The Stuttering Principle Revisited: On the Expressiveness of Nested X and U Operators in the Logic LTL
by
Antonín Kučera,
Jan Strejček,
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.