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On Ω-automata and temporal logic

Authors:

M. Y. VardiAuthors Info & Claims

STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

Pages 127 - 137

https://doi.org/10.1145/73007.73019

Published: 01 February 1989 Publication History

Abstract

We study here the use of different representation for infinitary regular languages in extended temporal logic. We focus on three different kinds of acceptance conditions for finite automata on infinite words, due to Büchi, Streett, and Emerson and Lei (EL), and we study their computational properties. Our finding is that Büchi, Streett, and EL automata span a spectrum of succinctness. EL automata are exponentially more succinct than Büchi automata, and complementation of EL automata is doubly exponential. Streett automata are of intermediate complexity. While translating from Streett automata to Büchi automata involves an exponential blow-up, so does the translation from EL automata to Streett automata. Furthermore, even though Streett automata are exponentially more succinct than Büchi automata, complementation of Streett automata is only exponential. As a result, we show that the decision problem for ETL_EL, where temporal connectives are represented by EL automata, is EXPSPACE-complete, and the decision problem for ETL_S, where temporal connectives are represented by Streett automata, is PSPACE-complete.

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Cited By

Boker ULehtinen K(2023)When a Little Nondeterminism Goes a Long WayACM SIGLOG News10.1145/3584676.358468210:1(24-51)Online publication date: 14-Feb-2023
https://dl.acm.org/doi/10.1145/3584676.3584682
Havlena VLengál OLi YŠmahlíková BTurrini A(2023)Modular Mix-and-Match Complementation of Büchi AutomataTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-30823-9_13(249-270)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30823-9_13
John TJantsch SBaier CKlüppelholz S(2022)From Emerson-Lei automata to deterministic, limit-deterministic or good-for-MDP automataInnovations in Systems and Software Engineering10.1007/s11334-022-00445-718:3(385-403)Online publication date: 1-Sep-2022
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Index Terms

On Ω-automata and temporal logic
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Number-theoretic computations
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Algebraic language theory

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cover image ACM Conferences

STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

February 1989

600 pages

ISBN:0897913078

DOI:10.1145/73007

Editor:
D. S. Johnson

Copyright © 1989 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 February 1989

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STOC89: 21st Annual ACM Symposium on the Theory of Computing

May 14 - 17, 1989

Washington, Seattle, USA

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STOC '89 Paper Acceptance Rate 56 of 196 submissions, 29%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Boker ULehtinen K(2023)When a Little Nondeterminism Goes a Long WayACM SIGLOG News10.1145/3584676.358468210:1(24-51)Online publication date: 14-Feb-2023
https://dl.acm.org/doi/10.1145/3584676.3584682
Havlena VLengál OLi YŠmahlíková BTurrini A(2023)Modular Mix-and-Match Complementation of Büchi AutomataTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-30823-9_13(249-270)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30823-9_13
John TJantsch SBaier CKlüppelholz S(2022)From Emerson-Lei automata to deterministic, limit-deterministic or good-for-MDP automataInnovations in Systems and Software Engineering10.1007/s11334-022-00445-718:3(385-403)Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s11334-022-00445-7
Renkin FSchlehuber-Caissier PDuret-Lutz APommellet A(2022)Dissecting ltlsyntFormal Methods in System Design10.1007/s10703-022-00407-661:2-3(248-289)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s10703-022-00407-6
Hahn EPerez MSchewe SSomenzi FTrivedi AWojtczak D(2022)Alternating Good-for-MDPs AutomataAutomated Technology for Verification and Analysis10.1007/978-3-031-19992-9_19(303-319)Online publication date: 21-Oct-2022
https://doi.org/10.1007/978-3-031-19992-9_19
Duret-Lutz ARenault EColange MRenkin FGbaguidi Aisse ASchlehuber-Caissier PMedioni TMartin ADubois JGillard CLauko H(2022)From Spot 2.0 to Spot 2.10: What’s New?Computer Aided Verification10.1007/978-3-031-13188-2_9(174-187)Online publication date: 6-Aug-2022
https://doi.org/10.1007/978-3-031-13188-2_9
Li YTurrini AFeng WVardi MZhang L(2022)Divide-and-Conquer Determinization of Büchi Automata Based on SCC DecompositionComputer Aided Verification10.1007/978-3-031-13188-2_8(152-173)Online publication date: 6-Aug-2022
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John TJantsch SBaier CKlüppelholz S(2021)Determinization and Limit-Determinization of Emerson-Lei AutomataAutomated Technology for Verification and Analysis10.1007/978-3-030-88885-5_2(15-31)Online publication date: 12-Oct-2021
https://doi.org/10.1007/978-3-030-88885-5_2
Tian CWang WDuan ZHermanns HZhang LKobayashi NMiller D(2020)Making Streett Determinization TightProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394757(859-872)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394757
Renkin FDuret-Lutz APommellet A(2020)Practical “Paritizing” of Emerson-Lei AutomataAutomated Technology for Verification and Analysis10.1007/978-3-030-59152-6_7(127-143)Online publication date: 12-Oct-2020
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