相关论文: A variational description of the ground state stru…

A quantum machine consisting of interacting linear clusters of atoms is proposed for the 3SAT problem. Each cluster with two relevant states of collective motion can be used to register a Boolean variable. Given any 3SAT Boolean formula the…

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic…

We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of…

Several fragments of the satisfiability problem have been studied in the literature. Among these, Linear 3-SAT is a satisfaction problem in which each clause (viewed as a set of literals) intersects with at most one other clause; moreover,…

Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…

We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as…

In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…

Phase transition is an important feature of SAT problem. For random k-SAT model, it is proved that as r (ratio of clauses to variables) increases, the structure of solutions will undergo a sudden change like satisfiability phase transition…

We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…

The distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica…

A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often…

Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…

We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp…

Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…

Adversarial SAT (AdSAT) is a generalization of the satisfiability (SAT) problem in which two players try to make a boolean formula true (resp. false) by controlling their respective sets of variables. AdSAT belongs to a higher complexity…

The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…

Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…

Random $K$-satisfiability ($K$-SAT) is a model system for studying typical-case complexity of combinatorial optimization. Recent theoretical and simulation work revealed that the solution space of a random $K$-SAT formula has very rich…

Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…