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A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

Authors Julian Brunner , Benedikt Seidl , Salomon Sickert

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Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Interactive proof systems
Keywords
  • Automata Theory
  • Automata over Infinite Words
  • Deterministic Automata
  • Linear Temporal Logic
  • Model Checking
  • Verified Algorithms

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Abstract

We present a formalisation of the unified translation approach from linear temporal logic (LTL) to omega-automata from [Javier Esparza et al., 2018]. This approach decomposes LTL formulas into "simple" languages and allows a clear separation of concerns: first, we formalise the purely logical result yielding this decomposition; second, we develop a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the "simple" languages; third, we instantiate this generic theory to obtain a construction for deterministic Rabin automata (DRA). We extract from this particular instantiation an executable tool translating LTL to DRAs. To the best of our knowledge this is the first verified translation of LTL to DRAs that is proven to be double-exponential in the worst case which asymptotically matches the known lower bound.

Cite As Get BibTex

Julian Brunner, Benedikt Seidl, and Salomon Sickert. A Verified and Compositional Translation of LTL to Deterministic Rabin Automata. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ITP.2019.11

Author Details

Julian Brunner
  • Technische Universität München, Germany
Benedikt Seidl
  • Technische Universität München, Germany
Salomon Sickert
  • Technische Universität München, Germany

Funding

This work was partially funded and supported by the German Research Foundation (DFG) project "Verified Model Checkers" (317422601).

Acknowledgements

The authors want to thank Manuel Eberl, Javier Esparza, Lars Hupel, Peter Lammich, and Tobias Nipkow for their helpful comments and technical expertise.

Supplementary Materials

  • The described Isabelle/HOL development is archived in the "Archive of Formal Proofs" and is split into the entries [Julian Brunner, 2017] and [Benedikt Seidl and Salomon Sickert, 2019].

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