Tree controlled grammars are context-free grammars where the associated language only contains those terminal words which have a derivation where the word of any level of the corresponding derivation tree belongs to a given regular language. We present some results on the power of such grammars where we restrict the regular languages to some known subclasses of the family of regular languages.

Let T be a k-regular tree (k ≥ 3) and A = Aut(T ) its automorphism group. We analyze a generic finitely generated subgroup Γ of A. We show that Γ is free and establish a trichotomy on the closure Γ of Γ in A. It turns out that Γ is either discrete, compact or has index at most 2 in A.

We investigate the development of terms during cut-elimination in first-order logic and Peano arithmetic for proofs of existential formulas. The form of witness terms in cut-free proofs is characterized in terms of structured combinations of basic substitutions. Based on this result, a regular tree grammar computing witness terms is given and a class of proofs is shown to have only elementary c...

We explore the structure of the p-adic automorphism group Γ of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turán. We initiate the study of a general dimension theory of groups acting on rooted trees. We describe the relationship between dimension and other properties of groups such as solvability, existence of dense free...

We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the “cutoff phenomenon” in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any ε > 0, ...

We investigate percolation on the graph of the direct product T × Z of a regular tree T and the line Z, in which each 'tree' edge is open with probability τ and each 'line' edge with probability λ. There are three non-trivial phases, corresponding to the existence of 0, ∞, and 1 infinite open clusters. Such results may be obtained also for the graph T × Z d where d ≥ 2.

There has been recent interest in looking at what is required for a tree query language for linguistic corpora. One approach is to start from existing formal machinery, such as tree grammars and automata, to see what kind of machine is an appropriate underlying one for the query language. The goal of the paper is then to examine what is an appropriate machine for a linguistic tree query languag...

In this paper we propose a rich notion of directionality of predicates that combines modes and regular tree types. We provide a semantic soundness result for this notion and give inference systems to decide well-modedness of logic programs and goals. We show how this rich notion of directionality can be used to prove the universal termination of LD-resolution for logic programs with non-ground ...

erators (RTGs) are deployed along the Russian Federation’s Arctic coast to power remote lighthouses and navigation beacons. Similar RTGs were also used as power sources in other remote locations in the Russian Federation and elsewhere in the former Soviet Union. All Russian RTG’s have out-lived their lifespan and are in need of decommissioning. Radioactive incidents involving such sources, such...

For positive integers j ≥ k, the λj,k-number of graph G is the smallest span among all integer labelings of V (G) such that vertices at distance two receive labels which differ by at least k and adjacent vertices receive labels which differ by at least j. We prove that the λj,k-number of any r-regular graph is no less than the λj,k-number of the infinite r-regular tree T∞(r). Defining an r-regu...