License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2019.11
URN: urn:nbn:de:0030-drops-110664
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11066/
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Brunner, Julian ; Seidl, Benedikt ; Sickert, Salomon

A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

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LIPIcs-ITP-2019-11.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{brunner_et_al:LIPIcs:2019:11066,
  author =	{Julian Brunner and Benedikt Seidl and Salomon Sickert},
  title =	{{A Verified and Compositional Translation of LTL to Deterministic Rabin Automata}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{John Harrison and John O'Leary and Andrew Tolmach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11066},
  URN =		{urn:nbn:de:0030-drops-110664},
  doi =		{10.4230/LIPIcs.ITP.2019.11},
  annote =	{Keywords: Automata Theory, Automata over Infinite Words, Deterministic Automata, Linear Temporal Logic, Model Checking, Verified Algorithms}
}

Keywords: Automata Theory, Automata over Infinite Words, Deterministic Automata, Linear Temporal Logic, Model Checking, Verified Algorithms
Collection: 10th International Conference on Interactive Theorem Proving (ITP 2019)
Issue Date: 2019
Date of publication: 05.09.2019
Supplementary Material: 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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