A subfamily G⊆F⊆2[n] of sets is a non-induced (weak) copy poset P in F if there exists bijection i:P→G such that p≤Pq implies i(p)⊆i(q). In the case where addition holds and only i(p)⊆i(q), then G an induced (strong) F. We consider minimum number sat(n,P) [resp. sat⁎(n,P)] family F⊆2[n] can have without containing [induced] being maximal with respect to this property, i.e., any G∈2[n]∖F creates...

We investigate the complexity of satis ability problems that surprisingly to the best of our knowledge have not yet been considered in the literature CNF SAT which we also denote by SAT asks for an assignment for a given formula that satis es all of its clauses While SAT is NP complete what is the complexity of SAT where it is asked for an assignment that satis es an odd number of clauses We sh...

The parameterized satisfiability problem over a set of Boolean relations Γ (SAT(Γ)) is the problem of determining whether a conjunctive formula over Γ has at least one model. Due to Schaefer’s dichotomy theorem the computational complexity of SAT(Γ), modulo polynomial-time reductions, has been completely determined: SAT(Γ) is always either tractable or NP-complete. More recently, the problem of...

The problem of determining whether a propositional Boolean formula can be true is called the Boolean Satisfiability Problem or SAT. SAT is an important and widely studied problem in computer science. In practice, SAT is a core problem in many applications such as Electronic Design Automation (EDA) and Artificial Intelligence (AI). This thesis investigates various problems in the design and impl...

Due to the widespread demands for efficient Propositional Satisfiability (SAT) solvers and its derivatives in Electronic Design Automation applications, methods to boost the performance of the SAT solver are highly desired. This dissertation aims to enhance the performance of SAT and related SAT solving problems. A hybrid solution to boost SAT solver performance is proposed as an initial attack...

We investigate how SAT coaching (also known as “SAT Prep”) affects the value of the SAT as an evaluative tool, vis-á-vis other applicant signals such as high school transcript and letters of recommendation. Theoretically, we develop a simple “meritocratic” model of selective college admission that illustrates how SAT Prep may alter the emphasis a college places on SAT scores, depending on perce...

Propositional model counting (#SAT), i.e., counting the number of satisfying assignments of a propositional formula, is a problem of significant theoretical and practical interest. Due to the inherent complexity of the problem, approximate model counting, which counts the number of satisfying assignments to within given tolerance and confidence level, was proposed as a practical alternative to ...

A growing number of problem domains are successfully being tackled by SAT solvers. This thesis contributes to that trend by pushing the state-of-the-art of core SAT algorithms and their implementation, but also in several important application areas. It consists of five papers: the first details the implementation of the SAT solver MINISAT and the other four papers discuss specific issues relat...

We provide some evidence that Unique k-SAT is as hard to solve as general k-SAT, where k-SAT denotes the satisfiability problem for k-CNFs with at most k literals in each clause and Unique k-SAT is the promise version where the given formula has 0 or 1 solutions. Namely, defining for each k > 1, sk = inf{δ > 0 | ∃ a O(2)-time randomized algorithm for k-SAT} and, similarly, σk = inf{δ > 0 | ∃ a ...