11 research outputs found
CSP dichotomy for ω-categorical monadically stable structures
The constraint satisfaction problem (CSP) over a structure A with a finite relational signature, denoted by CSP(A), is the problem of deciding whether a given finite structure B with the same signature as A has a homomorphism to A.
Using concepts and techniques from universal algebra, Bulatov and Zhuk proved independently that if A is finite, then the CSP over A is always in P or NP-complete. Following this result, it is a natural question to ask when and how this dichotomy can be generalized for infinite structures. The infinite-domain CSP dichotomy conjecture (originally formulated by Bodirsky and Pinsker [BPP14]) states that the same complexity dichotomy holds for first-order reducts of finitely bounded homogeneous structures. This conjecture has been solved for many special classes of structures. In this thesis we are developing new techniques involving canonical polymorphisms to attack this conjecture. Using these techniques we prove a new CSP dichotomy result, namely we show that the CSP over every finitely related ω-categorical monadically stable structure is in P or NP-complete
Canonical Polymorphisms of Ramsey Structures and the Unique Interpolation Property
Constraint satisfaction problems 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
obtain polynomial-time tractability results for such CSPs is a certain
reduction to polynomial-time tractable finite-domain CSPs defined over k-types,
for a sufficiently large k. We give sufficient conditions when this method can
be applied and illustrate how to use the general results to prove a new
complexity dichotomy for first-order expansions of the basic relations of the
spatial reasoning formalism RCC5
Taylor is prime
We study the Taylor varieties and obtain new characterizations of them via
compatible reflexive digraphs. Based on our findings, we prove that in the
lattice of interpretability types of varieties, the filter of the types of all
Taylor varieties is prime
Infinitely many reducts of homogeneous structures
Funding: National Research, Development and Innovation Fund of Hungary, financed under the FK 124814 funding scheme (second author).This work is dedicated to Tamás E. Schmidt. It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.PostprintPeer reviewe
CSP dichotomy for ω-categorical monadically stable structures
The constraint satisfaction problem (CSP) over a structure A with a finite relational signature, denoted by CSP(A), is the problem of deciding whether a given finite structure B with the same signature as A has a homomorphism to A.
Using concepts and techniques from universal algebra, Bulatov and Zhuk proved independently that if A is finite, then the CSP over A is always in P or NP-complete. Following this result, it is a natural question to ask when and how this dichotomy can be generalized for infinite structures. The infinite-domain CSP dichotomy conjecture (originally formulated by Bodirsky and Pinsker [BPP14]) states that the same complexity dichotomy holds for first-order reducts of finitely bounded homogeneous structures. This conjecture has been solved for many special classes of structures. In this thesis we are developing new techniques involving canonical polymorphisms to attack this conjecture. Using these techniques we prove a new CSP dichotomy result, namely we show that the CSP over every finitely related ω-categorical monadically stable structure is in P or NP-complete
CSP dichotomy for ω-categorical monadically stable structures
The constraint satisfaction problem (CSP) over a structure A with a finite relational signature, denoted by CSP(A), is the problem of deciding whether a given finite structure B with the same signature as A has a homomorphism to A.
Using concepts and techniques from universal algebra, Bulatov and Zhuk proved independently that if A is finite, then the CSP over A is always in P or NP-complete. Following this result, it is a natural question to ask when and how this dichotomy can be generalized for infinite structures. The infinite-domain CSP dichotomy conjecture (originally formulated by Bodirsky and Pinsker [BPP14]) states that the same complexity dichotomy holds for first-order reducts of finitely bounded homogeneous structures. This conjecture has been solved for many special classes of structures. In this thesis we are developing new techniques involving canonical polymorphisms to attack this conjecture. Using these techniques we prove a new CSP dichotomy result, namely we show that the CSP over every finitely related ω-categorical monadically stable structure is in P or NP-complete
Infinitely many reducts of homogeneous structures
This work is dedicated to Tamás E. Schmidt.It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts