Related papers: Clustering of solutions in hard satisfiability pro…
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution…
It is crucial to generate crafted SAT formulas with predefined solutions for the testing and development of SAT solvers since many SAT formulas from real-world applications have solutions. Although some generating algorithms have been…
Let $Z(F)$ be the number of solutions of a random $k$-satisfiability formula $F$ with $n$ variables and clause density $\alpha$. Assume that the probability that $F$ is unsatisfiable is $O(1/\log(n)^{1+\e})$ for $\e>0$. We show that…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
Much of the recent work on random constraint satisfaction problems has been inspired by ingenious but non-rigorous approaches from physics. The physics predictions typically come in the form of distributional fixed point problems that are…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data…
The satisfiability problem is one of the most famous problems in computer science. Its NP-completeness has been used to argue that SAT is intractable. However, there have been tremendous advances that allow SAT solvers to solve instances…
Relation between problem hardness and solution space structure is an important research aspect. Model d-k-CSP generates very hard instances when $r=1$ and $r$ is near 1, where $r$ represents normalized constraint density. We find that when…
The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the…
Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond…
We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the…