A quadratic algorithm for testing of omega-codes

Authors:
Nguyen Dinh Han;Phan Trung Huy;Dang Quyet Thang
Affiliations:
Hung Yen University of Technology and Education, Vietnam;Hanoi University of Science and Technology, Vietnam;Nam Dinh University of Technology and Education, Vietnam
Venue:
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part I
Year:
2012

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A quadratic algorithm for testing of Z-codes

ACIIDS'13 Proceedings of the 5th Asian conference on Intelligent Information and Database Systems - Volume Part I

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Abstract

We consider a special class of codes, namely ω-codes related to infinite word which had been studied by many authors. Until now, the best algorithm to test whether a regular language X is an ω-code has time complexity O(n3), where n is the size of the transition monoid of the minimal automaton recognizing X. In this paper, with any monoid M saturating X (the transition monoid above is only a special case), we propose a new test and establish a quadratic testing algorithm with time complexity O(n2) to verify if X is an ω-code, where n is Card(M).