### 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

### License

BSD License

### Topics

- Computer science/Automata and formal languages

### Session LTL_Master_Theorem

- Syntactic_Fragments_and_Stability
- After
- Advice
- Master_Theorem
- Asymmetric_Master_Theorem
- Restricted_Master_Theorem
- Transition_Functions
- Quotient_Type
- Omega_Words_Fun_Stream
- DRA_Construction
- DRA_Implementation
- Extra_Equivalence_Relations
- DRA_Instantiation
- Code_Export

### Depends on

- Deriving class instances for datatypes
- Linear Temporal Logic
- Transition Systems and Automata

### Used by

- An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation

### Auto-related entries

- Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic
- Formalization of Refinement Calculus for Reactive Systems

## Cite

×

LTL_Master_Theorem-AFP

    @article{LTL_Master_Theorem-AFP,
      author  = {Benedikt Seidl and Salomon Sickert},
      title   = {A Compositional and Unified Translation of LTL into ω-Automata},
      journal = {Archive of Formal Proofs},
      month   = {April},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/LTL_Master_Theorem.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 20, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Apr 17, 2019 : Isabelle2018