On the freeze quantifier in Constraint LTL: decidability and complexity Stephane Demri, Ranko Lazic, and David Nowak   View Paper (PDF)   Return to Temporal Logic in Computer Science 1 Abstract Constraint LTL, a generalization of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints. The freeze quantifier can be part of the language, as in some real-time logics, but this variable-binding mechanism is quite general and ubiquitous in many logical languages (first-order temporal logics, hybrid logics, logics for sequence diagrams, navigation logics, etc.). We show that Constraint LTL over the simple domain (N,=) augmented with the freeze operator is undecidable which is a surprising result regarding the poor language for constraints (only equality tests). Many versions of freeze-free Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes sum _1^1 -completeness. On the positive side, we provide complexity results when the domain is finite (EXPSPACE-completeness) or when the formulae are flat in a sense introduced in the paper. ©2006 Association for Computing Machinery