We define an infinite class of 2-pile subtraction games, where the amount that can be subtracted from both piles simultaneously, is a function f of the size of the piles. Wythoff’s game is a special case. For each game, the 2nd player winning positions are a pair of complementary sequences, some of which are related to well-known sequences, but most are new. The main result is a theorem giving necessary and sufficient conditions on f so that the sequences are 2nd player winning positions. Sample games are presented, strategy complexity questions are discussed, and possible further studies are indicated.

The game of Go is an ideal problem domain for exploring machine learning: it has simple rules yet requires more and more complex strategies to play well as the board size is increased. Despite much effort, existing Go programs, which have largely employed knowledge based and symbolic AI techniques, have failed to achieve a standard much above an average human amateur. This paper examines the possibility of using evolutionary techniques in the specification of neural networks, to play Go. This is a much more difficult problem than the 'toy-problems' with which evolved neural networks have been successful to date. Results of a simple experiment using a Genetic Algorithm to evolve a Go position evaluation network are reported, the factors affecting performance are discussed, and proposals are made for more sophisticated networks and evolutionary schemes that may potentially be better suited to complex problems that involve an interaction of pattern recognition and serial reasoning. 1 In...

Tools for selective proactive as well as reactive information retrieval, information extraction, information organization and assimilation, knowledge discovery using heterogeneous, distributed knowledge and data sources constitute some of the key enabling technologies for managing the data overload and translating recent advances in automated data acquisition, digital storage, computers and communications into advances in decision support, scientific discovery and related applications. Such distributed knowledge networks (DKN) have to be able to effectively utilize multiple autonomous, often independently owned and operated information systems. Given the complexity of the such systems and the need for autonomy of the components, multi-agent systems, because of their modularity, offer an attractive framework for the design of DKN. In such multi-agent systems, satisfactory completion of the tasks at hand depend critically on effective communication and coordination among the agents. This...

iii This thesis describes a theory for representing, manipulating, and reasoning about structured pieces of knowledge in open collaborative systems. The theory’s design is motivated by both its general model as well as its target user commu-nity. Its model is structured information, with emphasis on classification, relative structure, equivalence, and interpretation. Its user community is meant to be non-mathematicians and non-computer scientists that might use the theory via computational tool support once inte-grated with modern design and development tools. This thesis discusses a new logic called kind theory that meets these challenges. The core of the work is based in logic, type theory, and universal algebras. The theory is shown to be efficiently implementable, and several parts of a full realization have already been constructed and are reviewed. Additionally, several software engineering concepts, tools, and technologies have been con-structed that take advantage of this theoretical framework. These constructs are discussed as well, from the perspectives of general software engineering and applied formal methods. Acknowledgements iv I am grateful to my initial primary adviser, Prof. K. Mani Chandy, for bringing me to Caltech and his willingness to let me explore many unfamiliar research fields of my own choosing. I am also appreciative of my second adviser, Prof. Jason Hickey, for his support, encouragement, feedback, and patience through the later years of my work. If Jason had not appeared at Caltech in Autumn of 1999, I may well have not finished my Ph.D. I am very much in debt to Joseph Goguen whose inspiring work started me on the path of using algebras and categories. José Meseguer and Francisco (Paco) Duran have been of tremendous help and inspiration in my use of Maude and rewriting logic.

Bongard problems present an outstanding challenge to artificial intelligence. They consist of visual pattern understanding problems on which the task of the pattern perceiver is to find an abstract aspect of distinction between two classes of figures. This paper examines the philosophical question of whether objects in Bongard problems can be ascribed an a priori, metaphysical, existence --- the ontological question of whether objects, and their boundaries, come pre-defined, independently of any understanding or context. This is an essential issue, because it determines whether a priori symbolic representations can be of use for solving Bongard problems. The resulting conclusion of this analysis is that in the case of Bongard problems there can be no units ascribed an a priori existence -- and thus the objects dealt with in any specific problem must be found by solution methods (rather than given to them). This view ultimately leads to the emerging alternatives to the philosophical doc...

Efforts to calculate values of the noncomputable Busy Beaver function are discussed in the light of algorithmic information theory. I would like to talk about some impossible problems that arise when one combines information theory with recursive function or computability theory. That is to say, I'd like to look at some unsolvable problems which arise when one examines computation unlimited by any practical 2 G. J. Chaitin bound on running time, from the point of view of information theory. The result is what I like to call "algorithmic information theory" [5]. In the Computer Recreations department of a recent issue of Scientific American [7], A. K. Dewdney discusses efforts to calculate the Busy Beaver function \Sigma. This is a very interesting endeavor for a number of reasons. First of all, the Busy Beaver function is of interest to information theorists, because it measures the capability of computer programs as a function of their size, as a function of the amount of informatio...

We characterize the pairs (G1 ; G2) of graphs on a shared vertex set that are intersection polysemic: those for which the vertices may be assigned subsets of a universal set such that G1 is the intersection graph of the subsets and G2 is the intersection graph of their complements. We also consider several special cases and explore bounds on the size of the universal set. 1 Introduction The idea of a C-intersection graph for a class C of sets is well known. It refers to any graph that arises from a collection of sets in C when one associates to each of the sets a vertex and understands vertices to be adjacent precisely when their respective sets have nonempty intersection. Any function from a vertex set V to C that embodies such an association is called a C-intersection representation of the resulting graph. So given a set \Sigma, every function f mapping vertices in V to subsets of \Sigma is a 2 \Sigma -intersection representation of some graph on V . But f additionally defines, i...

this paper is to interpret the 3n+1problem as an iterative procedure and to find an entire holomorphic map that extends the given map on the integers. This idea has been circulated by the third author for a decade or two. In this paper, we consider the problem from the point of view of holomorphic dynamics and show that the existence of any integer that is not eventually periodic implies the existence of a "wandering domain" for our entire holomorphic map. For a large class of entire holomorphic maps, it is known that there are no wandering domains. Unfortunately, this class does not include our maps. Nonetheless, we hope that this point of view might stimulate further progress. First observe that the image 3n+1 of an odd integer n is even and will be replaced by (3n+1)=2 in the next step. We can therefore equivalently consider the iteration n 7! n=2 if n is even and n 7! (3n+1)=2 if n is odd. The orbit 1 7! 4 7! 2 7! 1 turns into the orbit 1 7! 2 7! 1, while 0 and \Gamma1 are fixed points and \Gamma5 7! \Gamma7 7! \Gamma10 7! \Gamma5. It is for this map that Halbeisen and Hungerbuhler showed that the period of any extra cycle of positive integers must be more than 10

l 8, 1996. ffl Midterm exam. (10% of grade) ffl Final exam. (20% of grade) Academic Honesty Unless otherwise noted, all work in this course is to be your own (that includes programming assignments). The penalty for plagiarism or cheating is a 0.0 in this course in addition to whatever penalty is imposed by the Academic Conduct Committee. 1 Syllabus This course is about the concepts and constructs of programming languages. From J. C. Mitchell, Foundations for Programming Languages (unpublished manuscript): The mathematical analysis of programming languages begins with the formulation of "model" programming languages. For example, if we want to analyze procedure call mechanisms, we might begin by identifying a simple programming language whose main constructs are procedure declarations and calls. We may then analyze this simplified programming language without worrying about irrelevant details of a large

We describe a method to use non-deterministic state transition graphs as tools for exploration of complex processes. For any interesting process, the full state space will probably be large enough that it cannot be displayed nor explored in its entirety. Therefore we suggest that the visualization process only generate as much of the space as is necessary for the continued exploration.