# Determinising Parity Automata

@article{Schewe2014DeterminisingPA, title={Determinising Parity Automata}, author={Sven Schewe and Thomas Varghese}, journal={ArXiv}, year={2014}, volume={abs/1401.5394} }

Parity word automata and their determinisation play an important role in automata and game theory. We discuss a determinisation procedure for nondeterministic parity automata through deterministic Rabin to deterministic parity automata. We prove that the intermediate determinisation to Rabin automata is optimal. We show that the resulting determinisation to parity automata is optimal up to a small constant. Moreover, the lower bound refers to the more liberal Streett acceptance. We thus show…

## 19 Citations

### Tight Bounds for Complementing Parity Automata

- Computer ScienceMFCS
- 2014

A complementation procedure is established from transition labelled parity automata to transition labelled nondeterministic Buchi automata and it is proved to be tight up to an O(n) factor, where n is the size of the nondetergetic parity automaton.

### Approximate Automata for Omega-Regular Languages

- Computer ScienceATVA
- 2019

This work states that some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic \(\omega \)-automata, but properties cannot always be represented by automata with the desired acceptance condition and determinism.

### Parity and generalised Büchi automata : determinisation and complementation

- Computer Science
- 2014

A tight determinisation procedure for Buchi automata, which uses a simplification of Safra trees called history trees, and suitable data structures for the complementation procedures based on the data structure used for determinisation.

### Optimal transformations of Muller conditions

- Computer ScienceArXiv
- 2020

The alternating cycle decomposition transformation is introduced, and a strong optimality result is proved: for any given deterministic Muller automaton, the obtained parity automaton is minimal both in size and number of priorities among those automata admitting a morphism into the original Muller Automaton.

### Deterministic and game separability for regular languages of infinite trees

- MathematicsICALP
- 2021

It is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp.

### Optimal Transformations of Games and Automata Using Muller Conditions

- Computer ScienceICALP
- 2021

A new transformation is defined called the alternating cycle decomposition, inspired and extending Zielonka’s construction, which operates on transition systems, encompassing both automata and games, and preserves semantic properties through the existence of a locally bijective morphism.

### On Succinctness and Recognisability of Alternating Good-for-Games Automata

- Computer ScienceArXiv
- 2020

The complexity of deciding "half-GFGness", a property specific to alternating automata that only requires nondeterministic choices to be resolved in an online manner, is studied, and it is shown that this problem is strictly more difficult than GFGness check.

### Permutation Games for the Weakly Aconjunctive mu-Calculus

- Computer ScienceTACAS
- 2018

By showing that limit-deterministic parity automata can be used to recognize unsuccessful branches in pre-tableaux for the weakly aconjunctive $\mu$-calculus, satisfiability games of size $n$ with $\mathcal{O}(nk)$ priorities with alternation-depth $k$ are obtained.

### A Survey on Satisfiability Checking for the μ-Calculus through Tree Automata

- Computer ScienceArXiv
- 2022

This work views the non-emptiness checking of alternating tree automata by a reduction to solving parity games of a certain structure, so-called emptiness games, and shows how the construction of the emptiness games combines a (ﬁxed) structural part with (history-)determinization of parity word automata.

### On the (In)Succinctness of Muller Automata

- Computer ScienceCSL
- 2017

There is inconsistency and incompleteness in the literature results regarding the translations to and from Muller automata, and the Muller type can be considered less succinct than parity, Rabin, and Streett automata.

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