Querying graph patterns

On solving integral equations using Markov chain Monte Carlo methods

“…It is a tedious, but straightforward task to define the sets E 4 Before explaining the proof, we note that the single-exponential bound is easy to see (it was hinted at in the first paragraph of the introduction, and which was in fact used in connection with querying incomplete graph data in [7]). For each n, consider an expression e n = (0|1) * x 1 .…”

“…(1) We proved in [7] that there exists a word w ∈ Σ * and a class A of NFAs over alphabet ({0, 1} ∪ V) such that the problem of checking, for a given A ∈ A, whether w ∈ L(ν(A)), for each valuation ν for A, is a coNP-hard problem. It is clear from the construction in [7] that there is a polynomial time algorithm that, given an NFA A ∈ A, constructs a star-free regular expression e over alphabet ({0, 1} ∪ V) such that L(A) = L(e).…”

“…It is clear from the construction in [7] that there is a polynomial time algorithm that, given an NFA A ∈ A, constructs a star-free regular expression e over alphabet ({0, 1} ∪ V) such that L(A) = L(e). We can conclude, from Lemma 1, that the problem Membership (w) is coNP-hard, even if restricted to the class of star-free regular expressions.…”

“…At the same time, the concept of L (e) captures many query answering scenarios over graph databases with incomplete information [7]. One of the future directions of this work is to devise better algorithms for problems related to the certainty semantics under restrictions arising in the context of querying graph databases.…”

“…As in most data management applications, it is common that some information is missing, typically due to using data that is the result of another query or transformation [6][7][8]. For example, in a social network we may have edges a x  −→ b and a ′ x  −→ b ′ , saying that the relationship between a and b is the same as that between a ′ and b ′ .…”