
Necessary and Sufficient Condition for Satisfiability of a Boolean Formula in CNF and its Implications on P versus NP problem
In this paper, a necessary and sufficient condition for satisfiability o...
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NearBalanced Incomplete Block Designs with An Application to Poster Competitions
Judging scholarly posters creates a challenge to assign the judges effic...
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An Improved Exact Algorithm for the Exact Satisfiability Problem
The Exact Satisfiability problem, XSAT, is defined as the problem of fin...
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Subexponential complexity of regular linear CNF formulas
The study of regular linear conjunctive normal form (LCNF) formulas is o...
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Anova of Balanced Variance Component Models
Balanced linear models with fixed effects are taught in undergraduate pr...
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The Satisfiability Problem for Boolean Set Theory with a Choice Correspondence
Given a set U of alternatives, a choice (correspondence) on U is a contr...
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Fuzzy Maximum Satisfiability
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to ...
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Balanced incomplete block designs and exact satisfiability
The paper explores the correspondence between balanced incomplete block designs (BIBD) and certain linear CNF formulas by identifying the points of a block design with the clauses of the Boolean formula and blocks with Boolean variables. Parallel classes in BIBDs correspond to XSAT solutions in the corresponding formula. This correspondence allows for transfers of results from one field to the other. As a new result we deduce from known satisfiability theorems that the problem of finding a parallel class in a partially balanced incomplete block design is NPcomplete.
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