Related papers: Satisfiability and computing van der Waerden numbe…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
In this work, a functional variant of the polynomial analogue of the classical Gandy's fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of the recursive function does not go beyond the…
In this article, we show that the completion problem, i.e. the decision problem whether a partial structure can be completed to a full structure, is NP-complete for many combinatorial structures. While the gadgets for most reductions in…