Related papers: Dichotomy for Real Holant$^c$ Problems
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
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…
In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP) over a constraint language $\Gamma$ is tractable if and only if $\Gamma$ is preserved by a weak near-unanimity (WNU) operation. After many efforts and partial…
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…
We study formalisms for temporal and spatial reasoning in the modern context of Constraint Satisfaction Problems (CSPs). We show how questions on the complexity of their subclasses can be solved using existing results via the powerful use…
An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…
The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…
In a valued constraint satisfaction problem (VCSP), the goal is to find an assignment of labels to variables that minimizes a given sum of functions. Each function in the sum depends on a subset of variables, takes values which are rational…
A natural strengthening of an algorithm for the (promise) constraint satisfaction problem is its singleton version: we first fix a variable to an element from its domain, then run the algorithm, and remove the element from the domain if the…
We introduce the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K. This natural problem applies to…
We construct a theory of holant clones to capture the notion of expressibility in the holant framework. Their role is analogous to the role played by functional clones in the study of weighted counting Constraint Satisfaction Problems. We…
We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in…
We prove that P = NP implies #P = FP by exploiting the topological structure of 3SAT solution spaces. The argument proceeds via a dichotomy: any polynomial-time algorithm for 3SAT either operates without global knowledge of the…
We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
Assume $D$ is a finite set and $R$ is a finite set of functions from $D$ to the natural numbers. An instance of the minimum $R$-cost homomorphism problem ($MinHom_R$) is a set of variables $V$ subject to specified constraints together with…
A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation…
The classifications of temporal and phylogeny constraint languages stand among the most seminal complexity classifications within infinite-domain Constraint Satisfaction Problems (CSPs), yet remain the most mysterious in terms of algorithms…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…