Related papers: Adapting Real Quantifier Elimination Methods for C…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Solving avoidability problems in the area of string combinatorics often requires, in an initial step, the construction, via a computer program, of a very long word that does not contain any word that matches a given pattern. It is well…
Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
In recent years, the interest in interpretable classification models has grown. One of the proposed ways to improve the interpretability of a rule-based classification model is to use sets (unordered collections) of rules, instead of lists…
Polynomial quantified entailments with existentially and universally quantified variables arise in many problems of verification and program analysis. We present PolyQEnt which is a tool for solving polynomial quantified entailments in…
We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with…
We study Satisfiability Modulo Theories (SMT) enriched with the so-called Ramsey quantifiers, which assert the existence of cliques (complete graphs) in the graph induced by some formulas. The extended framework is known to have…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares…
Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
When Model Predictive Control (MPC) is used in real-time to control linear systems, quadratic programs (QPs) need to be solved within a limited time frame. Recently, several parametric methods have been proposed that certify the number of…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…