Algebraic Characterization of the Class of Languages recognized by Measure Only Quantum Automata

Carlo Comin; Maria Paola Bianchi

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arXiv · 1206.1702

Algebraic Characterization of the Class of Languages recognized by Measure Only Quantum Automata

Carlo Comin·Maria Paola Bianchi

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Abstract

We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa). We give an algebraic characterization of LMO, showing that the syntactic monoids of the languages in LMO are exactly the literal pseudovariety of J-trivial literally idempotent monoids, where J is the Green's relation determined by two-sided ideals. We also prove that LMO coincides with the literal variety of literally idempotent piecewise testable regular languages. This allows us to prove the existence of a polynomial time algorithm for deciding whether a regular language belongs to LMO.

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BibTeX RIS

Carlo Comin, Maria Paola Bianchi. 2012-07-16. Algebraic Characterization of the Class of Languages recognized by Measure Only Quantum Automata. https://arxiv.org/abs/1206.1702

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