Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-memory strategies in two-player infinite games   We study infinite two-player win/lose games $(A,B,W)$ where $A,B$ are finite
and $W \subseteq (A \times B)^\omega$. At each round Player 1 and Player 2
concurrently choose one action in $A$ and $B$, respectively. Player 1 wins iff
the generated sequence is in $W$. Each history $h \in (A \times B)^*$ induces a
game $(A,B,W_h)$ with $W_h := \{\rho \in (A \times B)^\omega \mid h \rho \in
W\}$. We show the following: if $W$ is in $\Delta^0_2$ (for the usual
topology), if the inclusion relation induces a well partial order on the
$W_h$'s, and if Player 1 has a winning strategy, then she has a finite-memory
winning strategy. Our proof relies on inductive descriptions of set complexity,
such as the Hausdorff difference hierarchy of the open sets.
  Examples in $\Sigma^0_2$ and $\Pi^0_2$ show some tightness of our result. Our
result can be translated to games on finite graphs: e.g. finite-memory
determinacy of multi-energy games is a direct corollary, whereas it does not
follow from recent general results on finite memory strategies.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph