相关论文: The SAT Phase Transition

Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially…

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…

As general theories, currently there are concentration inequalities (of random walk) only for the cases of independence and martingale differences. In this paper, the concentration inequalities are extended to more general situations. In…

Many procedures for SAT and SAT-related problems -- in particular for those requiring the complete enumeration of satisfying truth assignments -- rely their efficiency on the detection of partial assignments satisfying an input formula. In…

Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…

The runtime performance of modern SAT solvers is deeply connected to the phase transition behavior of CNF formulas. While CNF solving has witnessed significant runtime improvement over the past two decades, the same does not hold for…

We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of…

An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a…

Quantum k-SAT is the problem of deciding whether there is a n-qubit state which is perpendicular to a set of vectors, each of which lies in the Hilbert space of k qubits. Equivalently, the problem is to decide whether a particular type of…

Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist;…

Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…

Compact stars above a critical stellar mass develop large scalar fields in some scalar-tensor theories. This scenario, called spontaneous scalarization, has been an intense topic of study since it passes weak-field gravity tests naturally…

The Boolean Satisfiability Problem is perhaps one of the most well-known problems in theoretical computer science. On the one hand, it is proven to be NP-complete, which means that it is generally considered hard to solve. On the other…

We describe an extensive study of search in GSAT, an approximation procedure for propositional satisfiability. GSAT performs greedy hill-climbing on the number of satisfied clauses in a truth assignment. Our experiments provide a more…

A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in…

For large clause-to-variable ratio, typical K-SAT instances drawn from the uniform distribution have no solution. We argue, based on statistical mechanics calculations using the replica and cavity methods, that rare satisfiable instances…

Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…

We introduce a new model for the generation of random satisfiability problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt and Zecchina, which is a variant of the famous K-SAT model: it is extended to q-state…

We introduce the idea of an understanding with respect to a set of clauses as a satisfying truth assignment explained by the contexts of the literals in the clauses. Following this idea, we present a mechanical process that obtains, if it…