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One of the simplest models of computation is the decision tree model. In this model we are concerned with computing a function f: {0, 1}m → {0, 1} by using queries. Each query is given by specifying a function q on {0, l}m taken from some fixed family Q of allowed queries (the queries need not be Boolean). The answer given for the query is simply the value of q(x1, …, xm). The algorithm is completely adaptive, that is the i-th query asked may depend in an arbitrary manner on the answers received for the first i − 1 queries. The only wayto gain information about the input x is through these queries. The algorithm can therefore be described as a labeled tree, whose nodes are labeled by queries q ∈ Q, the outgoing edges of each node are labeled by the possible values of q(x1, …, xm), and the leaves are labeled by output values. Each sequence of answers describes a path in the tree to a node that is either the next query or the value of the output. In Figure 9.1 a decision tree is shown that computes (on inputs x1, …, x4) whether at least three of the input bits are 1s. It uses a family of queries Q consisting of all disjunctions of input variables and conjunctions of input variables.
The cost measure we are interested in is the number of queries performed on the worst case input; that is, the depth of the tree.
Definition 9.1: The decision tree complexity of a function f using the family of queries Q, denoted TQ(f), is the minimum cost decision tree algorithm over Q for f.
In Chapter 1 we saw that every communication protocol induces a partition of the space of possible inputs into monochromatic rectangles and learned of two lower bound techniques for the number of rectangles in such a partition. In this section we study how closely these combinatorial measures relate to communication complexity and to each other.
Covers and Nondeterminism
Although every protocol induces a partition of X × Y into f-monochromatic rectangles, simple examples show that the opposite is not true. In Figure 2.1, a partition of X × Y into monochromatic rectangles is given that do not correspond to any protocol. To see this, consider any protocol P for computing the corresponding function f. Since the function is not constant, there must be a first player who sends a message that is not constant. Suppose that this player is Alice. Since the messages that Alice sends on x, x′ and x″ are not all the same, there are two possibilities: (1) her messages on x and x′ are different. In this case the rectangle {x, x′} × {y} is not a monochromatic rectangle induced by the protocol P; or (2) her messages on x′ and x″ are different. In this case the rectangle {x′, x″} × {y″} is not a monochromatic rectangle induced by the protocol P. Similarly, if Bob is the first player to send a nonconstant message, then this message is inconsistent with either the rectangle {x} × {y′, y″) or with the rectangle {x″} × {y, y′}.
The paper presents background and motivation for a processing model that segments discourse into units that are simple, non-nested clauses, prior to the recognition of clause internal phrasal constituents, and experimental results in support of this model. One set of results is derived from a statistical reanalysis of the Swedish empirical data in Strangert, Ejerhed and Huber 1993 concerning the linguistic structure of major prosodic units. The other set of results is derived from experiments in segmenting part of speech annotated Swedish text corpora into clauses, using a new clause segmentation algorithm. The clause segmented corpus data is taken from the Stockholm Umeå Corpus (SUC), 1 M words of Swedish texts from different genres, part of speech annotated by hand, and from the Umeå corpus DAGENS INDUSTRI 1993 (DI93), 5 M words of Swedish financial newspaper text, processed by fully automatic means consisting of tokenizing, lexical analysis, and probabilistic POS tagging. The results of these two experiments show that the proposed clause segmentation algorithm is 96% correct when applied to manually tagged text, and 91% correct when applied to probabilistically tagged text.
The Editors are delighted to welcome this contribution from a venerable pioneer of algorithmic composition who is also a member of Organised Sound’s Advisory Board. In this article, edited from notes for a series of lectures delivered in Poland, and not previously published, Xenakis tackles first the questions arising from determinacy and indeterminacy, repetition and variation, symmetry and structure, and multidimensional musical space. He later describes his computer drawing interface, UPIC, and ends with a discussion of some of his statistical compositional methods employing a variety of probability distributions. Much of the article is illuminated by insights drawn from a lifetime’s work in the arts and sciences.
We present a model of text analysis for text-to-speech (TTS) synthesis based on (weighted) finite state transducers, which serves as the text analysis module of the multilingual Bell Labs TTS system. The transducers are constructed using a lexical toolkit that allows declarative descriptions of lexicons, morphological rules, numeral-expansion rules, and phonological rules, inter alia. To date, the model has been applied to eight languages: Spanish, Italian, Romanian, French, German, Russian, Mandarin and Japanese.
