| Institute of Informatics>>> Acta Cybernetica>>> Past Issues>>> Volume 19, Number 2, 2009>>> |
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Complexity of Problems Concerning Reset Words for Some Partial Cases of Automata
Abstract (in LaTeX format)
A word $w$ is called a reset word for a deterministic finite automaton $\mathrsfs{A}$ if it maps all states of $\mathrsfs{A}$ to one state. A word $w$ is called a compressing to $M$ states for a deterministic finite automaton $\mathrsfs{A}$ if it maps all states of $\mathrsfs{A}$ to at most $M$ states. We consider several subclasses of automata: aperiodic, $\mathrsfs{D}$-trivial, monotonic, partially monotonic automata and automata with a zero state. For these subclasses we study the computational complexity of the following problems. Does there exist a reset word for a given automaton? Does there exist a reset word of given length for a given automaton? What is the length of the shortest reset word for a given automaton? Moreover, we consider complexity of the same problems for compressing words.
Kewords: synchronization, automata, reset words, computational complexity.
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BibTeX entry
@article{Martyugin:2009:ActaCybernetica,author = {Pavel Martyugin},
title = {Complexity of Problems Concerning Reset Words for Some Partial Cases of Automata},
journal = {Acta Cybernetica},
volume = {19},
number= {2},
pages = {517--536},
year = {2009},
abstract = {A word $w$ is called a reset word for a deterministic finite automaton $\mathrsfs{A}$ if it maps all states of $\mathrsfs{A}$ to one state. A word $w$ is called a compressing to $M$ states for a deterministic finite automaton $\mathrsfs{A}$ if it maps all states of $\mathrsfs{A}$ to at most $M$ states. We consider several subclasses of automata: aperiodic, $\mathrsfs{D}$-trivial, monotonic, partially monotonic automata and automata with a zero state. For these subclasses we study the computational complexity of the following problems. Does there exist a reset word for a given automaton? Does there exist a reset word of given length for a given automaton? What is the length of the shortest reset word for a given automaton? Moreover, we consider complexity of the same problems for compressing words.},
keywords = {synchronization, automata, reset words, computational complexity}
}