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Three Variables Suffice for Real-Time Logic

  • Timos AntonopoulosEmail author
  • Paul Hunter
  • Shahab Raza
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)

Abstract

A natural framework for real-time specification is monadic first-order logic over the structure (ℝ, < , + 1)—the ordered real line with unary + 1 function. Our main result is that (ℝ, < , + 1) has the 3-variable property: every monadic first-order formula with at most 3 free variables is equivalent over this structure to one that uses 3 variables in total. As a corollary we obtain also the 3-variable property for the structure (ℝ, < ,f) for any fixed linear function f:ℝ → ℝ. On the other hand, we exhibit a countable dense linear order (E, < ) and a bijection f:E → E such that (E, < ,f) does not have the k-variable property for any k.

Keywords

Induction Hypothesis Linear Order Temporal Logic Atomic Formula 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 2015

Authors and Affiliations

  • Timos Antonopoulos
    • 1
    Email author
  • Paul Hunter
    • 2
  • Shahab Raza
    • 1
  • James Worrell
    • 1
  1. 1.Department of Computer ScienceOxford UniversityOxfordUK
  2. 2.Département d’InformatiqueUniversité Libre de BruxellesBruxellesBelgium

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