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.

Grammars Controlled by Petri Nets

Abstract: Formal language theory, introduced by Noam Chomsky in the 1950s as a tool for a description of natural languages [8–10], has also been widely involved in modeling and investigating phenomena appearing in computer science, artificial intelligence and other related fields because the symbolic representation of a modeled system in the form of strings makes its processes by information processing tools very easy: coding theory, cryptography, computation theory, computational linguistics, natural computing, and many other fields directly use sets of strings for the description and analysis of modeled systems. In formal language theory a model for a phenomenon is usually constructed by representing it as a set of words, i.e., a language over a certain alphabet, and defining a generative mechanism, i.e., a grammar which identifies exactly the words of this set. With respect to the forms of their rules, grammars and their languages are divided into four classes of Chomsky hierarchy: recursively enumerable, context-sensitive, context-free and regular.

When catalytic P systems with one catalyst can be computationally complete

Abstract: Catalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining computational completeness even with only one catalyst. In this paper, we show that one catalyst is sufficient for obtaining computational completeness if either catalytic rules have weak priority over non-catalytic rules or else instead of the standard maximally parallel derivation mode, we use the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration.

Which data types have Ω-complete initial algebra specifications?

Abstract: An algebraic specification is called ω-complete or inductively complete if all (open as well as closed) equations valid in its initial model are equationally derivable from it, i.e., if the equational theory of the initial model is identical to the equational theory of the specification. As the latter is recursively enumerable, the initial model of an ω-complete algebraic specification is a data type with a recursively enumerable equational theory. We show that if hidden sorts and functions are allowed in the specification, the converse is also true: every data type with a recursively enumerable equational theory has an ω-complete initial algebra specification with hidden sorts and functions. We also show that in the case of finite data types the hidden sorts can be dispensed with.

Action Logic is Undecidable

Abstract: Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. One of the operations of this logic is the Kleene star, which is axiomatized by an induction scheme. For a stronger system that uses an -rule instead (infinitary action logic), Buszkowski and Palka (2007) proved -completeness (thus, undecidability). Decidability of action logic itself was an open question, raised by Kozen in 1994. In this article, we show that it is undecidable, more precisely, -complete. We also prove the same undecidability results for all recursively enumerable logics between action logic and infinitary action logic, for fragments of these logics with only one of the two lattice (additive) connectives, and for action logic extended with the law of distributivity.