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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…
Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random $k$-SAT model well for all clause/variable densities and all inverse…
A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We furnish solid evidence, both theoretical and empirical, towards the existence of a deterministic algorithm for random sparse $\#\Omega(\log n)$-SAT instances, which computes the exact counting of satisfying assignments in sub-exponential…
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…
Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value…
A detailed Monte Carlo-study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies $\alpha_3 \leq 4.262$. If the assumption…
In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of…
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…
In this note I will review some of the recent results that have been obtained in the probabilistic approach to the random satisfiability problem. At the present moment the results are only heuristic. In the case of the random…
We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of…
Limits on the number of satisfying assignments for CNS instances with n variables and m clauses are derived from various inequalities. Some bounds can be calculated in polynomial time, sharper bounds demand information about the…
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula $\varphi$ in CNF such that exactly one literal in each clause is assigned to be "1" and the other literals in the same clause…
We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…
Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming…
For random CNF formulae with m clauses, n variables and an unrestricted number of literals per clause the transition from high to low satisfiability can be determined exactly for large n. The critical density m/n turns out to be strongly…
SARRIGUREN, a new complete algorithm for SAT based on counting clauses (which is valid also for Unique-SAT and #SAT) is described, analyzed and tested. Although existing complete algorithms for SAT perform slower with clauses with many…