相关论文: Pseudo-Boolean Proof Logging for Optimal Classical…
We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on algebraic properties, our algorithm exploits the regularity…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
We introduce a data-driven approach to analyze the performance of continuous optimization algorithms using generalization guarantees from statistical learning theory. We study classical and learned optimizers to solve families of parametric…
Model counting, or counting the satisfying assignments of a Boolean formula, is a fundamental problem with diverse applications. Given #P-hardness of the problem, developing algorithms for approximate counting is an important research area.…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems are based on sums…
The growing utilization of planning tools in practical scenarios has sparked an interest in generating multiple high-quality plans. Consequently, a range of computational problems under the general umbrella of top-quality planning were…
Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…
We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…
We explore the possibility of accelerating the formal verification of classical programs with a quantum computer. A common source of security flaws stems from the existence of common programming errors like use after free, null-pointer…
Nonnegativity certificates can be used to obtain tight dual bounds for polynomial optimization problems. Hierarchies of certificate-based relaxations ensure convergence to the global optimum, but higher levels of such hierarchies can become…
Requirements driven search-based testing (also known as falsification) has proven to be a practical and effective method for discovering erroneous behaviors in Cyber-Physical Systems. Despite the constant improvements on the performance and…
We consider the problem of minimizing a polynomial $f$ over the binary hypercube. We show that, for a specific set of polynomials, their binary non-negativity can be checked in a polynomial time via minimum cut algorithms, and we construct…
This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the…
During the execution of a test plan, a test manager may decide to drop a test case if its result can be inferred from already executed test cases. We show that it is possible to automatically generate a test plan to exploit the potential to…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that…
We study the problem of efficiently certifying upper bounds on the independence number of $\ell$-uniform hypergraphs. This is a notoriously hard problem, with efficient algorithms failing to approximate the independence number within…
Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce…
An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by…