License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2023.32
URN: urn:nbn:de:0030-drops-176843
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17684/
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Filiot, Emmanuel ; Jecker, Ismaël ; Löding, Christof ; Winter, Sarah

A Regular and Complete Notion of Delay for Streaming String Transducers

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LIPIcs-STACS-2023-32.pdf (0.8 MB)

Abstract

The notion of delay between finite transducers is a core element of numerous fundamental results of transducer theory. The goal of this work is to provide a similar notion for more complex abstract machines: we introduce a new notion of delay tailored to measure the similarity between streaming string transducers (SST). We show that our notion is regular: we design a finite automaton that can check whether the delay between any two SSTs executions is smaller than some given bound. As a consequence, our notion enjoys good decidability properties: in particular, while equivalence between non-deterministic SSTs is undecidable, we show that equivalence up to fixed delay is decidable. Moreover, we show that our notion has good completeness properties: we prove that two SSTs are equivalent if and only if they are equivalent up to some (computable) bounded delay. Together with the regularity of our delay notion, it provides an alternative proof that SSTs equivalence is decidable. Finally, the definition of our delay notion is machine-independent, as it only depends on the origin semantics of SSTs. As a corollary, the completeness result also holds for equivalent machine models such as deterministic two-way transducers, or MSO transducers.

BibTeX - Entry

@InProceedings{filiot_et_al:LIPIcs.STACS.2023.32,
  author =	{Filiot, Emmanuel and Jecker, Isma\"{e}l and L\"{o}ding, Christof and Winter, Sarah},
  title =	{{A Regular and Complete Notion of Delay for Streaming String Transducers}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17684},
  URN =		{urn:nbn:de:0030-drops-176843},
  doi =		{10.4230/LIPIcs.STACS.2023.32},
  annote =	{Keywords: Streaming string transducers, Delay, Origin}
}

Keywords: Streaming string transducers, Delay, Origin
Collection: 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Issue Date: 2023
Date of publication: 03.03.2023

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