9,704 research outputs found
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
Undirected Graphs of Entanglement Two
Entanglement is a complexity measure of directed graphs that origins in fixed
point theory. This measure has shown its use in designing efficient algorithms
to verify logical properties of transition systems. We are interested in the
problem of deciding whether a graph has entanglement at most k. As this measure
is defined by means of games, game theoretic ideas naturally lead to design
polynomial algorithms that, for fixed k, decide the problem. Known
characterizations of directed graphs of entanglement at most 1 lead, for k = 1,
to design even faster algorithms. In this paper we present an explicit
characterization of undirected graphs of entanglement at most 2. With such a
characterization at hand, we devise a linear time algorithm to decide whether
an undirected graph has this property
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