This paper describes a system for chordal analysis of tonal music. We establish that, in the worst case, the segmenting the music and labeling the harmonies takes on the order of 2^n steps, where n is number of notes in a piece of music. We show that, when segments of the music can be analyzed locally, the problem becomes O(n^2). We then show that the results of the O(n^2) search can be closely approximated through the use of a heuristic that allows O(n) time search. The results of the segmenting and chord labeling algorithms are then empirically measured against analyses derived from a basic music theory text and the statistical results are reported.

Every interactive system requires a presentation mechanism, to show the user the data it handles. Often, the relationship between the data and its presentation is complex; further, it is often mediated by astyle mechanism, allowing the user or a designer to describe how the data should be displayed. It is a standing engineering challenge to develop a presentation model that is exible, handling many kinds of data and layout; powerful, giving the user extensive control over appearance; and e cient enough for interactive work. In this dissertation, we propose a model of presentation by tree transformation. Because information often has a hierarchical logical structure, trees are widely used to represent documents and other data. The layout or presentation of a document is also often modeled as a computation over a tree. But these trees are not generally identical. In other words, presentation can be seen as a mapping between trees. Casting it as a formal tree transformation o ers both expressive, compact style speci cations and e cient implementation. We present a general framework for presentation by tree transformation. It has been implemented as part of Ensemble, a software development environment and multimedia document system

Acknowledgements I wish to thank: 1. my advisor, Bharat Jayaraman, to whom this dissertation owes its existence in an uncountable number of ways, 2. Surya Mantha of Xerox Corporation, for input at various crucial stages, 3. Xerox Corporation, for generously providing funds that supported most of this work, 4. the rest of my committee, namely, Prof. Alan L. Selman and Prof. Kenneth W. Regan, for their interest in my welfare, 5. the secretaries in the department of computer science, for, among other things, shielding me from administrivial vagaries of the University, 6. my friends, for believing in, supporting, and encouraging me through thick andthin. I shall refrain from enumerating names here for fear of making the list longer than the rest of my dissertation.

Dynamic programming has long been used as an algorithm design technique, with various mathematical theories proposed to model it. Here we take a different perspective, using a relational calculus to model the problems and solutions using dynamic programming. This approach serves to shed new light on the different styles of dynamic programming, representing them by different search strategies of the tree-like space of partial solutions. 1 INTRODUCTION AND HISTORY Dynamic programming is an algorithm design technique for solving many different types of optimization problem, applicable to such diverse fields as operations research (Ecker and Kupferschmid, 1988) and neutron transport theory (Bellman, Kagiwada and Kalaba, 1967). The mathematical theory of the subject dates back to 1957, when Richard Bellman (Bellman, 1957) first popularized the idea, producing a mathematical theory to model multi-stage decision processes and to solve related optimization problems. He was also the first to i...

In (Sojka and Ševeček 1994) we presented a case study of problems related to achieving quality hyphenation in TEX — especially pattern generation for flexive languages like Czech. It was shown that pretty much issues can be handled within the frame of good old TEX, but some of them definitely not, because TEX wasn’t primarily designed from the beginning as a universal tool for the typesetting of all kinds of publications in all languages, but typesetting of The Art of Computer Programming (Knuth 1968–) in American English was the initial motivation. In this paper we continue elaborating these issues, with the emphasis on the hyphenation problems in the presence of long compound words in Germanic (and Slavic) languages.

In the constructive programming community it is commonplace to see formal developments of textbook algorithms. In the algorithm design community, on the other hand, it may be well known that the textbook solution to a problem is not the most efficient possible. However, in presenting the more efficient solution, the algorithm designer will usually omit some of the implementation details, thus creating an algorithm gap between the abstract algorithm and its concrete implementation. This is in contrast to the formal development, which usually presents the complete concrete implementation of the less efficient solution. We claim that the algorithm designer is forced to omit some of the details by the relative expressive poverty of the Pascal-like languages typically used to present the solution; the greater expressiveness provided by a functional language allows the whole story to be told in a reasonable amount of space. We therefore hope to bridge the algorithm gap between ab...

26(2), Summer 2002), two errors occurred on page 39. The phrase “While O(n2) is better than O(n2) ” should instead read “While O(n2) is better than O(2n). ” Within each direct acyclic graph in Figure 12, as well as on the back cover, the second oval from the left should contain the number 2i in some cases it mistakenly contains the numer 3.

The harmonic analysis of tonal music by computer is an important area of interest in the computer music research community. While the problem is interesting in its own right, the ability to parse and use chords and harmonies in a tonal composition also adds an important dimension to a computer agent’s ability to manipulate musical material. Automated arranging, accompaniment, and phrasing are all aided by an understanding of the chordal structure of a piece. Although musicians analyze tonal music of all types, it is dif � cult to create algorithms that have this generality. In this article, we describe a set of algorithms for harmonic analysis that make minimal use of stylistic and contextual cues, such as metric strength, harmonic context, and known stylistic constraints. The system described in this article is purposefully simple in its approach. This allows us to specify its workings to the point where the work may be duplicated and extended by others. The system is designed both to explore basic computational properties of algorithms to solve the task and to provide a baseline against which other systems can be measured. In this way, it is possible to measure the change in performance introduced by use of such things as tonal context, voiceleading rules, and metrical information. We divide harmonic analysis into two tasks. Segmentation is the task of splitting the music into appropriate chunks (segments) for analysis. As a default, we assume segmentation takes place in the time dimension. Labeling is the task of giving each segment the proper quality and root pitch. Figure 1 shows a measure of music partitioned into labeled segments. The algorithms we describe in this article perform both segmentation and labeling. Previous research in the area of automated harmonic analysis

To the casual observer, T E X is not a state-of-the-art typesetting system. No flashy multilevel menus and interactive manipulation of text and graphics dazzle the onlooker. On a less superficial level, however, T E X is a very sophisticated program, first of all because of the ingeniousness of its built-in algorithms for such things as paragraph breaking and make-up of mathematical formulas, and second because of its almost complete programmability. The combination of these factors makes it possible for T E X to realize almost every imaginable layout in a highly automated fashion. Unfortunately, it also means that T E X has an unusually large number of commands and parameters, and that programming T E X can be far from easy. Anyone wanting to program in T E X, and maybe even the ordinary user, would seem to need two books: a tutorial that gives a first glimpse of the many nuts and bolts of T E X, and after that a systematic, complete reference manual. This book tries to fulfil the latter function. A T E Xer who has already made a start (using any of a number of introductory books on the market) should be able to use this book indefinitely thereafter. In this volume the universe of T E X is presented as about forty different subjects, each in a separate chapter. Each chapter starts out with a list of control sequences relevant to the topic of that chapter and proceeds to treat the theory of the topic. Most chapters conclude with remarks and examples. Globally, the chapters are ordered as follows. The chapters on basic mechanisms are first, the chapters on text treatment and mathematics are next, and finally there are some chapters on output and aspects of T E X's connections to the outside world. The book also contains a glossary of T E X commands, tables, and indexes b...

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