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

@article{EsparzaJavier2020AUT,
title={A Unified Translation of Linear Temporal Logic to $\omega$-Automata},
author={EsparzaJavier and Křet{\'i}nsk{\'y}Jan and SickertSalomon},
journal={Journal of the ACM},
year={2020},
volume={67},
pages={1-61}
}
• Published 17 October 2020
• Computer Science
• Journal of the ACM
We present a unified translation of LTL formulas into nondeterministic Buchi automata, limit-deterministic Buchi automata (LDBA), and deterministic Rabin automata (DRA). 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 languages that can be translated…
2 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.

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

Evidence is given that this theoretical clean and compositional approach does not lead to large automata per se and in fact in the case of DRAs yields significantly smaller automata compared to the previously known approach using determinisation of NBAs.

## References

SHOWING 1-10 OF 57 REFERENCES

### 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.

### 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.

### 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.

### Efficient Büchi Automata from LTL Formulae

• Computer Science
CAV
• 2000
We present an algorithm to generate small Buchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure,

### Rabinizer: Small Deterministic Automata for LTL(F, G)

• Computer Science
ATVA
• 2012
We present Rabinizer, a tool for translating formulae of the fragment of linear temporal logic with the operators F (eventually) and G (globally) into deterministic Rabin automata. Contrary to tools

### Effective Translation of LTL to Deterministic Rabin Automata: Beyond the (F, G)-Fragment

• Computer Science
ATVA
• 2013
This work presents a new translation to deterministic Rabin automata via alternating automata and deterministic transition-based generalized RabinAutomata that can produce significantly smaller automata compared to Rabinizer and ltl2dstar.

### From LTL to Deterministic Automata: A Safraless Compositional Approach

• Computer Science
CAV
• 2014
We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula i¾?. The automaton is the product of a master automaton and an array of slave automata, one

### 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.

### 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.

### 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.