Skip to Main content Skip to Navigation
Journal articles

Classical Automata on Promise Problems

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [41 references]  Display  Hide  Download

https://hal.inria.fr/hal-01349053
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, July 26, 2016 - 5:21:59 PM
Last modification on : Monday, November 13, 2017 - 3:22:01 PM

File

2717-9776-1-PB.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Viliam Geffert, Abuzer Yakaryilmaz. Classical Automata on Promise Problems. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.157-180. ⟨10.46298/dmtcs.2138⟩. ⟨hal-01349053⟩

Share

Metrics

Record views

38

Files downloads

812