Prime languages

Orna Kupferman; Jonathan Mosheiff

doi:10.1016/j.ic.2014.09.010

Prime languages

Orna Kupferman
, Jonathan Mosheiff

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We say that a deterministic finite automaton (DFA) A is composite if there are DFAs A₁,...,A_t such that L(A) = ∩_i=1^t L(A_i) and the index of every A_i is strictly smaller than the index of A. Otherwise, A is prime. We study the problem of deciding whether a given DFA is composite, the number of DFAs required in a decomposition, decompositions that are based on abstractions, methods to prove primality, and structural properties of DFAs that make the problem simpler or are retained in a decomposition. We also provide an algebraic view of the problem and demonstrate its usefulness for the special case of permutation DFAs.

Original language	English
Pages (from-to)	90-107
Number of pages	18
Journal	Information and Computation
Volume	240
DOIs	https://doi.org/10.1016/j.ic.2014.09.010
State	Published - 1 Jan 2015
Externally published	Yes

Keywords

DFA decomposition
Deterministic finite automaton (DFA)
Prime DFA
Prime regular languages
Regular languages

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Computer Science Applications
Computational Theory and Mathematics

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10.1016/j.ic.2014.09.010

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title = "Prime languages",

abstract = "We say that a deterministic finite automaton (DFA) A is composite if there are DFAs A1,...,At such that L(A) = ∩i=1t L(Ai) and the index of every Ai is strictly smaller than the index of A. Otherwise, A is prime. We study the problem of deciding whether a given DFA is composite, the number of DFAs required in a decomposition, decompositions that are based on abstractions, methods to prove primality, and structural properties of DFAs that make the problem simpler or are retained in a decomposition. We also provide an algebraic view of the problem and demonstrate its usefulness for the special case of permutation DFAs.",

keywords = "DFA decomposition, Deterministic finite automaton (DFA), Prime DFA, Prime regular languages, Regular languages",

author = "Orna Kupferman and Jonathan Mosheiff",

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doi = "10.1016/j.ic.2014.09.010",

language = "English",

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T1 - Prime languages

AU - Kupferman, Orna

AU - Mosheiff, Jonathan

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We say that a deterministic finite automaton (DFA) A is composite if there are DFAs A1,...,At such that L(A) = ∩i=1t L(Ai) and the index of every Ai is strictly smaller than the index of A. Otherwise, A is prime. We study the problem of deciding whether a given DFA is composite, the number of DFAs required in a decomposition, decompositions that are based on abstractions, methods to prove primality, and structural properties of DFAs that make the problem simpler or are retained in a decomposition. We also provide an algebraic view of the problem and demonstrate its usefulness for the special case of permutation DFAs.

AB - We say that a deterministic finite automaton (DFA) A is composite if there are DFAs A1,...,At such that L(A) = ∩i=1t L(Ai) and the index of every Ai is strictly smaller than the index of A. Otherwise, A is prime. We study the problem of deciding whether a given DFA is composite, the number of DFAs required in a decomposition, decompositions that are based on abstractions, methods to prove primality, and structural properties of DFAs that make the problem simpler or are retained in a decomposition. We also provide an algebraic view of the problem and demonstrate its usefulness for the special case of permutation DFAs.

KW - DFA decomposition

KW - Deterministic finite automaton (DFA)

KW - Prime DFA

KW - Prime regular languages

KW - Regular languages

UR - https://www.scopus.com/pages/publications/85028172321

U2 - 10.1016/j.ic.2014.09.010

DO - 10.1016/j.ic.2014.09.010

M3 - Article

AN - SCOPUS:85028172321

SN - 0890-5401

VL - 240

SP - 90

EP - 107

JO - Information and Computation

JF - Information and Computation

ER -

Prime languages

Abstract

Keywords

ASJC Scopus subject areas

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