Model checking
An Until hierarchy and other applications of an Ehrenfeucht-Fraïssé game for temporal logic
Information and Computation - Special issue: LICS 1996—Part 1
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Classifying discrete temporal properties
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Invariance Under Stuttering in a Temporal Logic without the "Until" Operator
Fundamenta Informaticae
Characteristic patterns for LTL
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Invariance Under Stuttering in a Temporal Logic without the "Until" Operator
Fundamenta Informaticae
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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.