Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Universal Attractor Decomposition Algorithm for Parity Games   An attractor decomposition meta-algorithm for solving parity games is given
that generalizes the classic McNaughton-Zielonka algorithm and its recent
quasi-polynomial variants due to Parys (2019), and to Lehtinen, Schewe, and
Wojtczak (2019). The central concepts studied and exploited are attractor
decompositions of dominia in parity games and the ordered trees that describe
the inductive structure of attractor decompositions.
  The main technical results include the embeddable decomposition theorem and
the dominion separation theorem that together help establish a precise
structural condition for the correctness of the universal algorithm: it
suffices that the two ordered trees given to the algorithm as inputs embed the
trees of some attractor decompositions of the largest dominia for each of the
two players, respectively.
  The universal algorithm yields McNaughton-Zielonka, Parys's, and
Lehtinen-Schewe-Wojtczak algorithms as special cases when suitable universal
trees are given to it as inputs. The main technical results provide a unified
proof of correctness and deep structural insights into those algorithms.
  A symbolic implementation of the universal algorithm is also given that
improves the symbolic space complexity of solving parity games in
quasi-polynomial time from $O(d \lg n)$---achieved by Chatterjee,
Dvo\v{r}\'{a}k, Henzinger, and Svozil (2018)---down to $O(\lg d)$, where $n$ is
the number of vertices and $d$ is the number of distinct priorities in a parity
game. This not only exponentially improves the dependence on $d$, but it also
entirely removes the dependence on $n$.

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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph