# One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata

@article{Esparza2018OneTT, title={One Theorem to Rule Them All: A Unified Translation of LTL into $\omega$-Automata}, author={Javier Esparza and Jan Křet{\'i}nsk{\'y} and Salomon Sickert}, journal={Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science}, year={2018} }

We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic Büchi automata, and nondeterministic Büchi automata. 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 into…

## 24 Citations

### 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.

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

- Computer ScienceJ. ACM
- 2019

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.

### A Compositional and Unified Translation of LTL into ω-Automata

- Computer ScienceArch. Formal Proofs
- 2019

This approach decomposes LTL formulas into simple languages and allows a clear separation of concerns, and instantiates this generic theory to obtain a construction for deterministic (state-based) Rabin automata (DRA).

### A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

- Computer ScienceITP
- 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.

### From linear temporal logic and limit-deterministic Büchi automata to deterministic parity automata

- Computer ScienceInt. J. Softw. Tools Technol. Transf.
- 2022

A single exponential translation from limit-deterministic Büchi automata (LDBA) to DPA is described and it is shown that it can be concatenated with a recent efficient translations from LTL to LDBA to yield a double exponential, ‘Safraless’ LTL-to-DPA construction.

### Seminator 2 Can Complement Generalized Büchi Automata via Improved Semi-determinization

- Computer ScienceCAV
- 2020

The second generation of the tool Seminator that transforms transition-based generalized Büchi automata (TGBAs) into equivalent semi-deterministic automata is presented, providing a new way to complement automata that is competitive with state-of-the-art complementation tools.

### An Efficient Normalisation Procedure for Linear Temporal Logic and Very Weak Alternating Automata

- MathematicsLICS
- 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.

### From Emerson-Lei automata to deterministic, limit-deterministic or good-for-MDP automata

- Computer ScienceInnov. Syst. Softw. Eng.
- 2022

A new determinization construction is introduced which determinizes several GBA separately and combines them using a product construction, and one version of the limit-determinization procedure yields good-for-MDP automata which can be used for quantitative probabilistic model checking.

### Owl: A Library for ω-Words, Automata, and LTL

- Computer ScienceATVA
- 2018

The library Owl is presented, which forms a backbone of several translations from LTL to automata and related tools by different authors and is apt for easy prototyping of new tools in this area.

### Determinization and Limit-determinization of Emerson-Lei automata

- Computer ScienceATVA
- 2021

This work introduces three new ways of translating TELA to GBA and gives a new determinization construction which determinizes several GBA separately and combines them using a product construction, which is competitive when compared with state-of-the-art determinization procedures.

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