# Action versus state based logics for transition systems

## Abstract

A temporal logic based on actions rather than on states is presented and interpreted over labelled transition systems. It is proved that it has essentially the same power as CTL*, a temporal logic interpreted over Kripke structures. The relationship between the two logics is established by introducing two mappings from Kripke structures to labelled transition systems and viceversa and two transformation functions between the two logics which preserve truth. A branching time version of the action based logic is also introduced. This new logic for transition systems can play an important role as an intermediate between Hennessy-Milner Logic and the modal μ-calculus. It is sufficiently expressive to describe safety and liveness properties but permits model checking in linear time.

## Keywords

Model Check Temporal Logic Atomic Proposition Label Transition System Process Algebra## Preview

Unable to display preview. Download preview PDF.

## 6. References

- [BCG88]M.C. Browne, E.M. Clarke & O. Grümberg: Characterizing Finite Kripke Structures in Propositional Temporal Logic.
*Theoret. Comp. Sci.*,**59**(1,2), 1988, pp. 115–131.Google Scholar - [CES89]E.M. Clarke, E.A. Emerson & A.P. Sistla: Automatic Verification of Finite State Concurrent Systems using Temporal Logic Specifications.
*ACM Toplas*,**8**(2), 1986, pp. 244–263.Google Scholar - [CLM89]E.M. Clarke, D.E. Long & K.L. Macmillan: Compositional Model Checking. In
*Proceedings 4th Annual Symposium on Logic in Computer Science (LICS)*, Asilomar, California, IEEE Computer Society Press, Washington, 1989, pp. 353–362.Google Scholar - [CPS88]Cleaveland, R., Parrow, J., Steffen, B. The Concurrency Workbench. In
*Automatic Verification Methods for Finite State Systems*(J. Sifakis, ed.) Lecture Notes in Computer Science**407**, Springer-Verlag, 1990, pp. 24–37.Google Scholar - [DV90a]R. De Nicola, & F.W. Vaandrager: Three Logics for Branching Bisimulations (Extended Abstract) in Proc. of the 5th Annual Symposium on Logic in Computer Science (
*LICS '90*), Philadelphia, USA, June 1990, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 118–129.Google Scholar - [DV90b]R. De Nicola, & F.W. Vaandrager: Three Logics for Branching Bisimulations, CWI Report CS-R9012, 1990.Google Scholar
- [EH86]E.A. Emerson & J.Y. Halpern: “Sometimes” and “Not Never” Revisited: on Branching Time versus Linear Time Temporal Logic.
*Journal of ACM*,**33**, 1, 1986, pp. 151–178.Google Scholar - [EL87]E.A. Emerson & C.L. Lei: Modalities for Model Checking: Branching Time Strikes Back.
*Science of Computer Programming*,**6**, 1987.Google Scholar - [ES89]E. A. Emerson & J. Srinivasan: Branching Time Temporal Logic. In
*Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency*, (de Bakker, de Roever and Rozenberg, eds.) Lecture Notes in Computer Science**354**, Springer-Verlag, 1989, pp. 123–172.Google Scholar - [GV90]J.F. Groote & F.W. Vaandrager: An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence. In
*Proceedings ICALP '90*, Warwick, Lecture Notes in Computer Sciences, Springer-Verlag, 1990.Google Scholar - [GW89]R.J. van Glabbeek & W.P. Weijland: Branching Time and Abstraction in Bisimulation Semantics (extended abstract). In
*Information Processing '89*(G.X. Ritter, ed.), Elsevier Science Publishers B.V. (North Holland), 1989, pp. 613–618.Google Scholar - [HM85]M. Hennessy & R. Milner: Algebraic Laws for Nondeterminism and Concurrency.
*Journal of ACM*,**32**, 1985, pp. 137–161.Google Scholar - [JKP90]B. Jonsson, A.H. Khan & J. Parrow: Implementing a model checking algorithm by adapting existing automated tools. In
*Automatic Verification Methods for Finite State Systems*(J. Sifakis, ed.) Lecture Notes in Computer Science**407**, Springer-Verlag, 1990, pp. 179–188.Google Scholar - [Lam83]L. Lamport: What Good Is Temporal Logic?,
*Information Processing '83*(R.E.A. Mason, ed.) Elsevier Science Publishers B.V. (North Holland), 1983, pp. 657–668.Google Scholar - [Lar88]K.G. Larsen: Proof Systems for Hennessy-Milner Logic with Recursion, in proceeding
*CAAP '88*(M. Dauchet & M. Nivat eds) Lecture Notes in Computer Science**299**, Springer-Verlag, 1988.Google Scholar - [Sti89]C. Stirling: Temporal Logics for CCS, in
*Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency*, (de Bakker, de Roever and Rozenberg, eds.) Lecture Notes in Computer Science**354**, Springer-Verlag, 1989, pp. 660–672.Google Scholar