Decidability Boundaries for the Finite-Image Property of Weighted Finite Automata

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

International Journal of Foundations of Computer Science Pub Date : 2023-07-25 DOI:10.1142/s0129054123450041

M. Droste, Zoltán Fülöp, Dávid Kószó

{"title":"Decidability Boundaries for the Finite-Image Property of Weighted Finite Automata","authors":"M. Droste, Zoltán Fülöp, Dávid Kószó","doi":"10.1142/s0129054123450041","DOIUrl":null,"url":null,"abstract":"A weighted finite automaton has the finite-image property if the image of the weighted language associated with it is finite. We show two undecidability results concerning the finite-image property of weighted finite automata over semirings, respectively strong bimonoids. Firstly, we give a computable idempotent commutative past-finite ordered semiring such that it is undecidable, for an arbitrary deterministic weighted finite automaton [Formula: see text] over that semiring, whether [Formula: see text] has the finite-image property. Secondly, we give a computable commutative past-finite monotonic ordered strong bimonoid such that it is undecidable, for an arbitrary weighted finite automaton [Formula: see text] over that strong bimonoid, whether [Formula: see text] has the finite-image property. This shows that recent decidability results for suitable weighted finite automata over past-finite monotonic strong bimonoids cannot be extended to natural classes of ordered semirings and ordered strong bimonoids without further assumptions.","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Foundations of Computer Science","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1142/s0129054123450041","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

Abstract

A weighted finite automaton has the finite-image property if the image of the weighted language associated with it is finite. We show two undecidability results concerning the finite-image property of weighted finite automata over semirings, respectively strong bimonoids. Firstly, we give a computable idempotent commutative past-finite ordered semiring such that it is undecidable, for an arbitrary deterministic weighted finite automaton [Formula: see text] over that semiring, whether [Formula: see text] has the finite-image property. Secondly, we give a computable commutative past-finite monotonic ordered strong bimonoid such that it is undecidable, for an arbitrary weighted finite automaton [Formula: see text] over that strong bimonoid, whether [Formula: see text] has the finite-image property. This shows that recent decidability results for suitable weighted finite automata over past-finite monotonic strong bimonoids cannot be extended to natural classes of ordered semirings and ordered strong bimonoids without further assumptions.

查看原文本刊更多论文

加权有限自动机有限映象性质的可判定边界

如果与之相关的加权语言的图像是有限的，则加权有限自动机具有有限图像属性。我们给出了关于半环上加权有限自动机有限像性质的两个不可判定结果，分别是强双峰。首先，对于任意确定性加权有限自动机[公式:见文]在该半环上是否具有有限象性质，我们给出了一个可计算幂等交换的过去有限有序半环，使得它是不可判定的。其次，对于任意加权的有限自动机[公式:见文]，我们给出了一个可计算的交换的过去有限单调有序强双拟体，使得它是不确定的，是否具有有限象性质。这表明，在没有进一步假设的情况下，最近关于合适加权有限自动机在过去有限单调强双峰上的可决性结果不能推广到有序半环和有序强双峰的自然类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Foundations of Computer Science 工程技术-计算机：理论方法

CiteScore

1.60

自引率

12.50%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing