Abstract

On the basis of run semantics and breadth-first algebraic semantics, the algebraic characterizations for a classes of formal power series over complete strong bimonoids are investigated in this paper. As recognizers, weighted pushdown automata with final states (WPDAs for short) and empty stack (WPDAs^{emptyset }) are shown to be equivalent based on run semantics. Moreover, it is demonstrated that for every WPDA there is an equivalent crisp-simple weighted pushdown automaton with final states by run semantics if the underlying complete strong bimonoid satisfies multiplicatively local finiteness condition. As another type of generators, weighted context-free grammars over complete strong bimonoids are introduced, which are proven to be equivalent to WPDAs^{emptyset } based on each one of both run semantics and breadth-first algebraic semantics. Finally examples are presented to illuminate the proposed methods and results.

Highlights

  • Weighted automata (Droste et al 2009) are classical automata in which the transitions carry weights

  • Based on run semantics and breadth-first algebraic semantics, we investigate weighted pushdown automata over complete strong bimonoids with final states and empty stack respectively and their recognizable languages

  • Based on breadth-first algebraic semantics and run semantics, we will investigate the relationship between weighted context-free grammars and weighted pushdown automata over complete strong bimonoids

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Summary

Introduction

Weighted automata (Droste et al 2009) are classical automata in which the transitions carry weights. Based on run semantics and breadth-first algebraic semantics, we investigate weighted pushdown automata over complete strong bimonoids with final states and empty stack respectively and their recognizable languages. Proposition 1 Let a formal power series fx: ∗ → A be x-recognizable by a weighted finite automaton over a complete strong bimonoid A, where x ∈ {r, b}.

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