Related papers: Tractable Combinations of Theories via Sampling
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…
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…
A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…
The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of…
What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…
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…
The celebrated Trakhtenbrot's theorem states that the set of finitely valid sentences of first-order logic is not computably enumerable. In this note we will extend this theorem by proving that the finite satisfiability problem of any…
A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…
Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
Let T be an SMT solver with no theory solvers except for Quantifier Instantiation. Given a set of first-order clauses S saturated by Resolution (with a valid literal selection function) we show that T is complete if its Trigger function is…
Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…
A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…
Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…