Emmanuel Filiot, Ismaël Jecker, Gabriele Puppis, Christof Löding, Anca Muscholl, Sarah Winter
{"title":"Finite-valued Streaming String Transducers","authors":"Emmanuel Filiot, Ismaël Jecker, Gabriele Puppis, Christof Löding, Anca Muscholl, Sarah Winter","doi":"arxiv-2405.08171","DOIUrl":null,"url":null,"abstract":"A transducer is finite-valued if for some bound k, it maps any given input to\nat most k outputs. For classical, one-way transducers, it is known since the\n80s that finite valuedness entails decidability of the equivalence problem.\nThis decidability result is in contrast to the general case, which makes\nfinite-valued transducers very attractive. For classical transducers, it is\nalso known that finite valuedness is decidable and that any k-valued finite\ntransducer can be decomposed as a union of k single-valued finite transducers. In this paper, we extend the above results to copyless streaming string\ntransducers (SSTs), answering questions raised by Alur and Deshmukh in 2011.\nSSTs strictly extend the expressiveness of one-way transducers via additional\nvariables that store partial outputs. We prove that any k-valued SST can be\neffectively decomposed as a union of k (single-valued) deterministic SSTs. As a\ncorollary, we obtain equivalence of SSTs and two-way transducers in the\nfinite-valued case (those two models are incomparable in general). Another\ncorollary is an elementary upper bound for checking equivalence of\nfinite-valued SSTs. The latter problem was already known to be decidable, but\nthe proof complexity was unknown (it relied on Ehrenfeucht's conjecture).\nFinally, our main result is that finite valuedness of SSTs is decidable. The\ncomplexity is PSpace, and even PTime when the number of variables is fixed.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"2010 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Formal Languages and Automata Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.08171","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A transducer is finite-valued if for some bound k, it maps any given input to
at most k outputs. For classical, one-way transducers, it is known since the
80s that finite valuedness entails decidability of the equivalence problem.
This decidability result is in contrast to the general case, which makes
finite-valued transducers very attractive. For classical transducers, it is
also known that finite valuedness is decidable and that any k-valued finite
transducer can be decomposed as a union of k single-valued finite transducers. In this paper, we extend the above results to copyless streaming string
transducers (SSTs), answering questions raised by Alur and Deshmukh in 2011.
SSTs strictly extend the expressiveness of one-way transducers via additional
variables that store partial outputs. We prove that any k-valued SST can be
effectively decomposed as a union of k (single-valued) deterministic SSTs. As a
corollary, we obtain equivalence of SSTs and two-way transducers in the
finite-valued case (those two models are incomparable in general). Another
corollary is an elementary upper bound for checking equivalence of
finite-valued SSTs. The latter problem was already known to be decidable, but
the proof complexity was unknown (it relied on Ehrenfeucht's conjecture).
Finally, our main result is that finite valuedness of SSTs is decidable. The
complexity is PSpace, and even PTime when the number of variables is fixed.