The full paper describes an environment for the generation of non-deterministic taggers, currently used for the development of a Spanish lexicon. In relation to previous approaches, our system includes the use of verification tools in order to assure the robustness of the generated taggers. A wide variety of user defined criteria can be applied for checking the exact properties of the system.
In computational linguistics, efficient recognition of phrases is an important prerequisite for many ambitious goals, such as automated extraction of terminology, part of speech disambiguation, and automated translation. If one wants to recognize a certain well-defined set of phrases, the question of which type of computational device to use for this task arises. For sets of phrases that are not too complex, as well as for many subtasks of the recognition process, finite state methods are appropriate and favourable because of their efficiency Gross and Perrin 1989; Silberztein 1993; Tapanainen 1995. However, if very large sets of possibly complex phrases are considered where correct resolution of grammatical structure requires morphological analysis (e.g. verb argument structure, extraposition of relative clauses, etc.), then the design and implementation of an appropriate finite state automaton might turn out to be infeasible in practice due to the immense number of morphological variants to be captured.
In the full paper in the companion volume, we introduce a new subclass of the context free languages, the meta-deterministic languages, which includes the deterministic languages, but also the languages that result if deterministic languages are combined via regular expressions.
Algorithmic composition and gambling, two activities associated (in the public mind) with the use of chance, are contrasted. Gambling is based on the concepts of winning and losing. Algorithmic composition is not, or should not be. Problems of mappings of information from one medium to another are considered, along with problems of reception for artworks made with these methods. In the end, the quality of attention given to an artwork may be more critical to its reception than any methods used to construct it. Mr. Yasser’s Piano, Tuning the Furniture of Chaos and Pi and the Square Root of Two, three recent algorithmic compositions by the author, are considered in the light of these thoughts.
Reaction–diffusion systems were first proposed by mathematician and computing forerunner Alan Turing in 1952. Originally intended as an explanation of plant phyllotaxis (the structure and arrangement of leaves in plants), reaction–diffusion now forms the basis of an area in biology which is as important as DNA research in the field of biological morphogenesis (Kauffman 1993). Reaction–diffusion systems were successfully utilised within the fields of computer animation and computer graphics to generate visually naturalistic patterning and textures such as animal furs (Turk 1991). More recently, reaction–diffusion systems have been applied to methods of half-tone printing, fingerprint enhancement, and have been proposed for use in sound synthesis (Sherstinsky 1994). The recent publication The Algorithmic Beauty of Seashells (Meinhardt 1995) uses various reaction–diffusion equations to explain patterned pigmentation markings on seashells. This article details an example of the application of reaction–diffusion systems to algorithmic composition within the field of computer music. The patterned data produced by reaction–diffusion systems is used to create a naturalistic soundscape in the piece cicada.
This paper describes the key aspects of a parser developed at the University of Pennsylvania from 1958 to 1959. The parser is essentially a cascade of finite state transducers. To the best of our knowledge, this is the first application of finite state transducers to parsing. This parser was recently faithfully reconstructed from the original documentation. Many aspects of this program have a close relationship to some of the recent work on finite state transducers.
Mirror-Rite is a work for ‘meta-trumpet’, computer and live electronics. The composition is neither notated nor stored, but forms itself as a complex of rule-based structures, transformations and processes around the improvisation of a live performer, its source of both energy and material. This article discusses the ways in which these algorithms deal with interactivity and projection in time, and how the handling of these aspects might permit the assembly of algorithmic elements into a complex dynamic whole, sensitive to (and existing solely within) present circumstances, but demonstrating unity between different performances.
The full paper explores the possibility of using Subsequential Transducers (SST), a finite state model, in limited domain translation tasks, both for text and speech input. A distinctive advantage of SSTs is that they can be efficiently learned from sets of input-output examples by means of OSTIA, the Onward Subsequential Transducer Inference Algorithm (Oncina et al. 1993). In this work a technique is proposed to increase the performance of OSTIA by reducing the asynchrony between the input and output sentences, the use of error correcting parsing to increase the robustness of the models is explored, and an integrated architecture for speech input translation by means of SSTs is described.
