TY - GEN

T1 - Church synthesis problem with parameters

AU - Rabinovich, Alexander

PY - 2006

Y1 - 2006

N2 - The following problem is known as the Church Synthesis problem: Input: an MLO formula ψ(X,Y). Task: Check whether there is an operator Y = F(X) such that Nat |= ∀Xψ(X, F(X)) (1) and if so, construct this operator. Büchi and Landweber proved that the Church synthesis problem is decidable; moreover, they proved that if there is an operator F which satisfies (1), then (1) can be satisfied by the operator defined by a finite state automaton. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a unary predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of 〈Nat, <, P〉 is decidable. We also show that the Büchi-Landweber theorem can be extended only to ultimately periodic parameters.

AB - The following problem is known as the Church Synthesis problem: Input: an MLO formula ψ(X,Y). Task: Check whether there is an operator Y = F(X) such that Nat |= ∀Xψ(X, F(X)) (1) and if so, construct this operator. Büchi and Landweber proved that the Church synthesis problem is decidable; moreover, they proved that if there is an operator F which satisfies (1), then (1) can be satisfied by the operator defined by a finite state automaton. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a unary predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of 〈Nat, <, P〉 is decidable. We also show that the Büchi-Landweber theorem can be extended only to ultimately periodic parameters.

UR - http://www.scopus.com/inward/record.url?scp=33750350459&partnerID=8YFLogxK

U2 - 10.1007/11874683_36

DO - 10.1007/11874683_36

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AN - SCOPUS:33750350459

SN - 3540454586

SN - 9783540454588

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 546

EP - 561

BT - Computer Science Logic - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Proceedings

PB - Springer Verlag

T2 - 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL

Y2 - 25 September 2006 through 29 September 2006

ER -