An algorithmic uniform method to measure the complexity of statements of finitely refutable statements [6, 7, 8], was used to classify fa-mous/interesting mathematical statements like Fermat's last theorem, Hilbert's tenth problem, the four colour theorem, the Riemann hypothesis, [9, 13, 14]. Working with inductive Turing machines of various orders [1] instead of classical computations, we prop...

In recent years, CP-nets have emerged as a useful tool for supporting preference elicitation, reasoning, and representation. CP-nets capture and support reasoning with qualitative conditional preference statements, statements that are relatively natural for users to express. In this paper, we extend the CP-nets formalism to handle another class of very natural qualitative statements one often u...

There was a time – in the dim historical past – when foundries actually made ASICs with only 5000 to 50,000 logic gates. But FPGAs and CPLDs conquered those markets and pushed ASIC silicon toward opportunities with more logic, volume, and speed. Today's largest FPGAs approach the few-million-gate size of a typical ASIC design, and continue to sprout embedded cores, such as CPUs, memories, and i...

We demonstrate an automated method for proving statements in temporal logic about continuous systems, even in the face of incomplete knowledge. The method combines an implemented, on-they , model-checking algorithm for statements in the temporal logic CTL* 3, 4, 5] with the output of the qualitative simulation algorithm QSIM 10, 12]. Based on the QSIM Guaranteed Coverage Theorem, we prove that ...

In this paper we advocate the integration of fault injection into a formal methods tool set. We start by giving some motivations from our past industrial experiences with VDM. Then, we report about our recent work on specification-based test case generation via model mutation. In this testing approach the idea is not to cover a specification structurally, e.g. all expressions/statements, but to...

A position statement is an official point of view or belief of the ADA. Position statements are issued on scientific or medical issues related to diabetes. They may be authored or unauthored and are published in ADA journals and other scientific/medical publications as appropriate. Position statements must be reviewed and approved by the Professional Practice Committee and, subsequently, by the...

A scientific statement is a scholarly synopsis of a topic related to diabetes, which may ormay not contain clinical or research recommendations. Any recommendations included represent the official point of view or belief of the ADA. Work Group Reports and Task Force Reports fall into this category. Scientific statements must be reviewed and approved by the Professional Practice Committee and, s...

Over the past two decades, I have been working on problems at the intersection of Algorithm Design, Optimization, Algorithmic Game and Economics Theories, Scientific Computation, and Parallel Processing. I am a theoretican who cares a lot about the practical impact of mathematical and algorithmic work and who appreciates interdisciplinary research. My main research interests include Smoothed An...

Let p(n, m) denote the number of partitions of n into exactly m parts. In this paper we uncover new congruences for the function p(n, m) and give an alternate proof to a known theorem in addition to extending it. The methods of proof rely on identifying generating functions to polynomials and then using the symmetric properties of those polynomials. The theorems proved here provide further moti...