2022/05/10 by Kozachinskiy, Alexander · 1 citation
#Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2205.04508
Kopczyński (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.