Two Variable vs. Linear Temporal Logic in Model Checking and Games

  • Michael Benedikt
  • Rastislav Lenhardt
  • James Worrell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)

Abstract

Verification tasks have non-elementary complexity for properties of linear traces specified in first-order logic, and thus various limited logical languages are employed. In this paper we consider two restricted specification logics, linear temporal logic (LTL) and two-variable first-order logic (FO2). LTL is more expressive, but FO2 is often more succinct, and hence it is not clear which should be easier to verify. In this paper we take a comprehensive look at the issue, giving a comparison of verification problems for FO2, LTL, and the subset of LTL expressively equivalent to FO2, unary temporal logic (UTL). We give two logic-to-automata translations which can be used to give upper bounds for FO2 and UTL; we apply these to get new bounds for both non-deterministic systems (hierarchical and recursive state machines, games) and for probabilistic systems (Markov chains, recursive Markov chains, and Markov decision processes). We couple this with lower-bound arguments for FO2 and UTL. Our results give both a unified approach to understanding the behavior of FO2 and UTL, along with a nearly comprehensive picture of the complexity of verification for these logics.

Keywords

Markov Chain Model Check Temporal Logic Markov Decision Process Linear Temporal Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michael Benedikt
    • 1
  • Rastislav Lenhardt
    • 1
  • James Worrell
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK

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