J. Do RAN 433 22 Chromosome classification and segmentation as exercises in knowing what to expect.

B.RANDELL 3 PROGRAM PROOF AND MANIPULATION 2 Some techniques for proving correctness of programs which alter data structures.

The two outstanding figures in the history of computer science are Alan Turing and John von Neumann, and they shared the view that logic was the key to understanding and automating computation. In particular, it was Turing who gave us in the mid-1930s the fundamental analysis, and the logical definition, of the concept of'computability by machine' and who discovered the surprising and beautiful basic fact that there exist universal machines which by suitable programming can be made to t This essay is an expanded and revised version of one entitled The Role of Logic in Computer Science and Artificial Intelligence, which was completed in January 1992 (and was later published in the Proceedings of the Fifth Generation computer Systems 1992 Conference). Since completing that essay I have had the benefit of extremely helpful discussions on many of the details with Professor Donald Michie and Professor I. J. Good, both of whom knew Turing well during the war years at Bletchley Park. Professor J. A. N. Lee, whose knowledge of the literature and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished. Further light has very recently been shed on the von Neumann side of the story by Norman Macrae's excellent biography John von Neumann (Macrae 1992). Accordingly, it seemed appropriate to undertake a more complete and thorough version of the FGCS'92 essay, focussing somewhat more on the interesting historical and biographical issues. I am grateful to Donald Michie and Stephen Muggleton for inviting me to contribute such a'second edition' to the present volume, and I would also like to thank the Institute for New Computer Technology (ICOT) for kind permission to make use of the FGCS'92 essay in this way. 1 LOGIC, COMPUTERS, TURING, AND VON NEUMANN

This paper describes some work on automatically generating finite counterexamples in topology, and the use of counterexamples to speed up proof discovery in intermediate analysis, and gives some examples theorems where human provers are aided in proof discovery by the use of examples.

K.A.PATON 411 24 Centromere finding: some shape descriptors for small chromosome outlines.

The equivalence problem for program schemes, or for programs, is reduced to the proving of a theorem in second-order logic. This work extends Manna's first-order logic reductions. Some examples of the technique are given together with a suggested method for obtaining proofs in special cases by firstorder methods. INTRODUCTION Several workers in recent years have considered using techniques and ideas of various mathematical theories of computation for proving interesting results about computer programs. This paper is concerned with two of these approaches.

F(n,$) as introduced here corresponds to A.N.Prior's (1957, 1968) expression Fir.

Networks as models of word storage: G. R. Kiss

An increasing number of Artificial Intelligence (Al) programs are implemented on high-performance workstations with a bitmap display, a mouse input device, and a keyboard. The programming environment (usually a dialect of LISP) generally provides support for multiple, overlapping windows, and various kinds of menus including pop up menus. The user can move, reshape, close, and scroll the windows. Additionally, a programmer can designate arbitrary regions of a window to be selectable with the mouse. This means that a user can invoke an action by pressing and releasing a mouse button while the mouse cursor is in the designated region.

Georgeff's controlled production systems 65 8.3.3