Clobber is an all-small game usually played on a checkerboard but the rules easily generalize to ... more Clobber is an all-small game usually played on a checkerboard but the rules easily generalize to play on an arbitrary graph. We show that, on a graph, determining the value of the game is NP-hard. We also examine clobber on a 1 × n and a 2 × n strip.
Proceedings of the 2019 27th ACM Joint Meeting on European Software Engineering Conference and Symposium on the Foundations of Software Engineering, 2019
Matlab/Simulink is a development and simulation language that is widely used by the Cyber-Physica... more Matlab/Simulink is a development and simulation language that is widely used by the Cyber-Physical System (CPS) industry to model dynamical systems. There are two mainstream approaches to verify CPS Simulink models: model testing that attempts to identify failures in models by executing them for a number of sampled test inputs, and model checking that attempts to exhaustively check the correctness of models against some given formal properties. In this paper, we present an industrial Simulink model benchmark, provide a categorization of different model types in the benchmark, describe the recurring logical patterns in the model requirements, and discuss the results of applying model checking and model testing approaches to identify requirements violations in the benchmarked models. Based on the results, we discuss the strengths and weaknesses of model testing and model checking. Our results further suggest that model checking and model testing are complementary and by combining them, we can significantly enhance the capabilities of each of these approaches individually. We conclude by providing guidelines as to how the two approaches can be best applied together.
We prove structural theorems about the distributive lattice of games born by day n .F or instance... more We prove structural theorems about the distributive lattice of games born by day n .F or instance, the number of join-irreducible elements is exactly twice the number of elements born by day n − 1. As an immediate corollary, all maximal chains on day n are of length exactly one plus double the number of born by day n −
ABSTRACT Many multiples of the number 123456789 are pandigital, meaning that they permute all 9 d... more ABSTRACT Many multiples of the number 123456789 are pandigital, meaning that they permute all 9 digits. For example, 123456789 times 4 is 493827156. We generalize this observation to any base, proving that the product is pandigital whenever the single digit multiplier (4) is relatively prime to the base minus one (9).
ABSTRACT this paper is (1) to give a very brief introduction to combinatorial game theory, (2) to... more ABSTRACT this paper is (1) to give a very brief introduction to combinatorial game theory, (2) to point the reader to more complete references on the topic, and (3) to instruct the prospective researcher on how to find open problems in the field
Tired of all those hand calculations? Of converting to canonical forms? Of calculating means and ... more Tired of all those hand calculations? Of converting to canonical forms? Of calculating means and temperatures? Of wondering if you've goofed? Wanted to play with the overheating operator, but don't have any patience? The Gamesman's Toolkit, written in C under UNIX, implements virtu- ally all of the material in nite combinatorial game theory. It is invaluable in analyzing games, and
More Games of No Chance 2002 Isbn 0 521 80832 4 Pags 25 30, Feb 19, 2002
We prove that games born by day n form a distributive lattice, but that the collection of all fin... more We prove that games born by day n form a distributive lattice, but that the collection of all finite games does not form a lattice.
BOOK REVIEWS 437 of this damage by stimulating others to improve portions of the proof in a more ... more BOOK REVIEWS 437 of this damage by stimulating others to improve portions of the proof in a more dramatic fashion and that the proof of the Classification will finally begin to receive the kind of second-generation attention which can lead to a better understanding of the simple groups. References 1. R. Solomon, On finite simple groups and their classification, Notices Amer. Math. Soc. 42 (1995), 231-239.
7.1 Introduction Eggs are natural objects that possess very complex surfaces, namely their shells... more 7.1 Introduction Eggs are natural objects that possess very complex surfaces, namely their shells, characterized by such features as pinholes, \starry nights", cage marks or thin shells, stretch marks, strains or discolouration, as well as internal aws such as blood in the yolks, etc. At present the candling of eggs for these features is done by two means: 1] Manual, which is labour intensive, and may cause some mechanical intrusion; reliable, if the eggs are of good quality; i.e. detection rates greater than 90% with false positives less than 1%; awed by high false positives if eggs of poor quality. 2] Mechanical, which is eeective but intrusive; prone to failure after very little usage; this method requires maintenance and may be unreliable if eggs of very poor quality. This problem has been considered in some detail and at considerable cost ($1.5 million) over the last three years. The method of looking for cracks is based upon the Batelle patent (U.S. patent 4,161,366) with...
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Papers by David Wolfe