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Using methods and ideas from statistical mechanics, we propose a simple method for obtaining rigorous upper bounds for satisfiability transition in random boolean expressions composed of N variables and M clauses with K variables per…
Horn-satisfiability or Horn-SAT is the problem of deciding whether a satisfying assignment exists for a Horn formula, a conjunction of clauses each with at most one positive literal (also known as Horn clauses). It is a well-known…
The amount of information in satisfiability problem (SAT) is considered. SAT can be polynomial-time solvable when the solving algorithm holds an exponential amount of information. It is also established that SAT Kolmogorov complexity is…
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…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
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 problem 2-quantum-satisfiability (2-QSAT) is the generalisation of the 2-CNF-SAT problem to quantum bits, and is equivalent to determining whether or not a spin-1/2 Hamiltonian with two-body terms is frustration-free. Similarly to the…
The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be…
Unlike its cousin 3SAT, the NAE-3SAT (not-all-equal-3SAT) problem has the property that spectral/SDP algorithms can efficiently refute random instances when the constraint density is a large constant (with high probability). But do these…
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 prove that throughout the satisfiable phase, the logarithm of the number of satisfying assignments of a random 2-SAT formula satisfies a central limit theorem. This implies that the log of the number of satisfying assignments exhibits…
We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires…
A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…
In this paper we determine the complexity of a broad class of problems that extends the temporal constraint satisfaction problems. To be more precise we study the problems Poset-SAT($\Phi$), where $\Phi$ is a given set of quantifier-free…
This note considers checking satisfiability of sets of propositional clauses (SAT instances). It shows that "unipolar sets" of clauses (containing no positive or no negative clauses) provide an "early sign" of satisfiability of SAT…
Consider a system of $m$ polynomial equations $\{p_i(x) = b_i\}_{i \leq m}$ of degree $D\geq 2$ in $n$-dimensional variable $x \in \mathbb{R}^n$ such that each coefficient of every $p_i$ and $b_i$s are chosen at random and independently…
Let F be a random k-SAT formula on n variables, formed by selecting uniformly and independently m = rn out of all possible k-clauses. It is well-known that if r>2^k ln 2, then the formula F is unsatisfiable with probability that tends to 1…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible…
The satisfiability problem is known to be $\mathbf{NP}$-complete in general and for many restricted cases. One way to restrict instances of $k$-SAT is to limit the number of times a variable can be occurred. It was shown that for an…