We consider the informal concept of “computability” or “effective calculability” and two of the formalisms commonly used to define it, “(Turing) computability” and “(general) recursiveness.” We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a careful historical and conceptual analysis of computability and recursion we make several recommendations in section §7 about preserving the intensional differences between the concepts of “computability” and “recursion.” Specifically we recommend that: the term “recursive ” should no longer carry the additional meaning of “computable” or “decidable;” functions defined using Turing machines, register machines, or their variants should be called “computable” rather than “recursive;” we should distinguish the intensional difference between Church’s Thesis and Turing’s Thesis, and use the latter particularly in dealing with mechanistic questions; the name of the subject should be “Computability Theory” or simply Computability rather than

The conventional wisdom presented in most computability books and historical papers is that there were several researchers in the early 1930’s working on various precise definitions and demonstrations of a function specified by a finite procedure and that they should all share approximately equal credit. This is incorrect. It was Turing alone who achieved the characterization, in the opinion of Gödel. We also explore Turing’s oracle machine and its analogous properties in analysis. Keywords: Turing a-machine, computability, Church-Turing Thesis, Kurt Gödel, Alan Turing, Turing o-machine, computable approximations,

This thesis deals with some aspects of the physics of disordered systems. It consists of four papers and an introductory part. An introduction

This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational algebra or computational biology are given.

Introduction: Strings, Grammars & Formal Languages Stochastic context-free grammars, or SCFGs, are generative systems of stochastic languages. In other words, a SCFG specifies a probability distribution over the set of all possible strings that are concatenated from a finite alphabet . Definition 1 An alphabet is a finite set of symbols. It denoted here by }. Definition 2 The kth power of an alphabet , denoted , is the set of strings of length k made from the elements of . Example 1 For the alphabet 1}, where |V| = 2. will be set of strings, made from the elements of , that are of length 1, or 1}. Likewise, 01, 10, 11}, {000, 001, 010, 011, 100, 101, 110, 111}, etc. Definition 3 # , or Kleene closure of , is the union of all powers of the alphabet, or # = . . . . Definition 4 A formal language L is defined as L # . In other words, L is a (possibly infinite) set of strings, each formed by concatenation from a finite set of

Stochastic context-free grammars, or SCFGs, are generative systems of stochastic languages. In other words, a SCFG specifies a probability distribution over the set of (all possible) strings that are concatenated from a finite alphabet V.

In this chapter we will describe and analyze a simulation of a factual information seeking system for a subsection of the "yellow pages". The subsection contains information about (i) car hire (ii) restaurants, and (iii) personal insurance. The simulation was