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We investigate the complexity of several problems concerning Las Vegas finite automata. Our results are as follows.
(1) The membership problem for Las Vegas finite automata is in NL.
(2) The nonemptiness and inequivalence problems for Las Vegas finite automata are NL-complete.
(3) Constructing for a given Las Vegas finite automaton a minimum state deterministic finite automaton is in NP.
These results provide partial answers to some open problems posed by Hromkovič
and Schnitger [
...
The paper treats the question whether there
always exists a minimal nondeterministic finite automaton of states whose equivalent minimal deterministic finite automaton has states for any integers and with .
Partial answers to this question were given by Iwama, Kambayashi, and Takaki (2000) and by Iwama, Matsuura, and Paterson (2003).
In the present paper, the question is completely solved by presenting appropriate automata for all values of and . However,
in order to give an explicit construction...
The cyclic shift of a language , defined as =, is an operation known to preserve both regularity and context-freeness. Its descriptional complexity has been addressed in Maslov’s pioneering paper on the state complexity of regular language operations [Soviet Math. Dokl. 11 (1970) 1373–1375], where a high lower bound for partial DFAs using a growing alphabet was given. We improve this result by using a fixed 4-letter alphabet, obtaining a lower bound (n-1)! 2, which shows that the state complexity...
The cyclic shift of a language , defined as SHIFT() = {},
is an operation known to preserve both regularity and context-freeness.
Its descriptional complexity has been addressed in Maslov's
pioneering paper on the state complexity of regular language operations
[
(1970) 1373–1375],
where a high lower bound for partial DFAs using a growing alphabet was given.
We improve this result by using a fixed 4-letter alphabet,
obtaining a lower bound (n-1)! . 2(n-1)(n-2),
which shows that...
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