Paper Info
Title
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.
Year
DOI
Venue
2015
10.1007/978-3-319-09704-6_12
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
Keywords
Field
DocType
descriptional complexity,promise problems,nondeterministic automata,probabilistic automata,alternating automata
Discrete mathematics,Algebra,Automaton,Mathematics
Journal
Volume
Issue
ISSN
17.0
2.0
1462-7264
Citations 
PageRank 
References 
10
0.53
27
Authors
2
Name
Order
Citations
PageRank
Viliam Geffert145942.93
Abuzer Yakaryilmaz216825.31