# Computing the Width of Non-deterministic Automata

@article{Kuperberg2019ComputingTW, title={Computing the Width of Non-deterministic Automata}, author={Denis Kuperberg and Anirban Majumdar}, journal={ArXiv}, year={2019}, volume={abs/1811.00483} }

We introduce a measure called width, quantifying the amount of nondeterminism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input. We describe an incremental determinisation construction on NFAs, which can be more efficient than the full powerset determinisation, depending on the width of the input NFA. This construction can be generalised to infinite words, and…

## 4 Citations

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.

Between Deterministic and Nondeterministic Quantitative Automata

- Computer Science
- 2022

The possible generalization of such notions from Boolean to quantitative automata is analyzed, and it is suggested that it depends on the following key characteristics of the considered notion N– whether it is syntactic or semantic, and if semantic,Whether it is word-based or language-based.

On the Succinctness of Alternating Parity Good-for-Games Automata

- Computer ScienceFSTTCS
- 2020

This work presents a single exponential determinisation procedure and an Exptime upper bound to the problem of recognising whether an alternating automaton is GFG, and studies the complexity of deciding "half-GFGness", a property specific to alternating automata that only requires nondeterministic choices to be resolved in an online manner.

A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct

- Computer ScienceMFCS
- 2021

It is proved that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL) and this class is orthogonal to unambiguous CFL.

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