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...

Let (k, s)-SAT refer the family of satisfiability problems restricted to CNF formulas with exactly k distinct literals per clause and at most s occurrences of each variable. Kratochv́ıl, Savický and Tuza [6] show that there exists a function f(k) such that for all s ≤ f(k), all (k, s)-SAT instances are satisfiable whereas for k ≥ 3 and s > f(k), (k, s)-SAT is NP-complete. We define a new functio...

Background & Aims: Brucellosis is a public health problem in many developing countries, including Iran. Diagnosis is based on history, clinical manifestations and positive serum agglutination test (SAT) or Wright test. The purpose of this study was to evaluate the diagnostic value of SAT in pediatric Brucellosis. Methods: In this prospective study, during 2 years, 52 patients with clinical feat...

Die rasante technologische Entwicklung der letzten zwei Jahrzehnte ermöglicht heute die dauerhafte Speicherung riesiger Datenmengen durch den Computer. In fast allen Wissenschaften werden große Datenmengen gespeichert, die analysiert und verstanden werden müssen. Aber nicht nur in der Wissenschaft, sondern auch in kommerziellen Anwendungen und auch im alltäglichen Leben entstehen große Datenmen...

Motivated both by the work of Anstee, Griggs, and Sali on forbidden submatrices and also by the extremal sat-function for graphs, we introduce sat-type problems for matrices. Let F be a family of k-row matrices. A matrix M is called F-admissible if M contains no submatrix F ∈ F (as a row and column permutation of F ). A matrix M without repeated columns is F-saturated if M is F-admissible but t...

Definition 1.1. Let USAT ⊆ SAT be the set of formulas φ such that φ has a unique satisfying assignment. Let UP be the set of languages A such that there is a polytime TM M and a polynomial p such that x ∈ A⇔ ∃!y ∈ {0, 1}p(|x|) (M(x, y) = 1). Lemma 1.2 (Valiant-Vazirani). There is a randomized polynomial-computable reduction f from SAT to USAT with the following properties: [φ] ∈ SAT → [f(φ)] ∈ ...

We consider the algorithmic task of computing a maximal autarky for a clause-set F , i.e., a partial assignment which satisfies every clause of F it touches, and where this property is destroyed by adding any non-empty set of further assignments. We employ SAT solvers as oracles here, and we are especially concerned with minimising the number of oracle calls. Using the standard SAT oracle, log ...

Theorem proving is a challenging task for formal verification of systems. There exist many efforts to efficiently solve this problem, based for example on rewriting rules and/or SAT-based techniques. We propose an alternative of SAT-based techniques by using instead a counting SAT-based technique (denoted also #SAT). A SAT solver tests if a propositional formula F has at least one truth assignm...