( , ) k s SAT − is the propositional satisfiable problem restricted to instances where each clause has exactly k distinct literals and every variable occurs at most s times. It is known that there exits an exponential function f such that for ( ) s f k ≤ , all ( , ) k s SAT − instances are satisfiable, but ( , ( ) 1) k f k SAT + − is already NPcomplete ( 3 k ≥ ). Therefore, we call the function...

We establish the satisfiability threshold for random $k$-SAT all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_{\rm sat}(k)$ such that formula of clause $\alpha$ is high probability satisfiable $\alpha\lt \alpha_{\rm sat}$, and unsatisfiable $\alpha>\alpha_{\rm sat}$. show given explicitly by one-step replica symmetry breaking prediction from stat...

association of satellite rna with cucumber mosaic virus (cmv) leads to either attenuation or enhancement of the viral symptoms. for detection of the satellite rnas in iranian isolates of cmv, plant samples showing viral symptoms were collected from different farms in the provinces of east- and west- azerbayjan and ardebil. these samples were inoculated onto the experimental host plants in green...

Max-SAT is an extensively studied optimization problem and variations of Max-SAT (like Partial Max-SAT and Weighted Max-SAT) can be used for computing minimal diagnoses. In this report we (1) describe a family of algorithms for computing minimal diagnoses based on Max-SAT and (2) experimentally evaluate the performance and optimality of these algorithms on a benchmark consisting of 74XXX/ISCAS8...

In recent years, Parallel SAT solvers have leveraged with the so called Parallel Portfolio architecture. In this setting, a collection of independent ConflictDirected Clause Learning (CDCL) algorithms compete and cooperate through Clause Sharing. However, when the number of cores increases, systematic clause sharing between CDCLs can slow down the search performance. Previous work has shown how...

The theory of hierarchical Boolean satisfiability (SAT) solving proposed in this paper is based on a strict axiomatic system and introduces a new important notion of implicativity. The theory makes evident that increasing implicativity is the core of SAT-solving. We provide a theoretical basis for increasing the implicativity of a given SAT instance and for organizing SAT-solving in a hierarchi...

Description of a polynomial time reduction of SAT to 2-SAT of polynomial size.

We study the problem of building structure-aware SAT-solvers based on resolution. In this study, we use the idea of treating a resolution proof as a process of Boundary Point Elimination (BPE). We identify two problems of using SAT-algorithms with Conflict Driven Clause Learning (CDCL) for structure-aware SAT-solving. We introduce a template of resolution based SAT-solvers called BPE-SAT that i...

I discuss recent progress in developing and exploiting connections between SAT algorithms and circuit lower bounds. The centrepiece of the article is Williams’ proof that NEXP * ACC0, which proceeds via a new algorithm for ACC0-SAT beating brute-force search. His result exploits a formal connection from non-trivial SAT algorithms to circuit lower bounds. I also discuss various connections in th...

In a regular (d,k)-CNF formula, each clause has length k and variable appears d times. A structure such as this is symmetric, the satisfiability problem of symmetric called (d,k)-SAT for short. The exact 2-(d,k)-SAT that formula F, if there truth assignment T, then exactly two literals in F are true. If contains only positive or negative literals, satisfiable T with size 2n/k 2-exactly satisfia...