Related papers: Finding the right path: statistical mechanics of c…
On finite structures, there is a well-known connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has…
Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…
We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satisfiable to a region where almost all…
Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value…
This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…
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;…
Solving combinatorial optimization problems involve satisfying a set of hard constraints while optimizing some objectives. In this context, exact or approximate methods can be used. While exact methods guarantee the optimal solution, they…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
Wordle presents an algorithmically rich testbed for constraint satisfaction problem (CSP) solving. While existing solvers rely on information-theoretic entropy maximization or frequency-based heuristics without formal constraint treatment,…
In this work, we study verification and synthesis problems for safety specifications over unknown discrete-time stochastic systems. When a model of the system is available, barrier certificates have been successfully applied for ensuring…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
The complexity of the promise constraint satisfaction problem $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$ is largely unknown, even for symmetric $\mathbf{A}$ and $\mathbf{B}$, except for the case when $\mathbf{A}$ and $\mathbf{B}$ are…
In a broad class of sparse random constraint satisfaction problems(CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica…
This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains.…
We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…
We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and…