Nesting Until and Since in Linear Temporal Logic

  • Denis Thérien
  • Thomas Wilke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2285)


We provide an effective characterization of the “until-since hierarchy” of linear temporal logic, that is, we show how to compute for a given temporal property the minimal nesting depth in “until” and “since” required to express it. This settles the most prominent classi- fication problem for linear temporal logic. Our characterization of the individual levels of the “until-since hierarchy” is algebraic: for each n, we present a decidable class of finite semigroups and show that a temporal property is expressible with nesting depth at most n if and only if the syntactic semigroup of the formal language associated with the property belongs to the class provided. The core of our algebraic characterization is a new description of substitution in linear temporal logic in terms of block products of finite semigroups.


Temporal Logic Wreath Product Linear Temporal Logic Propositional Variable Semigroup Variety 
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 2002

Authors and Affiliations

  • Denis Thérien
    • 1
  • Thomas Wilke
    • 2
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada
  2. 2.Computer Science DepartmentCAUKielGermany

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