There are two distinct types of creativity: the flash out of the blue (inspiration? genius?), and the process of incremental revisions (hard work). Not only are we years away from modelling the former, we do not even begin to understand it. The latter is algorithmic in nature and has been modelled in many systems both musical and non-musical. Algorithmic composition is as old as music composition. It is often considered a cheat, a way out when the composer needs material and/or inspiration. It can also be thought of as a compositional tool that simply makes the composer’s work go faster. This article makes a case for algorithmic composition as such a tool. The ‘hard work’ type of creativity often involves trying many different combinations and choosing one over the others. It seems natural to express this iterative task as a computer algorithm. The implementation issues can be reduced to two components: how to understand one’s own creative process well enough to reproduce it as an algorithm, and how to program a computer to differentiate between ‘good’ and ‘bad’ music. The philosophical issues reduce to the question who or what is responsible for the music produced?
In spite of the wide availability of more powerful (context free, mildly context sensitive, and even Turing-equivalent) formalisms, the bulk of the applied work on language and sublanguage modeling, especially for the purposes of recognition and topic search, is still performed by various finite state methods. In fact, the use of such methods in research labs as well as in applied work actually increased in the past five years. To bring together those developing and using extended finite state methods to text analysis, speech/OCR language modeling, and related CL and NLP tasks with those in AI and CS interested in analyzing and possibly extending the domain of finite state algorithms, a workshop was held in August 1996 in Budapest as part of the European Conference on Artificial Intelligence (ECAI'96).
In language processing, finite state models are not a lesser evil that bring simplicity and efficiency at the cost of accuracy. On the contrary, they provide a very natural framework to describe complex linguistic phenomena. We present here one aspect of parsing with finite state transducers and show that this technique can be applied to complex linguistic situations.
Finite automata and various extensions of them, such as transducers, are used in areas as diverse as compilers, spelling checking, natural language grammar checking, communication protocol design, digital circuit simulation, digital flight control, speech recognition and synthesis, genetic sequencing, and Java program verification. Unfortunately, as the number of applications has grown, so has the variety of implementations and implementation techniques. Typically, programmers will be confused enough to resort to their text books for the most elementary algorithms. Recently, advances have been made in taxonomizing algorithms for constructing and minimizing automata and in evaluating various implementation strategies Watson 1995. Armed with this, a number of general-purpose toolkits have been developed at universities and companies. One of these, FIRE Lite, was developed at the Eindhoven University of Technology, while its commercial successor, FIRE Engine II, has been developed at Ribbit Software Systems Inc. Both of these toolkits provide implementations of all of the known algorithms for constructing automata from regular expressions, and all of the known algorithms for minimizing deterministic finite automata. While the two toolkits have a great deal in common, we will concentrate on the structure and use of the noncommercial FIRE Lite. The prototype version of FIRE Lite was designed with compilers in mind. More recently, computation linguists and communications protocol designers have become interested in using the toolkit. This has led to the development of a much more general interface to FIRE Lite, including the support of both Mealy and Moore regular transducers. While such a toolkit may appear extremely complex, there are only a few choices to be made. We also consider a ‘recipe’ for making good use of the toolkits. Lastly, we consider the future of FIRE Lite. While FIRE Engine II has obvious commercial value, we are committed to maintaining a version which is freely available for academic use.
There are currently two philosophies for building grammars and parsers: hand-crafted, wide coverage grammars; and statistically induced grammars and parsers. Aside from the methodological differences in grammar construction, the linguistic knowledge which is overt in the rules of handcrafted grammars is hidden in the statistics derived by probabilistic methods, which means that generalizations are also hidden and the full training process must be repeated for each domain. Although handcrafted wide coverage grammars are portable, they can be made more efficient when applied to limited domains, if it is recognized that language in limited domains is usually well constrained and certain linguistic constructions are more frequent than others. We view a domain-independent grammar as a repository of portable grammatical structures whose combinations are to be specialized for a given domain. We use Explanation-Based Learning (EBL) to identify the relevant subset of a handcrafted general purpose grammar (XTAG) needed to parse in a given domain (ATIS). We exploit the key properties of Lexicalized Tree-Adjoining Grammars to view parsing in a limited domain as finite state transduction from strings to their dependency structures.