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M-ambiguity Sequences for Parikh Matrices and Their Periodicity Revisited

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M-ambiguity Sequences for Parikh Matrices and Their Periodicity Revisited

10$

Ghajendran Poovanandran & Wen Chean Teh 

Abstract

The introduction of Parikh matrices by Mateescu et al. in 2001 has sparked numerous new investigations in the theory of formal languages by various researchers, among whom is Şerbănuţă. Recently, a decade-old conjecture by Şerbǎnuţǎ on the M-ambiguity of words has disproved, leading to new possibilities in the study of such words. In this paper, we investigate how selective repeated duplications of letters in a word affect the M-ambiguity of the resulting words. The corresponding M-ambiguity of each of those words is then presented in sequences, which we term as M-ambiguity sequences. We show that nearly all patterns of M-ambiguity sequences are attainable. Finally, by employing certain algebraic approach and some underlying theory in integer programming, we show that repeated periodic duplications of letters of the same type in a word result in an M-ambiguity sequence that is ultimately periodic.

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Year 2020
Language English
Format PDF
DOI 10.1007/s40840-019-00867-w