TY - JOUR

T1 - Deciding path size of nondeterministic (and input-driven) pushdown automata

AU - Han, Yo Sub

AU - Ko, Sang Ki

AU - Salomaa, Kai

N1 - Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2023/1/4

Y1 - 2023/1/4

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).

KW - Ambiguity

KW - Decidability

KW - Input-driven pushdown automaton

KW - Measures of nondeterminism

KW - Path size

UR - http://www.scopus.com/inward/record.url?scp=85141506268&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2022.10.023

DO - 10.1016/j.tcs.2022.10.023

M3 - Article

AN - SCOPUS:85141506268

SN - 0304-3975

VL - 939

SP - 170

EP - 181

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -