# A Unified Translation of Linear Temporal Logic to ω-Automata

@article{Sickert2019AUT,
title={A Unified Translation of Linear Temporal Logic to $\omega$-Automata},
author={Salomon Sickert},
journal={Journal of the ACM (JACM)},
year={2019},
volume={67},
pages={1 - 61}
}
• Salomon Sickert
• Published 17 October 2020
• Computer Science
• Journal of the ACM (JACM)
We present a unified translation of linear temporal logic (LTL) formulas into deterministic Rabin automata (DRA), limit-deterministic Büchi automata (LDBA), and nondeterministic Büchi automata (NBA). The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive Boolean combination of…
7 Citations
An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata
• Mathematics
LICS
• 2020
This work presents a direct and purely syntactic normalisation procedure for LTL yielding a normal form, comparable to the one by Chang, Manna, and Pnueli, that has only a single exponential blow-up.
Almost-Symbolic Synthesis via ∆2-Normalisation for Linear Temporal Logic
• Computer Science
• 2022
An almost-symbolic version of this classic idea that performs the following steps: normalisation of the specification into a Boolean combination of “simple” fragment of LTL, translation of each “ simple” subformula into a deterministic automaton, encoding of each automaton into a binary decision diagram (BDD), and construction of a parity automaton by operations on the BDD.
Practical Applications of the Alternating Cycle Decomposition
• Computer Science
TACAS
• 2022
The first practical implementation of the Alternating Cycle Decomposition in two different tools, Owl and Spot, is presented, and it is shown how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for ω-automata.
Divide-and-Conquer Determinization of Büchi Automata based on SCC Decomposition
• Computer Science
ArXiv
• 2022
This work classify the strongly connected components of the given NBA as inherently weak, deterministic accepting, and nondeterministic accepting; this results in an easier handling of the determinization algorithm that takes advantage of the structure of that SCC.
Modernising Strix
• Computer Science
• 2022
The architectural changes applied to Strix, a tool for LTL reactive synthesis, that were made in preparation for SYNTCOMP 2021 are described and a new parity game solving algorithm is made use of.
LTL-Constrained Steady-State Policy Synthesis
A unified solution reducing the multi-type specification to a multi-dimensional long-run average reward for Markov decision processes (MDP) is provided, enabled by Limit-Deterministic Büchi Automata (LDBA) and allows for an elegant solution through a simple linear programme.
The Reactive Synthesis Competition (SYNTCOMP): 2018-2021
• Computer Science
ArXiv
• 2022
The evaluation scheme and the experimental setup of SYNTCOMP are described and the results of the experimental evaluations are presented, including a ranking of tools with respect to quantity and quality of solutions.

## References

SHOWING 1-10 OF 119 REFERENCES
A Unified Translation of Linear Temporal Logic to ω-Automata
• Computer Science
• 2020
A unified translation of LTL formulas into nondeterministic Buchi automata, limit-deterministic LTL automata (LDBA), and deterministic Rabin Automata (DRA) is presented.
One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata
• Computer Science
LICS
• 2018
A unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic Büchi Automata, and nondeterministicBüchi automata derived from one single Master Theorem of purely logical nature is presented.
A Verified and Compositional Translation of LTL to Deterministic Rabin Automata
• Computer Science
ITP
• 2019
This work develops a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the “simple” languages and extracts from this particular instantiation an executable tool translating LTL to DRAs.
Deterministic Automata for the (F,G)-fragment of LTL
• Computer Science
CAV
• 2012
This work presents a direct translation of the ( F, G )-fragment of LTL into deterministic ω-automata with no determinization procedure involved and investigates the complexity of this translation and provides experimental results and compare them to the traditional method.
From LTL and Limit-Deterministic Büchi Automata to Deterministic Parity Automata
• Computer Science
TACAS
• 2017
This paper describes a single exponential translation from limit-deterministic Buchi automata (LDBA) to DPA, and shows that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, “Safraless” LTL-to-DPA construction.
LTL to Büchi Automata Translation: Fast and More Deterministic
• Computer Science
TACAS
• 2012
Improvements in the algorithm are introduced by Gastin and Oddoux translating LTL formulae into Buchi automata via very weak alternating co-BuchiAutomata and generalized Buchi Automata based on specific properties of any formula.
LTL to Deterministic Emerson-Lei Automata
• Computer Science
GandALF
• 2017
A new translation from linear temporal logic to deterministic Emerson-Lei automata with a Muller acceptance condition symbolically expressed as a Boolean formula is introduced, which is an enhanced product construction that exploits knowledge of its components to reduce the number of states.
Automata with Generalized Rabin Pairs for Probabilistic Model Checking and LTL Synthesis
• Computer Science
CAV
• 2013
This work considers deterministic automata with acceptance condition given as disjunction of generalized Rabin pairs (DGRW) as an alternative to DRW, and presents algorithms for probabilistic model-checking as well as game solving for DGRW conditions.
Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata
This procedure computes simulation relations for alternating Buchi automata in an early stage and uses them in an on the-fly fashion to decrease the time and space consumption without sacrificing the potential of simulation relations.
Improving Automata Generation for Linear Temporal Logic by Considering the Automaton Hierarchy
It is shown how large parts of the formulas can be translated to the simpler logic CTL, which accelerates the LTL model checking by orders of magnitude which is shown by experimental results.