The Algebraic Theory of Parikh Automata
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 theories of typed monoids and of rational series are used to characterize the language classes that arise algebraically. Complexity bounds are...
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Published in | Theory of computing systems Vol. 62; no. 5; pp. 1241 - 1268 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.07.2018
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | 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 theories of typed monoids and of rational series are used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment of the unambiguous Parikh automata languages in NC
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. Affine Parikh automata, where each transition applies an affine transformation on the registers, are also considered. Relying on these characterizations, the landscape of relationships and closure properties of the classes at hand is completed, in particular over unary languages. |
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ISSN: | 1432-4350 1433-0490 |
DOI: | 10.1007/s00224-017-9817-2 |