Abstract Given an unsatisfiable Boolean formula F in CNF, subset of clauses U is called Minimal Unsatisfiable Subset (MUS) if every proper satisfiable. Since MUSes serve as explanations for the unsatisfiability , find applications a wide variety domains. The availability efficient SAT solvers has aided development scalable techniques finding and enumerating past two decades. Building on recent ...

A continuous open finite-to-one surjection f preserves Cantor rank. If the domain of f is a Hausdorff compact space, Cantor degree variations are bounded by the maximal size of the finite fibres. If the fibres are infinite, we show inequalities involving the maximal and minimal rank of the fibres. A closed preorder on a denumerable Hausdorff compact space is the intersection of clopen preoders....

Recently there has been exciting progress in our understanding of algorithmic randomness for reals, its calibration, and its connection with classical measures of complexity such as degrees of unsolvability. In this paper, I will give a biased review of (some of) this progress. In particular, I will concentrate upon randomness for reals. In this paper “real” will mean a member of Cantor space 2...

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...