the corresponding transition is in fact impossible in the whole system.
The efficiency of the method depends in fact on the accuracy with which the designer is able to approximate the possible sequences of the context, but its correctness does not. The proof of the correctness of the method is based on a preorder relation similar to the one defined by Walker.
This work has been partially supported by ESPRIT Basic Research Action ‘Spec’
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
A. Bouajjani, J.-C. Fernandez, N. Halbwachs. Minimal Model Generation, this volume
E.M. Clarke, E.A. Emerson, E. Sistla. Automatic Verification of Finite State Concurrent Systems using Temporal Logic Specification: A Practical Approach, POPL 1983
E.M. Clarke, D.E. Long, K.L. McMillan. Compositional Model Checker, LICS, 1989
R. Cleaveland, J. G. Parrow and B. Steffen. The Concurrency Workbench, Proceeding of the Workshop on Automatic Verification Methods for Finite State Systems, Grenoble, France, 1989, LNCS 407
R. Cleveland, J. G. Parrow and B. Steffen. A Semantics based Verification Tool for Finite State Systems, in the proceedings of the Ninth International Symposium on Protocol Specification, Testing, and Verification; North Holland, 1989
R. Cleveland, and B. Steffen. When is “Partial” Complete? A Logic-Based Proof Technique using Partial Specifications, in Proceedings of LICS'90, 1990
Fernandez, J.-C. Aldébaran: Un Système de Vérification par Réduction de Processus Communicants, Ph.D. Thesis, Université de Grenoble, 1988
J.C. Fernandez, J.Ph. Schwartz, J.Sifakis. An Example of Specification and Verification in Cesar, Proceedings of ‘The Analysis of Concurrent Systems', 1983, LNCS 207
Caspi P., Halbwachs N., Pilaud N., Plaice J. LUSTRE, a declarative language for programming synchronous systems, Proceedings of 14th POPL, Munich, 1987
B. Josko. MCTL — An extension of CTL for modular verification of concurrent systems, Workshop on Temporal Logic in Specification 1987, LNCS 398
R.P. Kurshan, K. McMillan. A Structural Induction Theorem for Processes, in ACM Symposium on Principles of Distributes Computing, 1989
H.Krumm. Projections of the Reachability Graph and Environment Models, two approaches to facilitate the functional analysis of Systems of cooperating finite state machines, Proceedings of the Workshop on Automatic Verification of Finite State Systems, Grenoble 89, LNCS 407.
Larsen, K.G., and B. Thomsen. Compositional Proofs by Partial Specification of Processes, in Proceedings LICS'88, 1988
K.G. Larsen, L. Xinxin. Compositionality through an Operational Semantics of Contexts, in Proceedings ICALP'90, LNCS, 1990
R. Milner. A Calculus for Communicating Systems, LNCS 92, 1980
R. Milner. Communication and Concurrency, Prentice Hall, 1989
E.-R. Olderog. Nets, Terms and Formulas: Three Views of Concurrent Processes, Habilitationsschrift, Universität Kiel, to appear in Tracts in Theoretical Computer Science, Cambridge University Press
A.Pnueli. In Transition from Global to Modular Temporal Reasoning about Programs, in Logics and Models for Concurrent Systems, Nato ASI Series F, Vol. 13, Springer Verlag
G. Shurek, O. Grumberg. The Modular Framework of Computer-aided Verification: Motivation, Solutions And Evaluation Criteria, this volume
Z. Stadler, O. Grumberg. Network Grammars, Communication Behaviours and Automatic Verification, in Proceeding of the Workshop on Automatic Verification Methods for Finite State Systems, Grenoble, France, 1989, LNCS 407
B. Steffen. Characteristic Formulae, in Proceedings ICALP 1989
C. Stirling. Modal Logics for Communicating Systems, TCS 49, pp. 311–347, 1987
C. Stirling and D. J. Walker. Local Model Checking in the Modal Mu-Calculus, in Proceedings CAAP 1989
D.J. Walker. Bisimulation and Divergence in CCS, in Proceedings LICS 1988
G. Winskel. Compositional Checking of Validity on Finite State Processes, Workshop on Theories of Communication, CONCUR, 1990
P. Wolper, V. Lovinfosse. Verifying Properties of Large sets of Processes with Network Invariants, in Proceeding of the Workshop on Automatic Verification Methods for Finite State Systems, Grenoble, France, 1989, LNCS 407
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Graf, S., Steffen, B. (1991). Compositional minimization of finite state systems. In: Clarke, E.M., Kurshan, R.P. (eds) Computer-Aided Verification. CAV 1990. Lecture Notes in Computer Science, vol 531. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023732
Download citation
DOI: https://doi.org/10.1007/BFb0023732
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54477-7
Online ISBN: 978-3-540-38394-9
eBook Packages: Springer Book Archive