Abstract
We define a notion of πα equivalence of two execution sequences, where π is the set of variables shared between the two sequences and α is a set of variables disjoint from π appearing in only one of them. We call the set of variables α as auxiliary variables. We extend the notion of πα equivalence to formulas in temporal logics, and there by to classes of temporal logics. Under such a notion, we provide sound and complete translation scheme from Propositional Temporal Interval Logic(PTIL) to Linear Time Propositional Temporal Logic (PTL). We do so via the introduction of a chop operator into PTL. The PTIL that we consider is of Swartz, Melliar-Smith variety[13]. The translations that we give are Polynomial in space and time. Together with the results of Sistla and Clarke[14], we conclude that the satisfiability problem for PTIL is PSpace. Known decision procedures for PTIL are exponential in space[9]. The translations provide a means with which synchronization skeletons could be synthesized from specifications given in PTIL. We have constructed a prolog based prototype implementation of the synthesizer.
Preview
Unable to display preview. Download preview PDF.
References
Aaby,A.A and Narayana,K.T, Synthesis of Hardware from Propositional Temporal Interval Logic, Computer Science Research Report, 1988.
Ben-Ari, M., Manna, Z. and Pnueli, A., The Temporal Logic of Branching Time, Acta Informatica 20, (1983), pp. 207–226.
Clarke, E.M. and Emerson, E.A., Using Branching Time Temporal Logic to Synthesize Synchronization Skeletons, Science of Computer Programming 2, (1982), pp. 241–266.
Dill,D.L and Clarke,E.M, Automatic Verification of Asynchronous Circuits Using Temporal Logic, 1985 Chappel Hill Conference on VLSI,, May 1985.
Fujita,M., Tanaka,H. and Moto-oka,T., Specifying Hardware in Temporal Logic and Efficient Synthesis of State-Diagrams Using Prolog, Proceedings of the International Conference on Fifth Generation Computer Systems,, 1984.
Lichtenstein,O and Pnueli,A, Checking That Finite State Concurrent Programs Satisfy Their Linear Specifications, 12th ACM Symp. on Prin. of Prog. Lang.,, January 1985, pp. 97–107.
Lichtenstein,O, Pnueli,A and Zuck,L, The Glory of the Past, Proc. Logics of Programs, New-York, June 1985.
Manna, Z. and Wolper, P., Synthesis of Communicating Processes from Temporal Logic Specifications, Trans. Prog. Lang and Systems 6, 1 (January 1984), pp. 68–93.
Plaisted,D.A., A Low Level Language for Obtaining Decision Procedures for Classes of Temporal Logics, in Logics of Programs, vol. LNCS 164, Springer-Verlag, 1983, pp. 403–420.
Pnueli, A, Application of Temporal Logic to the Specification and Verification of Reactive Systems: A Survey of Current Trends, Lecture Notes in Computer Science 224, (1986), pp. 510–584, Springer-Verlag.
Pnueli,A., The Temporal Logic of Programs, IEEE Annual Symp. on Foundations of Computer Science,, November 1977.
Rosner,R. and Pnueli,A., A Choppy Logic, in Symposium on Logic in Computer Science, Cambridge,Massachusetts, 1986, pp. 306–313.
Schwartz,R.L., Melliar-Smith,P.M. and Vogt,F.H., An Interval Logic for Higher Level Temporal Reasoning, Conference on Principles of Distributed Computing,, 1983.
Sistla, A.P. and Clarke, E.M., The Complexity of Propositional Linear Temporal Logics, J. ACM 32, 3 (July 1985), pp. 733–749.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aaby, A.A., Narayana, K.T. (1988). Propositional temporal interval logic is PSPACE complete. In: Lusk, E., Overbeek, R. (eds) 9th International Conference on Automated Deduction. CADE 1988. Lecture Notes in Computer Science, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012834
Download citation
DOI: https://doi.org/10.1007/BFb0012834
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19343-2
Online ISBN: 978-3-540-39216-3
eBook Packages: Springer Book Archive