Abstract
The Parikh automaton model equips a finite automaton with integer registers and imposes a semilinear constraint on the set of their final settings. Here the theory of typed monoids is used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment of the unambiguous Parikh automata languages in NC1. Noting that DetAPA languages are positive supports of rational ℤ-series, DetAPA are further shown stronger than Parikh automata on unary langages. This suggests unary DetAPA languages as candidates for separating the two better known variants of uniform NC1. © 2013 Springer-Verlag.
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CITATION STYLE
Cadilhac, M., Krebs, A., & McKenzie, P. (2013). The algebraic theory of Parikh automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8080 LNCS, pp. 60–73). https://doi.org/10.1007/978-3-642-40663-8_7
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