The church synthesis problem with metric

Mark Jenkins, Joël Ouaknine, Alexander Rabinovich, James Worrell

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Church's Problem asks for the construction of a procedure which, given a logical specification φ(I, O) between input strings I and output strings O, determines whether there exists an operator F that implements the specification in the sense that φ(I, F (I)) holds for all inputs I. Büchi and Landweber gave a procedure to solve Church's problem for MSO specifications and operators computable by finite-state automata. We consider extensions of Church's problem in two orthogonal directions: (i) we address the problem in a more general logical setting, where not only the specifications but also the solutions are presented in a logical system; (ii) we consider not only the canonical discrete time domain of the natural numbers, but also the continuous domain of reals. We show that for every fixed bounded length interval of the reals, Church's problem is decidable when specifications and implementations are described in the monadic second-order logics over the reals with order and the +1 function.

Original languageEnglish
Title of host publicationComputer Science Logic 2011 - 25th International Workshop/20th Annual Conference of the EACSL, CSL 2011
Pages307-321
Number of pages15
DOIs
StatePublished - 2011
Event25th International Workshop on Computer Science Logic, CSL 2011/20th Annual Conference of the European Association for Computer Science Logic, EACSL - Bergen, Norway
Duration: 12 Sep 201115 Sep 2011

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume12
ISSN (Print)1868-8969

Conference

Conference25th International Workshop on Computer Science Logic, CSL 2011/20th Annual Conference of the European Association for Computer Science Logic, EACSL
Country/TerritoryNorway
CityBergen
Period12/09/1115/09/11

Keywords

  • Church's problem
  • Games
  • Monadic logic
  • Uniformization

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