Recursively enumerable language

About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.

On the Properties of Language Classes Defined by Bounded

Abstract: 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 �-LRAs) by allowing �-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and �-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 �-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.

Monodic Epistemic Predicate Logic

Abstract: We consider the monodic formulas of common knowledge predicate logic, which allow applications of epistemic operators to formulas with at most one free variable. We provide finite axiomatizations of the monodic fragment of the most important common knowledge predicate logics (the full logics are known to be not recursively enumerable) and single out a number of their decidable fragments. On the other hand, it is proved that the addition of the equality symbol to the monodic fragment makes it not recursively enumerable.

About Time-Varying Distributed H Systems

Abstract: A time-varying distributed H system (TVDH system) is a splicing system which has the following feature: at different moments one uses different sets of splicing rules (these sets are called components of TVDH system). The number of components is called the degree of the TVDH system. The passing from a component to another one is specified in a cycle. It was proved by both authors (1999) that TVDH systems of degree 2 generate all recursively enumerable languages. It was made by modelling Turing machines and, in that modelling, every language is generated "step by step" or "word by word". This solution is not a fully parallel one. A. Paun (1999) presented a complete parallel solution for TVDH systems of degree 4 by modelling type 0 formal grammars. Now we improved A. Paun's result by reducing the number of components of such TVDH systems down to 3. This question is open for 2 components, i.e. is it possible to construct TVDH systems of degree 2 which completely uses the parallel nature of molecular computations based on splicing operations (say model type 0 formal grammars). We consider also original G. Paun's definition of TVDH systems and suggest a slightly different definition of TVDH systems based on the definition of H systems - extended time-varying distributed H systems (ETVDH systems). For this new definition we proved that ETVDH systems with one component generate exactly the set of all regular languages and that with two components, they generate exactly the set of all recursively enumerable languages.