505 research outputs found
On the Properties of Language Classes Defined by Bounded Reaction Automata
Reaction automata are a formal model that has been introduced to investigate
the computing powers of interactive behaviors of biochemical reactions([14]).
Reaction automata are language acceptors with multiset rewriting mechanism
whose basic frameworks are based on reaction systems introduced in [4]. In this
paper we continue the investigation of reaction automata with a focus on the
formal language theoretic properties of subclasses of reaction automata, called
linearbounded reaction automata (LRAs) and exponentially-bounded reaction
automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by
lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and
investigate the closure properties of language classes accepted by both LRAs
and lambda-LRAs. Further, we establish new relationships of language classes
accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results
include the following : (i) the class of languages accepted by lambda-LRAs
forms an AFL with additional closure properties, (ii) any recursively
enumerable language can be expressed as a homomorphic image of a language
accepted by an LRA, (iii) the class of languages accepted by ERAs coincides
with the class of context-sensitive languages.Comment: 23 pages with 3 figure
Automatic Ordinals
We prove that the injectively omega-tree-automatic ordinals are the ordinals
smaller than . Then we show that the injectively
-automatic ordinals, where is an integer, are the ordinals
smaller than . This strengthens a recent result of Schlicht
and Stephan who considered in [Schlicht-Stephan11] the subclasses of finite
word -automatic ordinals. As a by-product we obtain that the
hierarchy of injectively -automatic structures, n>0, which was
considered in [Finkel-Todorcevic12], is strict.Comment: To appear in a Special Issue on New Worlds of Computation 2011 of the
International Journal of Unconventional Computing. arXiv admin note: text
overlap with arXiv:1111.150
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