TY - GEN
T1 - The church synthesis problem with metric
AU - Jenkins, Mark
AU - Ouaknine, Joël
AU - Rabinovich, Alexander
AU - Worrell, James
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Church's problem
KW - Games
KW - Monadic logic
KW - Uniformization
UR - http://www.scopus.com/inward/record.url?scp=84880194357&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.CSL.2011.307
DO - 10.4230/LIPIcs.CSL.2011.307
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AN - SCOPUS:84880194357
SN - 9783939897323
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 307
EP - 321
BT - Computer Science Logic 2011 - 25th International Workshop/20th Annual Conference of the EACSL, CSL 2011
T2 - 25th International Workshop on Computer Science Logic, CSL 2011/20th Annual Conference of the European Association for Computer Science Logic, EACSL
Y2 - 12 September 2011 through 15 September 2011
ER -