# Affine Parikh automata∗

Michaël Cadilhac; Alain Finkel; Pierre McKenzie

RAIRO - Theoretical Informatics and Applications (2012)

- Volume: 46, Issue: 4, page 511-545
- ISSN: 0988-3754

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topCadilhac, Michaël, Finkel, Alain, and McKenzie, Pierre. "Affine Parikh automata∗." RAIRO - Theoretical Informatics and Applications 46.4 (2012): 511-545. <http://eudml.org/doc/277829>.

@article{Cadilhac2012,

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.},

author = {Cadilhac, Michaël, Finkel, Alain, McKenzie, Pierre},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Automata; semilinear sets; affine functions; counter machines; automata},

language = {eng},

month = {11},

number = {4},

pages = {511-545},

publisher = {EDP Sciences},

title = {Affine Parikh automata∗},

url = {http://eudml.org/doc/277829},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Cadilhac, Michaël

AU - Finkel, Alain

AU - McKenzie, Pierre

TI - Affine Parikh automata∗

JO - RAIRO - Theoretical Informatics and Applications

DA - 2012/11//

PB - EDP Sciences

VL - 46

IS - 4

SP - 511

EP - 545

AB - 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.

LA - eng

KW - Automata; semilinear sets; affine functions; counter machines; automata

UR - http://eudml.org/doc/277829

ER -

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