The polynomial-size hierarchy is the hierarchy of 'minicomplexity' classes which correspond to two-way alternating finite automata with polynomially many states and finitely many alternations. It is defined by analogy to the polynomial-time hierarchy of standard complexity theory, and it has recently been shown to be strict above its first level. It is well-known that, apart from their definition in terms of polynomial-time alternating Turing machines, the classes of the polynomial-time hierarchy can also be characterized in terms of polynomial-time predicates, polynomial-time oracle Turing machines, and formulas of second-order logic. It is natural to ask whether analogous alternative characterizations are possible for the polynomial-size hierarchy, as well. Here, we answer this question affirmatively for predicates. Starting with the first level of the hierarchy, we experiment with several natural ways of defining what a 'polynomial-size predicate' should be, so that existentially quantified predicates of this kind correspond to polynomial-size two-way nondeterministic finite automata. After reaching an appropriate definition, we generalize to every level of the hierarchy. © 2014 Springer International Publishing.
CITATION STYLE
Kapoutsis, C. A. (2014). Predicate characterizations in the polynomial-size hierarchy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8493 LNCS, pp. 234–244). Springer Verlag. https://doi.org/10.1007/978-3-319-08019-2_24
Mendeley helps you to discover research relevant for your work.