Deciding path size of nondeterministic (and input-driven) pushdown automata

Yo Sub Han; Sang Ki Ko; Kai Salomaa

doi:10.1016/j.tcs.2022.10.023

Deciding path size of nondeterministic (and input-driven) pushdown automata

Yo Sub Han, Sang Ki Ko, Kai Salomaa

College of Computing

Research output: Contribution to journal › Article › peer-review

Abstract

The degree of ambiguity (respectively, the path size) of a nondeterministic automaton, on a given input, measures the number of accepting computations (respectively, the number of all computations). It is known that deciding the finiteness of the degree of ambiguity of a nondeterministic pushdown automaton is undecidable. Also, it is undecidable for a given k≥3 to decide whether the path size of a nondeterministic pushdown automaton is bounded by k. As the main result, we show that deciding the finiteness of the path size of a nondeterministic pushdown automaton can be done in polynomial time. Also, we show that the k-path problem for nondeterministic input-driven pushdown automata (respectively, for nondeterministic finite automata) is complete for exponential time (respectively, complete for polynomial space).

Original language	English
Pages (from-to)	170-181
Number of pages	12
Journal	Theoretical Computer Science
Volume	939
DOIs	https://doi.org/10.1016/j.tcs.2022.10.023
Publication status	Published - 2023 Jan 4

Bibliographical note

Funding Information:
Han was supported by the IITP grants (2018-0-00276, 2020-0-01361).Ko was supported by the NRF grant (2020R1A4A3079947).Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Publisher Copyright:
© 2022 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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10.1016/j.tcs.2022.10.023

Cite this

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title = "Deciding path size of nondeterministic (and input-driven) pushdown automata",

abstract = "The degree of ambiguity (respectively, the path size) of a nondeterministic automaton, on a given input, measures the number of accepting computations (respectively, the number of all computations). It is known that deciding the finiteness of the degree of ambiguity of a nondeterministic pushdown automaton is undecidable. Also, it is undecidable for a given k≥3 to decide whether the path size of a nondeterministic pushdown automaton is bounded by k. As the main result, we show that deciding the finiteness of the path size of a nondeterministic pushdown automaton can be done in polynomial time. Also, we show that the k-path problem for nondeterministic input-driven pushdown automata (respectively, for nondeterministic finite automata) is complete for exponential time (respectively, complete for polynomial space).",

author = "Han, {Yo Sub} and Ko, {Sang Ki} and Kai Salomaa",

note = "Funding Information: Han was supported by the IITP grants (2018-0-00276, 2020-0-01361).Ko was supported by the NRF grant (2020R1A4A3079947).Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

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doi = "10.1016/j.tcs.2022.10.023",

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AU - Salomaa, Kai

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PY - 2023/1/4

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N2 - The degree of ambiguity (respectively, the path size) of a nondeterministic automaton, on a given input, measures the number of accepting computations (respectively, the number of all computations). It is known that deciding the finiteness of the degree of ambiguity of a nondeterministic pushdown automaton is undecidable. Also, it is undecidable for a given k≥3 to decide whether the path size of a nondeterministic pushdown automaton is bounded by k. As the main result, we show that deciding the finiteness of the path size of a nondeterministic pushdown automaton can be done in polynomial time. Also, we show that the k-path problem for nondeterministic input-driven pushdown automata (respectively, for nondeterministic finite automata) is complete for exponential time (respectively, complete for polynomial space).

AB - The degree of ambiguity (respectively, the path size) of a nondeterministic automaton, on a given input, measures the number of accepting computations (respectively, the number of all computations). It is known that deciding the finiteness of the degree of ambiguity of a nondeterministic pushdown automaton is undecidable. Also, it is undecidable for a given k≥3 to decide whether the path size of a nondeterministic pushdown automaton is bounded by k. As the main result, we show that deciding the finiteness of the path size of a nondeterministic pushdown automaton can be done in polynomial time. Also, we show that the k-path problem for nondeterministic input-driven pushdown automata (respectively, for nondeterministic finite automata) is complete for exponential time (respectively, complete for polynomial space).

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Deciding path size of nondeterministic (and input-driven) pushdown automata

Abstract

Bibliographical note

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