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Energy Games over Totally Ordered Groups

Author Alexander Kozachinskiy

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Alexander Kozachinskiy
  • IMFD Chile & CENIA Chile, Santiago, Chile

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Alexander Kozachinskiy. Energy Games over Totally Ordered Groups. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 34:1-34:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Games on graphs
  • half-positionality
  • ordered groups


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