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Branching time temporal logic

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Book cover Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency (REX 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 354))

Abstract

Many important parallel computer programs exhibit ongoing behaviour that is characterized naturally in terms of infinite execution traces, which can be organized into “branching” trees, and which reflect the high degree of nondeterminism inherent in parallel computation. In this paper, we give a systematic account of Branching Time Temporal Logics, which provide a formal system for describing and reasoning about the correct behaviour of such programs. Several systems of branching time temporal logic that have appeared in the literature are presented, and significant related issues such as their axiomatizations, and decision procedures for their satisfiability and model checking problems are discussed. The applicability of their axiomatizations to formulate deductive systems of these temporal logics to reason about the correctness of concurrent programs is then described as is that of their decision procedures to the tasks of mechanical synthesis and verification. A comparison of the relative expressive power of these systems of branching time temporal logic is also presented, and their ability to specify important correctness properties of programs, including those that involve fairness, is discussed. Moreover, their expressiveness is related to both, the expressiveness of corresponding linear time temporal logics, as well as that of other standard formalisms such as the monadic second-order theory of many successors and finite-state tree automata. Finally, a comparison is undertaken between branching time temporal logics and linear time ones, particularly with respect to their adequacy for such applications as specifying and reasoning about the correctness of concurrent programs.

This work was supported in part by NSF grant DCR-8511354, ONR URI contract N00014-86-K-0763, and Netherlands NWO grant nf-3/nfb 62-500.

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Authors and Affiliations

  1. Department of Computer Sciences, The University of Texas at Austin, 78712, Austin, TX, USA

    E. Allen Emerson & Jai Srinivasan

  2. Mathematics and Computing Science Department, Technical University of Eindhoven, Eindhoven, The Netherlands

    E. Allen Emerson

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  1. E. Allen Emerson
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  2. Jai Srinivasan
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J. W. de Bakker W. -P. de Roever G. Rozenberg

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Emerson, E.A., Srinivasan, J. (1989). Branching time temporal logic. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds) Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency. REX 1988. Lecture Notes in Computer Science, vol 354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013022

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  • DOI: https://doi.org/10.1007/BFb0013022

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