Languages that capture complexity classes
SIAM Journal on Computing
Chromatically optimal rigid graphs
Journal of Combinatorial Theory Series B
Handbook of combinatorics (vol. 2)
Algebraic properties and dismantlability of finite posets
Discrete Mathematics
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Duality theorems for finite structures (characterising gaps and good characterisations)
Journal of Combinatorial Theory Series B
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
On sparse graphs with given colorings and homomorphisms
Journal of Combinatorial Theory Series B
First-Order Definable Retraction Problems for Posets and Reflexive Graphs
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
On Digraph Coloring Problems and Treewidth Duality
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Existential Positive Types and Preservation under Homomorphisisms
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Linear time low tree-width partitions and algorithmic consequences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A Characterisation of First-Order Constraint Satisfaction Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A Probabilistic Approach to the Dichotomy Problem
SIAM Journal on Computing
A new line of attack on the dichotomy conjecture
Proceedings of the forty-first annual ACM symposium on Theory of computing
Dualities in full homomorphisms
European Journal of Combinatorics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
NP by means of lifts and shadows
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Ontology-based data access: a study through disjunctive datalog, CSP, and MMSNP
Proceedings of the 32nd symposium on Principles of database systems
Constraints, MMSNP and expander relational structures
Combinatorica
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We present a definition of the class NP in combinatorial context as the set of languages of structures defined by finitely many forbidden lifted substructures. We apply this to special syntactically defined subclasses and show how they correspond to naturally defined (and intensively studied) combinatorial problems. We show that some types of combinatorial problems like edge colorings and graph decompositions express the full computational power of the class NP. We then characterize Constraint Satisfaction Problems (i.e. H-coloring problems) which are expressible by finitely many forbidden lifted substructures. This greatly simplifies and generalizes the earlier attempts to characterize this problem. As a corollary of this approach we perhaps find a proper setting of the Feder and Vardi analysis of CSP languages within the class MMSNP.