577 research outputs found
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
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
Datalog and Constraint Satisfaction with Infinite Templates
On finite structures, there is a well-known connection between the expressive
power of Datalog, finite variable logics, the existential pebble game, and
bounded hypertree duality. We study this connection for infinite structures.
This has applications for constraint satisfaction with infinite templates. If
the template Gamma is omega-categorical, we present various equivalent
characterizations of those Gamma such that the constraint satisfaction problem
(CSP) for Gamma can be solved by a Datalog program. We also show that
CSP(Gamma) can be solved in polynomial time for arbitrary omega-categorical
structures Gamma if the input is restricted to instances of bounded treewidth.
Finally, we characterize those omega-categorical templates whose CSP has
Datalog width 1, and those whose CSP has strict Datalog width k.Comment: 28 pages. This is an extended long version of a conference paper that
appeared at STACS'06. In the third version in the arxiv we have revised the
presentation again and added a section that relates our results to
formalizations of CSPs using relation algebra
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