Winning Sets of Regular Languages: Descriptional and Computational Complexity
Formal Languages and Automata Theory
2021-05-04 v1
Abstract
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target language. The turn orders that result in a win for Alice form a binary language that is regular whenever the target language is, and we prove some upper and lower bounds for its state complexity based on that of the target language. We also consider the computational complexity of membership and intersection problems of winning sets.
Cite
@article{arxiv.2105.00452,
title = {Winning Sets of Regular Languages: Descriptional and Computational Complexity},
author = {Pierre Marcus and Ilkka Törmä},
journal= {arXiv preprint arXiv:2105.00452},
year = {2021}
}
Comments
24 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:2004.13668