文章基本信息

标题：Finite-Valued Weighted Automata
本地全文：下载
作者：Emmanuel Filiot ; Raffaella Gentilini ; Jean-Francois Raskin 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2014
卷号：29
页码：133-145
DOI：10.4230/LIPIcs.FSTTCS.2014.133
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defined by k-valued automata, for all parameters k. We consider several measures to associate values with runs: sum, discounted-sum, and more generally values in groups. We define a general procedure which decides, given a bound k and a WA over a group, whether this automaton is k-valued. We also show that any k-valued WA over a group, under some general conditions, can be decomposed as a union of k unambiguous WA. While inclusion and equivalence are undecidable problems for arbitrary sum-automata, we show, based on this decomposition, that they are decidable for k-valued sum-automata, and k-valued discounted sum-automata over inverted integer discount factors. We finally show that the quantitative Church problem is undecidable for k-valued sum-automata, even given as finite unions of deterministic sum-automata.
关键词：Nested word; Transducer; Streaming