197 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
$\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, 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 $\Gamma$ 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
$\mathrm{CSP}(\Gamma)$ can be solved in polynomial time, or $\Gamma$ is
homomorphically equivalent to a finite transitive structure, or
$\mathrm{CSP}(\Gamma)$ is NP-complete.Comment: 35 pages, 2 figure

### The Complexity of Combinations of Qualitative Constraint Satisfaction Problems

The CSP of a first-order theory $T$ is the problem of deciding for a given
finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$
and $T_2$ be two theories with countably infinite models and disjoint
signatures. Nelson and Oppen presented conditions that imply decidability (or
polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the
assumption that $\mathrm{CSP}(T_1)$ and $\mathrm{CSP}(T_2)$ are decidable (or
polynomial-time decidable). We show that for a large class of
$\omega$-categorical theories $T_1, T_2$ the Nelson-Oppen conditions are not
only sufficient, but also necessary for polynomial-time tractability of
$\mathrm{CSP}(T_1 \cup T_2)$ (unless P=NP)

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