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.FSTTCS.2021.43
URN: urn:nbn:de:0030-drops-155541
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15554/
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Filiot, Emmanuel ; Winter, Sarah

Synthesizing Computable Functions from Rational Specifications over Infinite Words

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LIPIcs-FSTTCS-2021-43.pdf (0.8 MB)

Abstract

The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing computability notion over infinite inputs. We consider specifications which are rational relations of infinite words, i.e., specifications defined by non-deterministic parity transducers. We prove that the synthesis problem of computable functions from rational specifications is undecidable. We provide an incomplete but sound reduction to some parity game, such that if Eve wins the game, then the rational specification is realizable by a computable function. We prove that this function is even computable by a deterministic two-way transducer.
We provide a sufficient condition under which the latter game reduction is complete. This entails the decidability of the synthesis problem of computable functions, which we proved to be ExpTime-complete, for a large subclass of rational specifications, namely deterministic rational specifications. This subclass contains the class of automatic relations over infinite words, a yardstick in reactive synthesis.

BibTeX - Entry

@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2021.43,
  author =	{Filiot, Emmanuel and Winter, Sarah},
  title =	{{Synthesizing Computable Functions from Rational Specifications over Infinite Words}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czy, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15554},
  URN =		{urn:nbn:de:0030-drops-155541},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.43},
  annote =	{Keywords: uniformization, synthesis, transducers, continuity, computability}
}

Keywords: uniformization, synthesis, transducers, continuity, computability
Collection: 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)
Issue Date: 2021
Date of publication: 29.11.2021

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