Energy Games over Totally Ordered Groups
Group Theory
2022-08-17 v2 Computer Science and Game Theory
Combinatorics
Abstract
Kopczy\'{n}ski (ICALP 2006) conjectured that prefix-independent half-positional winning conditions are closed under finite unions. We refute this conjecture over finite arenas. For that, we introduce a new class of prefix-independent bi-positional winning conditions called energy conditions over totally ordered groups. We give an example of two such conditions whose union is not half-positional. We also conjecture that every prefix-independent bi-positional winning condition coincides with some energy condition over a totally ordered group on periodic sequences.
Keywords
Cite
@article{arxiv.2205.04508,
title = {Energy Games over Totally Ordered Groups},
author = {Alexander Kozachinskiy},
journal= {arXiv preprint arXiv:2205.04508},
year = {2022}
}
Comments
12 pages. v2 minor changes