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

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Title: Deciding path size of nondeterministic (and input-driven) pushdown automata.
Authors: Han, Yo-Sub1 (AUTHOR) emmous@yonsei.ac.kr, Ko, Sang-Ki1,2 (AUTHOR) sangkiko@kangwon.ac.kr, Salomaa, Kai1,3 (AUTHOR) ksalomaa@cs.queensu.ca
Source: Theoretical Computer Science. Jan2023, Vol. 939, p170-181. 12p.
Subjects: Polynomial time algorithms, Finite state machines, Decision making, Robots
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). • We show that finiteness of path size of nondeterministic pushdown automata can be solved in polynomial time. • We show that deciding k-path property is PSPACE complete for nondeterministic finite automata. • We show that deciding k-path property is exponential time complete for nondeterministic input-driven pushdown automata. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Deciding path size of nondeterministic (and input-driven) pushdown automata.
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  Data: <searchLink fieldCode="AR" term="%22Han%2C+Yo-Sub%22">Han, Yo-Sub</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> emmous@yonsei.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Ko%2C+Sang-Ki%22">Ko, Sang-Ki</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> sangkiko@kangwon.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Salomaa%2C+Kai%22">Salomaa, Kai</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> ksalomaa@cs.queensu.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22Theoretical+Computer+Science%22">Theoretical Computer Science</searchLink>. Jan2023, Vol. 939, p170-181. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+state+machines%22">Finite state machines</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+making%22">Decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Robots%22">Robots</searchLink>
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  Data: 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). • We show that finiteness of path size of nondeterministic pushdown automata can be solved in polynomial time. • We show that deciding k-path property is PSPACE complete for nondeterministic finite automata. • We show that deciding k-path property is exponential time complete for nondeterministic input-driven pushdown automata. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.tcs.2022.10.023
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 170
    Subjects:
      – SubjectFull: Polynomial time algorithms
        Type: general
      – SubjectFull: Finite state machines
        Type: general
      – SubjectFull: Decision making
        Type: general
      – SubjectFull: Robots
        Type: general
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      – TitleFull: Deciding path size of nondeterministic (and input-driven) pushdown automata.
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            NameFull: Han, Yo-Sub
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            NameFull: Ko, Sang-Ki
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            – D: 04
              M: 01
              Text: Jan2023
              Type: published
              Y: 2023
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