Q-resolution is a proof system for quantified Boolean formulas (QBFs) in prenex conjunctive normal form (PCNF) which underlies search-based QBF solvers with clause and cube learning (QCDCL). With the aim to derive and learn stronger clauses and cubes earlier in the search, we generalize the axioms of the Q-resolution calculus resulting in an exponentially more powerful proof system. The general...

The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066–1077]). We provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of R2 values (based on orthogonal coding) or sums of squared canonical correlatio...

In this paper we initiate the study of the AND-OR directed feedback vertex set problem from the viewpoint of approximation algorithms. This ANDOR feedback vertex set problem is motivated by a practical deadlock resolution problem that appears in the development of distributed database systems. This problem also turns out be a natural generalization of the directed feedback vertex set problem. A...

This paper is devoted to investigate resolution for quantified generalized clause-sets (QCLS). The soundness and refutation completeness are proved. Then quantified generalized Horn clause-sets are introduced for which a restricted resolution, called quantified positive unit resolution, is proved to be sound and refutationally complete. Moreover, it is shown that the satisfiability for quantifi...

In this paper, an α-resolution method for a set of lattice-valued Horn generalized clauses is established in lattice-valued propositional logic systemL P(X) based on lattice implication algebra. Firstly, the notions of lattice-valued Horn generalized clause, normal lattice-valued Horn generalized clause and unit latticevalued Horn generalized clause are given in L P(X). Then, the α-resolution o...