Weighted Logics for Nested Words and Algebraic Formal Power Series

Abstract

Nested words, a model for recursive programs proposed by Alur and Madhusudan, have recently gained much interest. In this paper we introduce quantitative extensions and study nested word series which assign to nested words elements of a semiring. We show that regular nested word series coincide with series definable in weighted logics as introduced by Droste and Gastin. For this, we establish a connection between nested words and series-parallel-biposets. Applying our result, we obtain a characterization of algebraic formal power series in terms of weighted logics. This generalizes a result of Lautemann, Schwentick and Thérien on context-free languages.KeywordsFormal Power SeriesRegular LanguageReturn PositionRecursive ProgramNest DepthThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.