An expressively complete linear time temporal logic for Mazurkiewicz traces

  • Authors:

  • P. S. Thiagarajan;I. Walukiewicz

  • Affiliations:

  • SPIC Mathematical Institute, 92 G. N. Chetty Road, T. Nagar, Chennai-600 017, India;Institute of Informatics, Warsaw University, Banacha 2, 02-096 Warsaw, Poland

  • Venue:
  • Information and Computation - Special issue: LICS'97
  • Year:
  • 2002

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Abstract

A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTL-specifications.We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also constitutes a characterisation of the so-called trace consistent (robust) LTL-specifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisadons of the same trace and hence are amenable to partial order reduction methods.