相关论文: Coarse and Sharp Thresholds of Boolean Constraint …
Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a $(\mathbb{Q}\cup\{\infty\})$-valued objective function given as a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on labels…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i =…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
We analyze the sketching approximability of constraint satisfaction problems on Boolean domains, where the constraints are balanced linear threshold functions applied to literals. In~particular, we explore the approximability of…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
Choosing decision variables deterministically (deterministic decision-making) can be regarded as a particular case of choosing decision variables probabilistically (probabilistic decision-making). It is necessary to investigate whether…
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 initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
We consider random systems of equations x_1 + ... + x_k = a; 0 <= a <= 2 which are interpreted as equations modulo 3: We show for k >= 15 that the satisfiability threshold of such systems occurs where the 2-core has density 1: We show a…
We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for…
The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled…
It is shown that under standard hypotheses, if stochastic approximation iterates remain tight, they converge with probability one to what their o.d.e. limit suggests. A simple test for tightness (and therefore a.s. convergence) is provided.…
A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point $p_{\mathrm {sd}}(q)=\sqrt{q}/(1+\sqrt{q})$, the Ising model with…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…