ECCC-Report TR13-040https://eccc.weizmann.ac.il/report/2013/040Comments and Revisions published for TR13-040en-usFri, 20 Jan 2017 17:45:02 +0200
Revision 2
| The Algebraic Theory of Parikh Automata |
Michaël Cadilhac,
Andreas Krebs,
Pierre McKenzie
https://eccc.weizmann.ac.il/report/2013/040#revision2 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.Fri, 20 Jan 2017 17:45:02 +0200https://eccc.weizmann.ac.il/report/2013/040#revision2
Revision 1
| The Algebraic Theory of Parikh Automata |
Michaël Cadilhac,
Andreas Krebs,
Pierre McKenzie
https://eccc.weizmann.ac.il/report/2013/040#revision1 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.Fri, 22 Jan 2016 07:55:36 +0200https://eccc.weizmann.ac.il/report/2013/040#revision1
Paper TR13-040
| The Algebraic Theory of Parikh Automata |
Michaël Cadilhac,
Andreas Krebs,
Pierre McKenzie
https://eccc.weizmann.ac.il/report/2013/040The 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 NC$^1$. Noting that DetAPA languages are positive supports of rational $\mathbb{Z}$-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 NC$^1$.Sun, 24 Mar 2013 07:39:16 +0200https://eccc.weizmann.ac.il/report/2013/040