Abstract
We consider the safety fragment of linear temporal logic with the freeze quantifier. The freeze quantifier is used to store a value from an infinite domain in a register for later comparison with other such values. We show that, for one register, satisfiability, refinement and model checking problems are decidable. The main result in the paper is that satisfiability is ExpSpace-complete. The proof of ExpSpace-membership involves a translation to a new class of faulty counter automata. We also show that refinement and model checking are not primitive recursive, and that dropping the safety restriction, adding past-time temporal operators, or adding one more register, each cause undecidability of all three decision problems.
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Lazić, R. (2006). Safely Freezing LTL. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_35
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DOI: https://doi.org/10.1007/11944836_35
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