189 research outputs found
New Ramsey Classes from Old
Let C_1 and C_2 be strong amalgamation classes of finite structures, with
disjoint finite signatures sigma and tau. Then C_1 wedge C_2 denotes the class
of all finite (sigma cup tau)-structures whose sigma-reduct is from C_1 and
whose tau-reduct is from C_2. We prove that when C_1 and C_2 are Ramsey, then
C_1 wedge C_2 is also Ramsey. We also discuss variations of this statement, and
give several examples of new Ramsey classes derived from those general results.Comment: 11 pages. In the second version, to be submitted for journal
publication, a number of typos has been removed, and a grant acknowledgement
has been adde
Distance Constraint Satisfaction Problems
We study the complexity of constraint satisfaction problems for templates
that are first-order definable in , the integers with
the successor relation. Assuming a widely believed conjecture from finite
domain constraint satisfaction (we require the tractability conjecture by
Bulatov, Jeavons and Krokhin in the special case of transitive finite
templates), we provide a full classification for the case that Gamma is locally
finite (i.e., the Gaifman graph of has finite degree). We show that
one of the following is true: The structure Gamma is homomorphically equivalent
to a structure with a d-modular maximum or minimum polymorphism and
can be solved in polynomial time, or is
homomorphically equivalent to a finite transitive structure, or
is NP-complete.Comment: 35 pages, 2 figure
- …