Abstract
In the first part of the paper, we present an algorithm for the construction of a quotient model under the equivalence induced by ACTL, the universal fragment of CTL. As this equivalence coincides with simulation equivalence, the achieved reduction is better than reductions achieved by methods based on bisimulation. Simulation equivalence is also the equivalence that is induced by ACTL*, hence, the reduced model allows model checking of any ACTL* formula. Furthermore it provides diagnostic information. In the second part, we restict our attention to single ACTL formulae. An algorithm is given that constructs a model which is reduced w.r.t. a specific formula.
The reduced models are constructed directly, without intermediate need for the full models. The approach, splitting of states w.r.t. formulae, yields a sequence of successively more refined models which at any stage preserve truth of formulae.
Currently working in ESPRIT project P6021: “Building Correct Reactive Systems (REACT)”.
Chapter PDF
Similar content being viewed by others
References
S, Bensalem, A. Bouajjani, C. Loiseaux, and J. Sifakis. Property preserving simulations. In CAV'92.
A. Bouajjani, J.-C. Fernandez, N. Halbwachs, P. Raymond, and C. Ratel. Minimal state graph generation. Science of Computer Programming, 18(3):247–271, 1992.
M.C. Brown, E.M. Clarke, and O. Grumberg. Characterizing finite Kripke structures in propositional temporal logic. Theoretical Computer Science, 59:115–131, 1988.
J.R. Burch, E.M. Clarke, K.L. McMillan, D.L. Dill, and L.J. Hwang. Symbolic model checking: 1020 states and beyond. In Proc. 5th LICS, 1990.
E.M. Clarke, O. Grumberg, and D.E. Long. Model checking and abstraction. In Proc. 19th POPL, 1992.
E.M. Clarke, E.A. Emerson, and A.P. Sistla. Automatic verification of finitestate concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2):244–263, 1986.
O. Coudert, J.C. Madre, and C. Berthet. Verifying temporal properties of sequential machines without building their state diagram. In CAV'90.
D.R. Dams and O. Grumberg. Abstract interpretation of reactive systems: Abstractions preserving ACTL*, ECTL* and CTL*. Technical report, Eindhoven University of Technology, Department of Computer Science, 1992.
D.L. Dill. Trace Theory for Automatic Hierarchical Verification of Speed-Independent Circuits. ACM Distinguished Dissertations. MIT Press, 1989.
E.A. Emerson and J.Y. Halpern. 'sometimes’ and ‘Not Never’ revisited: on branching time versus linear time temporal logic. J. of the ACM, 33(1):151–178, 1986.
E.A. Emerson and J. Srinivasan. Branching time temporal logic. In Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, Springer-Verlag, 1988.
R. Enders, F. Filkorn, and D. Taubner. Generating BDDs for symbolic model checking in CCS. In CAV'91.
P. Godefroid and P. Wolper. Using partial orders for the efficient verification of deadlock freedom and safety properties. In CAV'91.
S. Graf and C. Loiseaux. A tool for symbolic program verification and abstraction. In these proceedings.
S. Graf and B. Steffen. Compositional minimization of finite state processes. In CAV'90.
O. Grumberg and D.E. Long. Model checking and modular verification. In CONCUR'91, LNCS 527, Springer-Verlag, 1991.
A.J. Hu, D.L. Dill, A.J. Drexler, and C. Han Yang. Higher-level specification and verification with BDDs. In CAV'92.
R. Janicki and M. Koutny. On some implementation of optimal simulations. In CAV'90.
R. Kaivola and A. Valmari. The weakest compositional semantic equivalence preserving nexttime-less linear temporal logic. In CONCUR'92, LNCS 630, Springer-Verlag, 1992.
S. Katz and D. Peled. Verification of distributed programs using representative interleaving sequences. Distributed Computing, 6:107–120, 1992.
R.P. Kurshan. Analysis of discrete event coordination. In Proc. Workshop on Stepwise Refinement of Distributed Systems: Models, Formalisms, Correctness, LNCS 430, Springer-Verlag, 1989.
O. Lichtenstein and A. Pnueli. Checking that finite state concurrent programs satisfy their linear specification. In Proc. 12th POPL, 1985.
K. McMillan. Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In CA V'92.
R. Milner. An algebraic definition of simulation between programs. In IJCAI'71.
R. Paige and R. Tarjan. Three partition refinement algorithms. SIAM Journal on Computing, 16(6):973–989, 1987.
D. Park. Concurrency and automata on infinite sequences. In Proc. 5th GI-Conf. on Theoretical Computer Science, LNCS 104, Springer-Verlag, 1981.
D.K. Probst and H.F. Li. Using partial-order semantics to avoid the state explosion problem in asynchronous systems. In CAV'90.
J.P. Quielle and J. Sifakis. Specification and verification of concurrent systems in CESAR. In Proc. 5th Int. Symp. on Programming, LNCS 137, Springer-Verlag, 1981.
G. Shurek and O. Grumberg. The modular framework of computer-aided verification: Motivation, solutions and evaluation criteria. In CAV'90.
A. Valmari. A stubborn attack on state explosion. In CAV'90.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dams, D., Grumberg, O., Gerth, R. (1993). Generation of reduced models for checking fragments of CTL. In: Courcoubetis, C. (eds) Computer Aided Verification. CAV 1993. Lecture Notes in Computer Science, vol 697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56922-7_39
Download citation
DOI: https://doi.org/10.1007/3-540-56922-7_39
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56922-0
Online ISBN: 978-3-540-47787-7
eBook Packages: Springer Book Archive