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...

Full description

Saved in:
Bibliographic Details
Published inTheory of computing systems Vol. 62; no. 5; pp. 1241 - 1268
Main Authors Cadilhac, Michaël, Krebs, Andreas, McKenzie, Pierre
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2018
Springer Nature B.V
Subjects
Affine transformations
Automata theory
Computer Science
Containment
Languages
Monoids
Theory of Computation
Algebra
Circuits
Automata
Monoids
Typed monoids
Semilinear sets
Online AccessGet full text

Cover

More Information
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 1 . 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.
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-017-9817-2