Dynamic Complexity of the Dyck Reachability
Patricia Bouyer, Vincent Jug\'e
TL;DR
This paper investigates the dynamic complexity of Dyck reachability problems in graphs, revealing a dichotomy based on alphabet size, with some problems being P-complete and others in DynFO or NL.
Contribution
It establishes a clear complexity classification for Dyck reachability under dynamic updates, depending on the alphabet size, advancing understanding of dynamic graph problems.
Findings
Some Dyck reachability problems are P-complete.
Others are in DynFO or NL.
Complexity depends on the size of the Dyck alphabet.
Abstract
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete edges. We show a strong dichotomy between such problems, based on the size of the Dyck alphabet. Some of them are P-complete (under a strong notion of reduction) while the others lie either in DynFO or in NL.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · DNA and Biological Computing