Parikh Matrices and Strong M-Equivalence
Wen Chean Teh
TL;DR
This paper introduces strong M-equivalence as an order-independent alternative to Parikh matrices, providing characterizations for certain word classes and exploring its existential counterpart.
Contribution
It proposes strong M-equivalence to eliminate alphabet ordering dependence and characterizes it for specific word classes, also introducing its existential version.
Findings
Strong M-equivalence is order-independent.
Characterizations for restricted word classes are provided.
Existential strong M-equivalence is introduced.
Abstract
Parikh matrices have been a powerful tool in arithmetizing words by numerical quantities. However, the dependence on the ordering of the alphabet is inherited by Parikh matrices. Strong M-equivalence is proposed as a canonical alternative to M-equivalence to get rid of this undesirable property. Some characterization of strong M-equivalence for a restricted class of words is obtained. Finally, the existential counterpart of strong M-equivalence is introduced as well.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Algorithms and Data Compression