On the computation of quotients and factors of regular languages

Abstract

Quotients and factors are important notions in the design of various computational procedures for regular languages and for the analysis of their logical properties. We propose a new representation of regular languages, by linear systems of language equations, which is suitable for the following computations: language reversal, left quotients and factors, right quotients and factors, and factor matrices. We present algorithms for the computation of all these notions, and indicate an application of the factor matrix to the computation of solutions of a particular language reconstruction problem. The advantage of these algorithms is that they all operate only on linear systems of language equations, while the design of the same algorithms for other representations often require translation to other representations.

Keywords

regular language / language factorization / language quotient

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Acknowledgements

A preliminary version of this papen was presented in the 6th Asian Workshop on Foundations of Software (AWFS 2009) Mircea Marin was supported by JSPS Grant-in-Aid No. 20500025 for Scientific Research (C). Temur Kutsia was supported by the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce—Symbolic Computation Infrastructure for Europe (Contract No. 026133).

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg