3 research outputs found
Power of Counting by Nonuniform Families of Polynomial-Size Finite Automata
Lately, there have been intensive studies on strengths and limitations of
nonuniform families of promise decision problems solvable by various types of
polynomial-size finite automata families, where "polynomial-size" refers to the
polynomially-bounded state complexity of a finite automata family. In this line
of study, we further expand the scope of these studies to families of partial
counting and gap functions, defined in terms of nonuniform families of
polynomial-size nondeterministic finite automata, and their relevant families
of promise decision problems. Counting functions have an ability of counting
the number of accepting computation paths produced by nondeterministic finite
automata. With no unproven hardness assumption, we show numerous separations
and collapses of complexity classes of those partial counting and gap function
families and their induced promise decision problem families. We also
investigate their relationships to pushdown automata families of polynomial
stack-state complexity.Comment: (A4, 10pt, 21 pages) This paper corrects and extends a preliminary
report published in the Proceedings of the 24th International Symposium on
Fundamentals of Computation Theory (FCT 2023), Trier, Germany, September
18-24, 2023, Lecture Notes in Computer Science, vol. 14292, pp. 421-435,
Springer Cham, 202