Topology, morphisms, and randomness in the space of formal languages [electronic resource] /

by Kephart, David. E.

ABSTRACT: This paper outlines and implements a systematic approach to the establishment, investigation, and testing of distances and topologies on language spaces. The collection of all languages over a given number of symbols forms a semiring, appropriately termed a language space. Families of languages are defined by interrelations among words. The traditional classification begins with the syntax rules or grammar of the language, that is, the word-transformations by which the entire language can be produced from a single axiom, or starting word. The study of distances between languages as objects and of the topologies induced by language distances upon spaces of languages has been of a limited character. Known language distances introduce topologically awkward features into a language space, such as total disconnectedness.