Online mechanism design has been widely applied to various practical applications. However, designing a strategy-proof online mechanism is much more challenging than that in a static scenario due to short of knowledge of future information. In this paper, we investigate online auctions with time discounting values, in contrast to the flat values studied in most of existing work. We present a st...

We show how theorem proving and methods for handling real algebraic constraints can be combined for hybrid system verification. In particular, we highlight the interaction of deductive and algebraic reasoning that is used for handling the joint discrete and continuous behaviour of hybrid systems. We illustrate proof tasks that occur when verifying scenarios with cooperative traffic agents. From...

Suppose we have been sold on the idea that formalised proofs in an LCF system should resemble their written counterparts, and so consist of formulas that only provide signposts for a fully verified proof. To be practical, most of the fully elaborated verification must then be done by way of general purpose proof procedures. Now if these are the only procedures we implement outside the kernel of...

Proof is a construct of mathematical communities over many generations and is introduced to new generations as they develop cognitively in a social context. Here I present a practical framework for this development in simple terms that nevertheless has deep origins. The framework builds on an analysis of the growth of mathematical ideas based on genetic facilities set-before birth. It unfolds a...

Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, a...

Probabilistic predicate transformers provide a semantics for imperative programs containing both demonic and probabilistic nondeterminism. Like the (standard) predicate transformers popularised by Dijkstra, they model programs as functions from final results to the initial conditions sufficient to achieve them. This paper presents practical proof rules, using the probabilistic transformers, for...

Constraint interval arithmetic is a sublanguage of BNR Prolog which o ers a new approach to the old problem of deriving numerical consequences from algebraic models. Since it is simultaneously a numerical computation technique and a proof technique, it bypasses the traditional dichotomy between (numeric) calculation and (symbolic) proofs. This interplay between proof and calculation can be used...

Fifty years ago, the author published a paper in Operations Research with the title, “A proof for the queuing formula: L = ãW ” [Little, J. D. C. 1961. A proof for the queuing formula: L = ãW . Oper. Res. 9(3) 383–387]. Over the years, L = ãW has become widely known as “Little’s Law.” Basically, it is a theorem in queuing theory. It has become well known because of its theoretical and practical...

We present a working implementation of a dynamics based architecture for visual sensing. This architecture provides field rate estimates of the positions and velocities of two independent falling balls in the face of repeated visual occlusions and departures from the field of view. The practical success of this system can be attributed to the interconnection of two strongly nonlinear dynamical ...

Proof search for the structural synthesis of programs (SSP) — a deductive program synthesis method which is suited for compositional programming in large and is in practical use in a number of programming environments is explained. SSP is based on a decidable logical calculus where complexity of the proof search is still PSPACE. This requires paying special attention to the efficiency of search...