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Feder-Vardi conjecture, which proposed that every finite-domain Constraint Satisfaction Problem (CSP) is either in P or it is NP-complete, has been solved independently by Bulatov and Zhuk almost ten years ago. Bodirsky-Pinsker conjecture…
In recent years, much attention has been placed on the complexity of graph homomorphism problems when the input is restricted to ${\mathbb P}_k$-free and ${\mathbb P}_k$-subgraph-free graphs. We consider the directed version of this…
We establish a framework that allows us to transfer results between some constraint satisfaction problems with infinite templates and promise constraint satisfaction problems. On the one hand, we obtain new algebraic results for…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
We investigate the `local consistency implies global consistency' principle of strict width among structures within the scope of the Bodirsky-Pinsker dichotomy conjecture for infinite-domain Constraint Satisfaction Problems (CSPs). Our main…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
The constraint satisfaction problem (CSP) can be formulated as a homomorphism problem between relational structures: given a structure $\mathcal{A}$, for any structure $\mathcal{X}$, whether there exists a homomorphism from $\mathcal{X}$ to…
Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite…
The Feder-Vardi dichotomy conjecture for Constraint Satisfaction Problems (CSPs) with finite templates, confirmed independently by Bulatov and Zhuk, has an extension to certain well-behaved infinite templates due to Bodirsky and Pinsker…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
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…
Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…
Fagin defined the class $NP$ by the means of Existential Second-Order logic. Feder and Vardi expressed it (up to polynomial equivalence) by special fragments of Existential Second-Order logic (SNP), while the authors used forbidden expanded…
We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the…
The Dichotomy Conjecture for constraint satisfaction problems (CSPs) states that every CSP is in P or is NP-complete (Feder-Vardi, 1993). It has been verified for conservative problems (also known as list homomorphism problems) by A.…
Two major milestones on the road to the full complexity dichotomy for finite-domain constraint satisfaction problems were Bulatov's proof of the dichotomy for conservative templates, and the structural dichotomy for smooth digraphs of…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…