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.

Energy-Controlled P Systems

Abstract: As already considered in [13], we investigate P systems where each evolution rule "produces" or "consumes" some quantity of energy, in amounts which are expressed as integer numbers. Yet in contrast to P systems with energy accounting as considered in [13], for energy-controlled P systems we demand that in each evolution step and in each membrane the total energy consumed by the application of a multiset of evolution rules has to be the maximum possible within a specific non-negative range. Only equipped with this control feature, energy-controlled P systems are very powerful. In the case of multisets of symbol objects we find that energy-controlled P systems with even only one membrane and an energy range of {0, 1} for the total energy involved in an evolution step characterize the recursively enumerable sets of vectors of natural numbers (without using catalysts or priorities or membrane dissolving features). In the case of string objects similar results can be obtained. Energy-controlled P systems with even only one membrane and the minimal energy range of {0} for the total energy involved in an evolution step at least generate any set of vectors of natural numbers that can be generated by matrix grammars without appearance checking.

Inductive Inference of Recursive Functions: Complexity Bounds

Abstract: This survey includes principal results on complexity of inductive inference for recursively enumerable classes of total recursive functions Inductive inference is a process to find an algorithm from sample computations In the case when the given class of functions is recursively enumerable it is easy to define a natural complexity measure for the inductive inference, namely, the worst-case mindchange number for the first n functions in the given class Surely, the complexity depends not only on the class, but also on the numbering, ie which function is the first, which one is the second, etc It turns out that, if the result of inference is Goedel number, then complexity of inference may vary between log2n+o(log2n) and an arbitrarily slow recursive function If the result of the inference is an index in the numbering of the recursively enumerable class, then the complexity may go up to const·n Additionally, effects previously found in the Kolmogorov complexity theory are discovered in the complexity of inductive inference as well