Related papers: On the Usefulness of Predicates
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
We show that computing even very coarse approximations of critical points is intractable for simple classes of nonconvex functions. More concretely, we prove that if there exists a polynomial-time algorithm that takes as input a polynomial…
Probabilistically checkable proofs of proximity (PCPP) are proof systems where the verifier is given a 3SAT formula, but has only oracle access to an assignment and a proof. The verifier accepts a satisfying assignment with a valid proof,…
In this paper, we present a polynomial-time algorithm that approximates sufficiently high-value Max 2-CSPs on sufficiently dense graphs to within $O(N^{\varepsilon})$ approximation ratio for any constant $\varepsilon > 0$. Using this…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…
In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…
Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
The m-sophistication of a finite binary string x is introduced as a generalization of some parameter in the proof that complexity of complexity is rare. A probabilistic near sufficient statistic of x is given which length is upper bounded…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
In this paper, we present a novel approach for conformal prediction (CP), in which we aim to identify a set of promising prediction candidates -- in place of a single prediction. This set is guaranteed to contain a correct answer with high…
We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…
This paper studies complete $k$-Constraint Satisfaction Problems (CSPs), where an $n$-variable instance has exactly one nontrivial constraint for each subset of $k$ variables, i.e., it has $\binom{n}{k}$ constraints. A recent work started a…
In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…
We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…
Replicability, introduced by (Impagliazzo et al. STOC '22), is the notion that algorithms should remain stable under a resampling of their inputs (given access to shared randomness). While a strong and interesting notion of stability, the…
Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen…