In this paper we survey the field of Hochschild cohomology for von Neumann algebras. We describe the basic definitions and results without assuming background knowledge beyond some familiarity with von Neumann algebra theory. We offer no formal proofs of results, although we give detailed references to the literature. Instead, we concentrate on explaining the main techniques and how they are ap...

In this Appendix we provide additional details on some of the ideas developed in the paper, “Efficiency with Endogenous Population Growth,” (2006). We first give the formal proof that A-efficiency is generically non-empty. The second section extends the notions of efficient fertility developed in the paper for the discrete case to environments in which fertility is a continuous choice variable....

Designs are often modiied for use in new circumstances. If formal proof is to be an acceptable veriication methodology for industry , it must be capable of tracking design changes quickly. We describe our experiences formally verifying an implementation of an ATM network component, and on our subsequent veriication of modiied designs. Three of the designs veriied are in use in a working network...

In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming, are a perfect candidate to next apply this curiosity to. The advantages of using proof assistants is that they allow one to write formally verified proofs a...

Gödel’s famous incompleteness theorems (there are two of them) concern the ability of a formal system to state and derive all true statements, and only true statements, in some fixed domain; and concern the ability of logic to determine if a formal system has that property. They were developed in the early 1930s. Very loosely, the first theorem says that in any “sufficiently rich” formal proof ...

The topic of this thesis is the relationship between formal and informal proofs. Chapter One opens the discussion by examining what a proof is, when two proofs are identical, what the purpose of proving is and how to distinguish the two categories of proof. Chapters Two and Three focus in on informal and formal proof respectively, with the latter also including descriptions of various computati...

This paper is concerned with proof methods for the temporal property of eventuality (a type of liveness) in systems of polynomial ordinary differential equations (ODEs) evolving under constraints. This problem is of a more general interest to hybrid system verification, where reasoning about temporal properties in the continuous fragment is often a bottleneck. Much of the difficulty in handling...

The CLaM proof planner has been interfaced to the HOL interactive theorem prover to provide the power of proof planning to people using HOL for formal verification, etc. The interface sends HOL goals to CLaM for planning and translates plans back into HOL tactics that solve the initial goals. The project homepage can be found at http://www.cl.cam.ac.uk/Research/HVG/Clam.HOL/intro.html.

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a seco...