Related papers: Scale-Free Random SAT Instances
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…
Scale-free distributions and correlation functions found in financial data are reminiscent of the scale invariance of physical observables in the vicinity of a critical point. Here, we present empirical evidence for a transition phenomenon,…
A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying…
Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase space methods, namely the positive P-representation. In this approach the moments of quantum observables are evaluated as moments of…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate…
The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to…
We extend the knowledge about so-called structural restrictions of $\mathrm{\#SAT}$ by giving a polynomial time algorithm for $\beta$-acyclic $\mathrm{\#SAT}$. In contrast to previous algorithms in the area, our algorithm does not proceed…
The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbors interactions. In order to generate the random magnetic fields, we have considered random…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
Probing heavy new physics beyond the Standard Model (SM) increasingly relies on global effective field theory (EFT) likelihoods. We introduce differentiable, multi-scale EFT likelihoods that combine renormalization-group evolution,…
The spectral density for random matrix $\beta$ ensembles can be written in terms of the average of the absolute value of the characteristic polynomial raised to the power of $\beta$, which for even $\beta$ is a polynomial of degree…
Let $\mathcal{P}_{\beta}^{(V)} (N_{\cal I})$ be the probability that a $N\times N$ $\beta$-ensemble of random matrices with confining potential $V(x)$ has $N_{\cal I}$ eigenvalues inside an interval ${\cal I}=[a,b]$ of the real line. We…
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…
Let $\varPhi$ be a uniformly distributed random $k$-SAT formula with $n$ variables and $m$ clauses. For clauses/variables ratio $m/n \leq r_{k\text{-SAT}} \sim 2^k\ln2$ the formula $\varPhi$ is satisfiable with high probability. However, no…
Stochastic Boolean Satisfiability (SSAT) is a logical formalism to model decision problems with uncertainty, such as Partially Observable Markov Decision Process (POMDP) for verification of probabilistic systems. SSAT, however, is limited…
We present DeepSAT, a novel end-to-end learning framework for the Boolean satisfiability (SAT) problem. Unlike existing solutions trained on random SAT instances with relatively weak supervision, we propose applying the knowledge of the…
We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…