Abstract
Let [Formula: see text] be a complete star-omega semiring and [Formula: see text] be an alphabet. For a weighted [Formula: see text]-pushdown automaton [Formula: see text] with stateset [Formula: see text], [Formula: see text], we show that there exists a mixed algebraic system over a complete semiring-semimodule pair [Formula: see text] such that the behavior [Formula: see text] of [Formula: see text] is a component of a solution of this system. In case the basic semiring is [Formula: see text] or [Formula: see text] we show that there exists a mixed context-free grammar that generates [Formula: see text]. The construction of the mixed context-free grammar from [Formula: see text] is a generalization of the well known triple construction and is called now triple-pair construction for [Formula: see text]-pushdown automata.
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