License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2017.30
URN: urn:nbn:de:0030-drops-77198
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7719/
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Pradic, Pierre ; Riba, Colin

A Curry-Howard Approach to Church's Synthesis

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LIPIcs-FSCD-2017-30.pdf (0.6 MB)

Abstract

Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic over infinite words, Church's synthesis can theoretically be solved algorithmically using automata and games. We revisit Church's synthesis via the Curry-Howard correspondence by introducing SMSO, a non-classical subsystem of MSO, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model.

BibTeX - Entry

@InProceedings{pradic_et_al:LIPIcs:2017:7719,
  author =	{Pierre Pradic and Colin Riba},
  title =	{{A Curry-Howard Approach to Church's Synthesis}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Dale Miller},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7719},
  URN =		{urn:nbn:de:0030-drops-77198},
  doi =		{10.4230/LIPIcs.FSCD.2017.30},
  annote =	{Keywords: Intuitionistic Arithmetic, Realizability, Monadic Second-Order Logic on Infinite Words}
}

Keywords: Intuitionistic Arithmetic, Realizability, Monadic Second-Order Logic on Infinite Words
Collection: 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)
Issue Date: 2017
Date of publication: 30.08.2017

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