Related papers: Phase Transition in Unrestricted Random SAT
From a stability perspective, a renewable generation (RG)-rich power system is a constrained system. As the quasistability boundary of a constrained system is structurally very different from that of an unconstrained system, finding the…
The QXORSAT problem is the quantified version of the satisfiability problem XORSAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated with random QXORSAT instances. We give a…
We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is…
Equilibrium statistical physics is applied to layered neural networks with differentiable activation functions. A first analysis of off-line learning in soft-committee machines with a finite number (K) of hidden units learning a perfectly…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
In QCD with two flavors of massless quarks, the chiral phase transition is plausibly in the same universality class as the classical four component Heisenberg antiferromagnet. Therefore, renormalization group techniques developed in the…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…
The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…
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…
Metallic states near the Mott insulator show a variety of quantum phases including various magnetic, charge ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a…
We provide a comprehensive view of various phase transitions in random $K$-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant ($M=2$) and semi-infinite…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
Information-theoretic phase transitions, such as the measurement-induced phase transition (MIPT), characterize the robustness of quantum dynamics to local monitoring and are naturally formulated in terms of trajectories conditioned on…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…
We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree (number of occurrences) of variables in various forms of redundancy-free boolean conjunctive normal forms…
We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\alpha=M/N$ close to the…