Complexity Results on Register Pushdown Automata
Ryoma Senda, Yoshiaki Takata, Hiroyuki Seki
TL;DR
This paper investigates the computational complexity of membership and emptiness problems in register pushdown automata, revealing complexity reductions for specific subclasses, which impacts their theoretical understanding and practical applications.
Contribution
It establishes new complexity bounds for membership problems in nondecreasing and growing RPDA subclasses, refining previous results for these automata.
Findings
Membership problem is PSPACE-complete for nondecreasing RPDA.
Membership problem is NP-complete for growing RPDA.
Emptiness problem remains EXPTIME-complete for these subclasses.
Abstract
Register pushdown automata (RPDA) is an extension of classical pushdown automata to handle data values in a restricted way. RPDA attracts attention as a model of a query language for structured documents with data values. The membership and emptiness problems for RPDA are known to be EXPTIME-complete. This paper shows the membership problem becomes PSPACE-complete and NP-complete for nondecreasing and growing RPDA, respectively, while the emptiness problem remains EXPTIME-complete for these subclasses.
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Taxonomy
Topicssemigroups and automata theory · Machine Learning and Algorithms · Logic, programming, and type systems