Technical Reports

The report FIMU-RS-2002-03

The Stuttering Principle Revisited: On the Expressiveness of Nested X and U Operators in the Logic LTL

by Antonín Kuèera, Jan Strejèek, A full version of the paper presented at CSL`02. July 2002, 24 pages.

FIMU-RS-2002-03. Available as Postscript, PDF.

Abstract:

It is known that LTL formulae without the `next` operator are invariant under the so-called stutter-equivalence of words. In this paper we extend this principle to general LTL formulae with given nesting depths of the `next` and `until` operators. This allows us to prove the semantical strictness of three natural hierarchies of LTL formulae, which are parametrized either by the nesting depth of just one of the two operators, or by both of them. As another interesting corollary we obtain an alternative characterization of LTL languages, which are exactly the regular languages closed under the generalized form of stutter equivalence. We also indicate how to tackle the state-space explosion problem with the help of presented results.