Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The complexity of bidirected reachability in valence systems   We study the complexity of bidirected reachability problems arising in many
areas of program analysis. We formulate the problem abstractly in terms of
bidirected valence automata over graph monoids, an algebraic framework that
generalizes many models of automata with storage, including CFL-reachability,
interleaved Dyck reachability, vector addition systems over naturals or
integers, and models involving complex combinations of stacks and counters. Our
main result is a characterization of the decidability and complexity of the
bidirected reachability problem for different graph classes. In particular, we
characterize the complexity of bidirected reachability for every graph class
for which reachability is known to be decidable. We show that there is a
remarkable drop in complexity in going from the reachability to the bidirected
reachability problems for many natural models studied previously. Our
techniques are algebraic, and exploit the underlying group structure of the
bidirected problem. As a consequence of our results, we characterize the
complexity of bidirectional reachability of a number of open problems in
program analysis, such as the complexity of different subcases of bidirectional
interleaved Dyck reachability.

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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: econ