Bounded Parikh Automata
Micha\"el Cadilhac (DIRO, Universit\'e de Montr\'eal), Alain Finkel, (LSV, ENS Cachan & CNRS), Pierre McKenzie (DIRO, Universit\'e de Montr\'eal)
TL;DR
This paper investigates the class of bounded languages recognized by Parikh automata, showing they coincide with those recognized by deterministic Parikh automata and are characterized by semilinear iteration sets.
Contribution
It establishes the equivalence between bounded languages recognized by PA and deterministic PA, characterizing them via semilinear iteration sets.
Findings
Bounded languages recognized by PA are the same as those recognized by deterministic PA.
The class of recognized languages is characterized by semilinear sets.
The results connect bounded PA languages with well-understood semilinear properties.
Abstract
The Parikh finite word automaton model (PA) was introduced and studied by Klaedtke and Ruess in 2003. Here, by means of related models, it is shown that the bounded languages recognized by PA are the same as those recognized by deterministic PA. Moreover, this class of languages is the class of bounded languages whose set of iterations is semilinear.
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