The Power of Counting Steps in Quantitative Games
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910500710776832 |
|---|---|
| author | Bose, Sougata Ibsen-Jensen, Rasmus Purser, David Totzke, Patrick Vandenhove, Pierre |
| author_facet | Bose, Sougata Ibsen-Jensen, Rasmus Purser, David Totzke, Patrick Vandenhove, Pierre |
| contents | We study deterministic games of infinite duration played on graphs and focus on the strategy complexity of quantitative objectives. Such games are known to admit optimal memoryless strategies over finite graphs, but require infinite-memory strategies in general over infinite graphs.
We provide new lower and upper bounds for the strategy complexity of mean-payoff and total-payoff objectives over infinite graphs, focusing on whether step-counter strategies (sometimes called Markov strategies) suffice to implement winning strategies. In particular, we show that over finitely branching arenas, three variants of limsup mean-payoff and total-payoff objectives admit winning strategies that are based either on a step counter or on a step counter and an additional bit of memory. Conversely, we show that for certain liminf total-payoff objectives, strategies resorting to a step counter and finite memory are not sufficient. For step-counter strategies, this settles the case of all classical quantitative objectives up to the second level of the Borel hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Power of Counting Steps in Quantitative Games Bose, Sougata Ibsen-Jensen, Rasmus Purser, David Totzke, Patrick Vandenhove, Pierre Computer Science and Game Theory Formal Languages and Automata Theory Logic in Computer Science We study deterministic games of infinite duration played on graphs and focus on the strategy complexity of quantitative objectives. Such games are known to admit optimal memoryless strategies over finite graphs, but require infinite-memory strategies in general over infinite graphs. We provide new lower and upper bounds for the strategy complexity of mean-payoff and total-payoff objectives over infinite graphs, focusing on whether step-counter strategies (sometimes called Markov strategies) suffice to implement winning strategies. In particular, we show that over finitely branching arenas, three variants of limsup mean-payoff and total-payoff objectives admit winning strategies that are based either on a step counter or on a step counter and an additional bit of memory. Conversely, we show that for certain liminf total-payoff objectives, strategies resorting to a step counter and finite memory are not sufficient. For step-counter strategies, this settles the case of all classical quantitative objectives up to the second level of the Borel hierarchy. |
| title | The Power of Counting Steps in Quantitative Games |
| topic | Computer Science and Game Theory Formal Languages and Automata Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2406.17482 |