Efficient Parallel Path Checking for Linear-Time Temporal Logic With Past and Bounds

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Lars Kuhtz, Bernd Finkbeiner

Published: 2012, Last Modified: 26 Jan 2026Log. Methods Comput. Sci. 2012EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Path checking, the special case of the model checking problem where the model under consideration is a single path, plays an important role in monitoring, testing, and verification. We prove that for linear-time temporal logic (LTL), path checking can be efficiently parallelized. In addition to the core logic, we consider the extensions of LTL with bounded-future (BLTL) and past-time (LTL+Past) operators. Even though both extensions improve the succinctness of the logic exponentially, path checking remains efficiently parallelizable: Our algorithm for LTL, LTL+Past, and BLTL+Past is in AC^1(logDCFL) \subseteq NC.