{"title":"Bideterministic weighted automata","authors":"Peter Kostolányi","doi":"10.1016/j.ic.2023.105093","DOIUrl":null,"url":null,"abstract":"<div><p>A finite automaton<span><span> is called bideterministic if it is both deterministic and codeterministic – that is, if it is deterministic and its transpose is deterministic as well. The study of such automata in a weighted setting is initiated. All trim bideterministic weighted automata over integral domains and over positive semirings are proved to be minimal. On the contrary, it is observed that this property does not hold over </span>commutative rings in general: non-minimal trim bideterministic weighted automata do exist over all semirings that are not zero-divisor free, and over many such semirings, these automata might not even admit equivalents that are both minimal and bideterministic. The problem of determining whether a given rational series is realised by a bideterministic automaton is shown to be decidable over fields and over tropical semirings. An example of a positive semiring over which this problem becomes undecidable is given as well.</span></p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105093"},"PeriodicalIF":0.8000,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0890540123000962","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
A finite automaton is called bideterministic if it is both deterministic and codeterministic – that is, if it is deterministic and its transpose is deterministic as well. The study of such automata in a weighted setting is initiated. All trim bideterministic weighted automata over integral domains and over positive semirings are proved to be minimal. On the contrary, it is observed that this property does not hold over commutative rings in general: non-minimal trim bideterministic weighted automata do exist over all semirings that are not zero-divisor free, and over many such semirings, these automata might not even admit equivalents that are both minimal and bideterministic. The problem of determining whether a given rational series is realised by a bideterministic automaton is shown to be decidable over fields and over tropical semirings. An example of a positive semiring over which this problem becomes undecidable is given as well.
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Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as
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