John G. Sanderson (auth.)'s A Relational Theory of Computing PDF

By John G. Sanderson (auth.)

ISBN-10: 3540099875

ISBN-13: 9783540099871

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Gn (a1 , . . , am )). 46 F. 2. e. if f ∈ C (n) , g1 , . . , gn ∈ C (m) then always f [g1 , . . , gn ] ∈ C. The set of all clones of functions on D is denoted by LOD . If F ⊆ OD is a set of functions, then clone F := {C ⊆ OD | C is a clone and F ⊆ C} denotes the clone, generated by F . ) Examples of clones are the set OD of all functions on D, the set JD of all elementary functions, or the set of all monotone Boolean functions on the twoelement set D = {0, 1}. We mention that clone is an algebraic closure operator on OD , and LOD is the corresponding algebraic lattice.

28. [Frozen variables] – If Γ ⊇ Inv(N2 ), then Frozen-Var(Γ ) is DP-complete. – Otherwise, if Γ ⊇ Inv(I0 ) or Γ ⊇ Inv(I1 ), then Frozen-Var(Γ ) is coNP-complete. – In all other cases Frozen-Var(Γ ) is in P. Connectivity properties of the solution space were investigated by Gopalan, Kolatitis, Maneva and Papadimitriou in [GKMP06]. In particular they studied the st-connectivity problem defined as follows. Problem: Input: Question: st-Conn(Γ ) a Γ -formula φ, and two satisfying assignments s and t of φ Is there a path in G(φ), the subgraph of the n-dimensional hypercube induced by the solutions of φ, from s to t?

In: Proceedings of the 37th Symposium on Theory of Computing, pp. 376–385. : Optimal satisfiability for propositional calculi and constraint satisfaction problems. : The complexity of satisfiability problems. In: Proccedings 10th Symposium on Theory of Computing, pp. 216–226. ACM Press, New York (1978) Boolean Constraint Satisfaction Problems: When Does Post’s Lattice Help? : Algebraic Techniques for Satisfiability Problems. : The Weak Base Method for Constraint Satisfaction. : Word problems requiring exponential time.

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John G. Sanderson (auth.)'s A Relational Theory of Computing PDF
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