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… 

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References

SHOWING 1-10 OF 42 REFERENCES

LTL to Büchi Automata Translation: Fast and More Deterministic

TLDR
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.

Efficient Büchi Automata from LTL Formulae

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,

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

TLDR
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 to Deterministic Automata: A Safraless Compositional Approach

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

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

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

TLDR
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.

Rabinizer 3: Safraless Translation of LTL to Small Deterministic Automata

TLDR
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.

Fast LTL to Büchi Automata Translation

TLDR
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.

Limit Deterministic and Probabilistic Automata for LTL ∖ GU

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,

Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata

TLDR
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.