Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strategy Complexity of Reachability in Countable Stochastic 2-Player
  Games   We study countably infinite stochastic 2-player games with reachability
objectives. Our results provide a complete picture of the memory requirements
of $\varepsilon$-optimal (resp. optimal) strategies. These results depend on
whether the game graph is infinitely branching and on whether one requires
strategies that are uniform (i.e., independent of the start state). Our main
result is that $\varepsilon$-optimal (resp. optimal) Maximizer strategies in
infinitely branching turn-based reachability games require infinite memory.
This holds even under very strong restrictions. Even if all states have an
almost surely winning Maximizer strategy, strategies with a step counter plus
finite private memory are still useless. Regarding uniformity, we show that for
Maximizer there need not exist positional uniformly $\varepsilon$-optimal
strategies even in finitely branching turn-based games, whereas there always
exists one that uses one bit of public memory, even in concurrent games with
finite action sets.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc