A Compositional and Unified Translation of LTL into ω-Automata


Title: A Compositional and Unified Translation of LTL into ω-Automata
Authors: Benedikt Seidl (benedikt /dot/ seidl /at/ tum /dot/ de) and Salomon Sickert (s /dot/ sickert /at/ tum /dot/ de)
Submission date: 2019-04-16
Abstract: We present a formalisation of the unified translation approach of linear temporal logic (LTL) into ω-automata from [1]. 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 instantiate this generic theory to obtain a construction for deterministic (state-based) 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 from LTL to DRAs that is proven to be double exponential in the worst case which asymptotically matches the known lower bound.

[1] Javier Esparza, Jan Kretínský, Salomon Sickert. One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata. LICS 2018

  author  = {Benedikt Seidl and Salomon Sickert},
  title   = {A Compositional and Unified Translation of LTL into ω-Automata},
  journal = {Archive of Formal Proofs},
  month   = apr,
  year    = 2019,
  note    = {\url{https://isa-afp.org/entries/LTL_Master_Theorem.html},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Deriving, LTL, Transition_Systems_and_Automata
Used by: LTL_Normal_Form
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.