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Extra resources for Language and Automata Theory and Applications: 11th International Conference, LATA 2017, Umeå, Sweden, March 6-9, 2017, Proceedings

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Pim ·a = pw (a), and thus φw = pw . It is easy to see that, for p > 0, p distributes over inf and . In the following, we assume that pi = 0 for i = 1, . . , k, and we will write pw · a instead of φw (a). A q-run r of M is a run with r(ε) = q. We denote the set of all q-runs of M as R(q). , rweight(r) := w∈Σ ∗ pw · wt(r, w), and thus weight(r) = in(q) + rweight(r). Consequently, if we define μ(q) := inf rweight(r) (for every q ∈ Q) r∈R(q) then ( M , tul ) = minq∈Q {in(q) + μ(q)} . Hence, in order to compute the behavior of M on tul , it suffices to calculate the values μ(q) for all q ∈ Q.

Tm }. We build the looping tree automaton At = (Σ, Qt , L, Δt , {t0 }) as follows: Qt := {t0 , t1 , . . , tm } and Δt := {(ti , ti (ε), tiσ1 , . . , tiσk ) | 1 ≤ i ≤ m}. It is easy to see that t = t0 is the only tree accepted by At . The automaton At constructed in the above proof actually has a very specific syntactic shape (see Definition 9 below), which ensures that it accepts only one tree. Definition 9 (Representing Looping Tree Automaton (rLTA)). A representing looping tree automaton is a looping tree automaton A = (Σ, P, L, Δ, {ps }) such that Δ satisfies the following condition: – for every p ∈ P , there exists a unique symbol lp ∈ L and a unique tuple (p1 , .

3. Wrappers defined in monadic Datalog are implemented as queries, whose definitions can be local and only need to consider as much context as required by the query conditions. This distinguishes them from tree automata, which, even in flavors able to define monadic queries, always recognise a language of trees and conceptually traverse the entire input tree. This makes tree automata more brittle in real-world wrapping scenarios, and causes them to require a greater effort from the programmer, much of which is directed towards accepting a large enough tree language, rather than the essence of the wrapping task at hand.

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