Affine Parikh automata^∗

¹ DIRO, Université de Montréal, CP 6128 succ. centre-ville, Montréal QC, H3C 3J7, Canada
cadilhac@iro.umontreal.ca, mckenzie@iro.umontreal.ca. The third author is supported by the Natural Sciences and Engineering Research Council of Canada.
² LSV, ENS Cachan, CNRS, 61, avenue du Président Wilson, 94235 Cachan Cedex, France
finkel@lsv.ens-cachan.fr Ce travail a bénéficié d’une aide de l’Agence Nationale de la Recherche portant la référence “REACHARD-ANR-11-BS02-001”

Received: 4 November 2011
Accepted: 30 April 2012

Abstract

The Parikh finite word automaton (PA) was introduced and studied in 2003 by Klaedtke and Rueß. Natural variants of the PA arise from viewing a PA equivalently as an automaton that keeps a count of its transitions and semilinearly constrains their numbers. Here we adopt this view and define the affine PA, that extends the PA by having each transition induce an affine transformation on the PA registers, and the PA on letters, that restricts the PA by forcing any two transitions on the same letter to affect the registers equally. Then we report on the expressiveness, closure, and decidability properties of such PA variants. We note that deterministic PA are strictly weaker than deterministic reversal-bounded counter machines.