# Deterministic Automata for the (F,G)-fragment of LTL

@article{Ketnsk2012DeterministicAF, title={Deterministic Automata for the (F,G)-fragment of LTL}, author={Jan Křet{\'i}nsk{\'y} and Javier Esparza}, journal={ArXiv}, year={2012}, volume={abs/1204.5057} }

When dealing with linear temporal logic properties in the setting of e.g. games or probabilistic systems, one often needs to express them as deterministic omega-automata. In order to translate LTL to deterministic omega-automata, the traditional approach first translates the formula to a non-deterministic Buchi automaton. Then a determinization procedure such as of Safra is performed yielding a deterministic ω-automaton. We present a direct translation of the ( F , G )-fragment of LTL into…

## 52 Citations

Small Deterministic Automata for LTL\GU

- Computer Science
- 2013

A tool that generates automata for LTL U does not occur in any G-formula (but F still can) and is significantly smaller than deterministic Rabin automata generated by state-of-the-art tools.

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

- Computer ScienceATVA
- 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…

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.

Limit Deterministic and Probabilistic Automata for LTL ∖ GU

- Computer Science, MathematicsTACAS
- 2015

LTL i¾? GU is a fragment of linear temporal logic LTL, where negations appear only on propositions, and formulas are built using the temporal operators X next, F eventually, G always, and U until,…

Rabinizer 3: Safraless Translation of LTL to Small Deterministic Automata

- Computer ScienceATVA
- 2014

This paper presents a tool for translating LTL formulae into deterministic ω-automata, the first tool that covers the whole LTL that does not use Safra’s determinization or any of its variants, and shows that this leads to significant speed-up of probabilistic LTL model checking, especially with the generalized Rabin automata.

Probabilistic Büchi Automata for LTL\GU

- Computer Science
- 2015

This work construction is a new, improved EXPTIME model checking algorithm for Markov Decision Processes and LTL\GU formulae that is exponential in the size of the formula.

Automata with Generalized Rabin Pairs for Probabilistic Model Checking and LTL Synthesis

- Computer ScienceCAV
- 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.

Rabinizer 4: From LTL to Your Favourite Deterministic Automaton

- Computer ScienceCAV
- 2018

Rabinizer 4 is presented, a tool set for translating formulae of linear temporal logic to different types of deterministic \(\omega \)-automata and enhancements both in terms of the size of the automata and the computational time are shown, due to algorithmic as well as implementation improvements.

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 ScienceLICS
- 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.

## References

SHOWING 1-10 OF 30 REFERENCES

From LTL to Symbolically Represented Deterministic Automata

- Computer ScienceVMCAI
- 2008

This paper generates symbolic descriptions of equivalent deterministic parity automata which was so far not possible for full LTL, using a new determinization procedure for ω-automata that stem from LTL formulas.

On-the-Fly Stuttering in the Construction of Deterministic omega -Automata

- Computer Science, LinguisticsCIAA
- 2007

The notion of partial stutter insensitiveness is introduced and the construction of deterministic ω-automata is applied only on the subset of symbols for which stuttering is allowed, to reduce the size of the generated automaton.

On-the-Fly Stuttering in the Construction of Deterministic ω-Automata

- Linguistics, Computer Science
- 2007

The notion of partial stutter insensitiveness is introduced and the construction of potentially smaller deterministic ω-automata for such a property, e.g. using Safra’s determinization construction, is proposed.

The Blowup in Translating LTL to Deterministic Automata

- Computer ScienceMoChArt
- 2010

The problem of the exact blow-up of the translation of LTL formulas to nondeterministic automata is solved and the lower bound for the translation is tightened to 22Ω(n).

Efficient Büchi Automata from LTL Formulae

- Computer ScienceCAV
- 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,…

Experiments with deterministic omega-automata for formulas of linear temporal logic

- Computer ScienceTheor. Comput. Sci.
- 2006

On the complexity of omega -automata

- Computer Science[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
- 1988

The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case, and can be used to obtain an improved complementation construction for Buchi automata that is essentially optimal.

Deterministic generators and games for Ltl fragments

- Computer Science, MathematicsTOCL
- 2004

This paper identifies LTL fragments of lower complexity and shows tightness of the double-exponential bound on the size as well as the longest distance for deterministic generators for LTL, even in the absence of "next" and "until" modalities.

Optimizations for LTL Synthesis

- Computer Science2006 Formal Methods in Computer Aided Design
- 2006

This work constitutes the first implementation of a synthesis algorithm for full LTL by careful optimization of all intermediate automata, and uses an incremental algorithm to compute the emptiness of nondeterministic Buchi tree automata.

Fast LTL to Büchi Automata Translation

- Computer ScienceCAV
- 2001

An algorithm to generate Buchi automata from LTL formulae is presented and compared with Spin: the experiments show that the algorithm is much more efficient than Spin.