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Regular Linear Temporal Logic with Past

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5944))

Abstract

This paper upgrades Regular Linear Temporal Logic (RLTL) with past operators and complementation. RLTL is a temporal logic that extends the expressive power of linear temporal logic (LTL) to all ω-regular languages. The syntax of RLTL consists of an algebraic signature from which expressions are built. In particular, RLTL does not need or expose fix-point binders (like linear time μ-calculus), or automata to build and instantiate operators (like \({\textrm{ETL}_*}\)).

Past operators are easily introduced in RLTL via a single previous-step operator for basic state formulas. The satisfiability and model checking problems for RLTL are PSPACE-complete, which is optimal for extensions of LTL. This result is shown using a novel linear size translation of RLTL expressions into 2-way alternating parity automata on words. Unlike previous automata-theoretic approaches to LTL, this construction is compositional (bottom-up). As alternating parity automata can easily be complemented, the treatment of negation is simple and does not require an upfront transformation of formulas into any normal form.

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Sánchez, C., Leucker, M. (2010). Regular Linear Temporal Logic with Past. In: Barthe, G., Hermenegildo, M. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2010. Lecture Notes in Computer Science, vol 5944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11319-2_22

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  • DOI: https://doi.org/10.1007/978-3-642-11319-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11318-5

  • Online ISBN: 978-3-642-11319-2

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