The Triple-Pair Construction for Weighted $\omega$-Pushdown Automata
Abstract
Let S be a complete star-omega semiring and Sigma be an alphabet. For a weighted omega-pushdown automaton P with stateset 1...n, n greater or equal to 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S<<Sigma*>>)^nxn, (S<<Sigma^omega>>)^n) such that the behavior ||P|| of P is a component of a solution of this system. In case the basic semiring is the Boolean semiring or the semiring of natural numbers (augmented with infinity), we show that there exists a mixed context-free grammar that generates ||P||. The construction of the mixed context-free grammar from P is a generalization of the well known triple construction and is called now triple-pair construction for omega-pushdown automata.
Keywords
Cite
@article{arxiv.1708.06463,
title = {The Triple-Pair Construction for Weighted $\omega$-Pushdown Automata},
author = {Manfred Droste and Zoltán Ésik and Werner Kuich},
journal= {arXiv preprint arXiv:1708.06463},
year = {2017}
}
Comments
In Proceedings AFL 2017, arXiv:1708.06226. The article was prepared as a joint work with the late Zolt\'an \'Esik (1951-2016) whose definite intention was to publish the results