Stuttering Equivalence Formalized in Isabelle/HOL

Stephan Merz

Abstract

Two omega-sequences are stuttering equivalent if they differ only by finite repetitions of elements. Stuttering equivalence is a fundamental concept in the theory of concurrent and distributed systems. Notably, Lamport argues that refinement notions for such systems should be insensitive to finite stuttering. Peled and Wilke show that all LTL (linear-time temporal logic) properties that are insensitive to stuttering equivalence can be expressed without the next-time operator. Stuttering equivalence is also important for certain verification techniques such as partial-order reduction for model checking.

We formalize stuttering equivalence in Isabelle/HOL. Our development relies on the notion of a stuttering sampling function that identifies blocks of identical sequence elements.

Archive of Formal Proofs, May 2012

Available as: [PDF | HTML | sources]

Reference

@InProceedings{merz:stuttering-equivalence,
  author =       {Stephan Merz},
  title =        {Stuttering Equivalence},
  journal =  {Archive of Formal Proofs},
  month =    may,
  year =     2012,
  note =     {\url{http://afp.sf.net/entries/Stuttering_Equivalence.shtml}, Formal proof development},
  ISSN =     {2150-914x},
}