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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.
@article{ITA_2012__46_4_511_0,
author = {Cadilhac, Micha\"el and Finkel, Alain and McKenzie, Pierre},
title = {Affine {Parikh} automata},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {511--545},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
doi = {10.1051/ita/2012013},
mrnumber = {3107862},
zbl = {1279.68136},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2012013/}
}
TY - JOUR AU - Cadilhac, Michaël AU - Finkel, Alain AU - McKenzie, Pierre TI - Affine Parikh automata JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 511 EP - 545 VL - 46 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2012013/ DO - 10.1051/ita/2012013 LA - en ID - ITA_2012__46_4_511_0 ER -
%0 Journal Article %A Cadilhac, Michaël %A Finkel, Alain %A McKenzie, Pierre %T Affine Parikh automata %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 511-545 %V 46 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2012013/ %R 10.1051/ita/2012013 %G en %F ITA_2012__46_4_511_0
Cadilhac, Michaël; Finkel, Alain; McKenzie, Pierre. Affine Parikh automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 4, pp. 511-545. doi: 10.1051/ita/2012013
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