Relations and language models

Abstract

We all use a variety of languages, ranging from high-level programming languages up to machine codes, to express our ideas representing procedures, which prescribe computers how to execute computational processes we have in mind. Just like finite sets, finite languages might be specified by listing all the strings. Apart from listing some trivial few -word languages, however, most specifications of this kind would be unbearably extensive and clumsy. More importantly, infinite languages, including almost all programing and natural languages, obviously cannot be specified by an exhaustive enumeration of their strings at all. Consequently, mathematical finite -size models for languages are central to this book as a whole. We base these models, customarily referred to as rewriting systems, upon relations (see Section 2.1). As a matter of fact, these systems underlie almost all language models covered in this book. The section defines rewriting systems in general, and concentrates its attention on using these systems as language -defining devices.