David Wolfe

• Professor (Associate) at Dalhousie University

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 t...

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 t...

How many ways can checkers be placed on an m × n board so that each square (whether or not it is occupied) is orthogonally adjacent to an odd number of checkers? After connecting the problem to graph theory and linear algebra, we provide an answer to this problem. The solution depends not only on the parity of m and n, but also, surprisingly, on th...

We survey the work done to date about games born by day n. Introduction Both number theory and combinatorial game theory are interesting in large part because of the wonderful interplay between algebraic and combinatorial structure. Here we survey some general results that investigate either the additive structure or the partial order of the games...

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).

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.

We prove structural theorems about the distributive lattice of games born by day n. For 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 − 1. 1 Introduction to combinato...

Introduction Partizan End Nim is a game played by two players called Left and Right. Initially there are n stacks of boxes in a row, each stack containing at least one box. Players take turns reducing the number of boxes from the stack on their respective side (Left removes from the leftmost stack, while Right removes from the rightmost stack). For...

We give upper and lower bounds on g(n) equal to the number of games born by day n. In particular, we give an upper bound of g(n + 1) g(n) + 2 + 2. For the lower bound, for all < 1, for suciently large n, g(n + 1) 2 .

We assess a player's long term expected winnings or losses at the game of blackjack without knowing the strategy employed. We do this by comparing the player's moves to those of a baseline strategy with known expected winnings. This allows an accurate estimate of the player's expectation to be found hundreds of times faster than the naive approach...

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.

In a Go endgame, each local area of play has a polynomial size canonical game tree and is insulated from all other local areas by live stones. Using techniques from combinatorial game theory, we prove that the Go endgame is PSPACE-hard.

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 flaws such as blood in the yolks, etc. At present the candling of eggs for these features is done by two...

We prove that a Markovian Open Queueing Network in which the service times are constant has lower average packet delay than the same network in which the service times are exponential (with the same mean). The proof is elementary, generalizing a similar result of Stamoulis and Tsitsiklis by removing the requirement that the network be layered. 1 Mo...

Let N be an open queueing network where the servers have generally distributed service times (with possibly different means) and the outside arrivals to the servers are Poisson. Define NC,FCFS (respectively, NE,FCFS ) to be queueing network N where each server has a constant (respectively, exponentially distributed) service time with the same mean...

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 virtually all of the material in finite combinatorial game theory. It is...

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. 2 What is combinatorial game theory?

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

Consider the problem of computing the average packet delay in a general dynamic packet-routing network with Poisson input stream, during steady-state. Any packet-routing network can be formulated as a queueing network, where each server has a constant service time. If each server had exponentially-distributed service time, queueing theory technique...

We consider the problem of computing the average packet delay in a general dynamic packet-routing network with Poisson input stream, during steady-state. Any packet-routing network can be formulated as a queueing network, where each server has a constant service time and the packets are served in a first-come-first served (FCFS) order. If each serv...

Let N be an open queueing network where the servers have generally distributed service times (with possibly different means) and the outside arrivals to the servers are Poisson. Define N C,FCFS (respectively, N E,FCFS ) to be queueing network N where each server has a constant (respectively, exponentially distributed) service time with the same mea...

We give a complete characterization of repeating Domineering snake positions.

We show that recognizing the facets of the traveling salesman problem polytope is Dp-complete.

We survey the work done to date about games born by day n.

A simple gambling paradox clarifies why it is so important to diversify and rebalance a portfolio.

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 virtually all of the material in finite combinatorial game theory. It is...

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 tw...

Real-world packet routing networks diier in many w ays from the networks which are analyzable by current-day queueing theory meth-ods. For example the service distributions in real-world networks are constant, whereas the vast majority of queueing theory applies most powerfully to exponential service distributions. Consequently, it is desirable to...