Viliam Geffert ; Abuzer Yakaryilmaz - Classical Automata on Promise Problems

dmtcs:2138 - Discrete Mathematics & Theoretical Computer Science, September 16, 2015, Vol. 17 no.2 - https://doi.org/10.46298/dmtcs.2138
Classical Automata on Promise Problems

Authors: Viliam Geffert ; Abuzer Yakaryilmaz

Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems. First, it was known that there is a family of unary promise problems solvable by quantum automata by using a single qubit, but the number of states required by corresponding one-way deterministic automata cannot be bounded by a constant. For this family, we show that even two-way nondeterminism does not help to save a single state. By comparing this with the corresponding state complexity of alternating machines, we then get a tight exponential gap between two-way nondeterministic and one-way alternating automata solving unary promise problems. Second, despite of the existing quadratic gap between Las Vegas realtime probabilistic automata and one-way deterministic automata for language recognition, we show that, by turning to promise problems, the tight gap becomes exponential. Last, we show that the situation is different for one-way probabilistic automata with two-sided bounded-error. We present a family of unary promise problems that is very easy for these machines; solvable with only two states, but the number of states in two-way alternating or any simpler automata is not limited by a constant. Moreover, we show that one-way bounded-error probabilistic automata can solve promise problems not solvable at all by any other classical model.


Volume: Vol. 17 no.2
Section: Automata, Logic and Semantics
Published on: September 16, 2015
Submitted on: October 14, 2014
Keywords: promise problems,descriptional complexity,nondeterministic automata,probabilistic automata,alternating automata,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


Share

Consultation statistics

This page has been seen 155 times.
This article's PDF has been downloaded 415 times.