We present a novel approach to solve quantified boolean formulas with one quantifier alternation (2QBF). The algorithm incrementally adds new constraints to the formula until the constraints describe a unique Skolem function or until the absence of a Skolem function is detected. Backtracking is required if the absence of Skolem functions depends on the newly introduced constraints. We present t...

Let D = (V, A)be a digraph. An injective function f: V(D) → {1,2, .... p} is said to be sign pairity difference cordial labeling if the induced arc f∗: A(D) {0,1} defined byf∗ ((μ, ν)) satisfiesthe condition that |ef 0-ef(1)| ≤ 1 where, ef(0) number of arcs with label 0 and ef(1) 1. In this paper, we analyze existence in digraphs Directed Path , Cycle, Outstar, Inwheel Downcomb by K.Palani et.al.

Stochastic Boolean satisfiability (SSAT) is a formalism allowing decision-making for optimization under quantitative constraints. Although SSAT solvers are active development, existing do not provide Skolem-function witnesses, which crucial practical applications. In this work, we develop new witness-generating solver, SharpSSAT, integrates techniques, including component caching, clause learni...

The subject of this note is a challenging conjecture about X-rays of permutations which is a special case of a conjecture regarding Skolem sequences. In relation to this, Brualdi and Fritscher [Linear Algebra and its Applications, 2014] posed the following problem: Determine a bijection between extremal Skolem sets and binary Hankel X-rays of permutation matrices. We give such a bijection, alon...