Two collapsing hierarchies of subregularly tree controlled languages

On Two Hierarchies of Subregularly Tree Controlled Languages

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. In this paper, we consider first the case that we take only such regular languages as the control set which can be represented by finite unions of monoids....

Subregularly Tree Controlled Grammars and Languages

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.

Collapsing Exact Arithmetic Hierarchies

We provide a uniform framework for proving the collapse of the hierarchy NC(C) for an exact arithmetic class C of polynomial degree. These hierarchies collapse all the way down to the third level of the AC-hierarchy, AC3(C). Our main collapsing exhibits are the classes C ∈ {C=NC,C=L,C=SAC,C=P}. NC(C=L) and NC(C=P) are already known to collapse [1,18,19]. We reiterate that our contribution is a ...

Hierarchies of String Languages Generated by Deterministic Tree Transducers

Subshifts, MSO Logic, and Collapsing Hierarchies

We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usua...