A. Sinclair – författare

This monograph is a slightly revised version of my PhD thesis [86], com­ pleted in the Department of Computer Science at the University of Edin­ burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob­ lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap­ proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim­ ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi­ sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.

This monograph is a slightly revised version of my PhD thesis [86], com­ pleted in the Department of Computer Science at the University of Edin­ burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob­ lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap­ proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim­ ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi­ sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.

This monograph is a slightly revised version of my PhD thesis [86], com­ pleted in the Department of Computer Science at the University of Edin­ burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob­ lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap­ proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim­ ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi­ sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.

It is obvious that the growing child manifests an increasing understanding of his language and facility to use it. A major part of the child lan­ guage literature is concerned with the child''s developing linguistic and communicative competence. Scattered evidence also shows, however, that children become progressively more aware of language as Zanguage. It is interesting to consider in what ways the internal structure and mechanisms of language become more accessible. Little is known about linguistic aware­ ness of this kind, the role it plays, or how it develops. When the new Projektgruppe fUr Psycholinguistik of the Max-Planck­ Gesellschaft was founded, "the child''s conception .of language," in analogy to Piaget''s "child''s conception of the physical world," become one of the research unit''s topics of study. As previous work on linguistic awareness was largely amorphous, we first organized a kind of conference workshop with some of those who had worked in the area. The aims of this meeting were to map out the field of study, detail the phenomena of interest, and define major theoretical issues. The meeting took place just after the creation of the project group, on May 3-7, 1977. The participants were psychologists and linguists who had either published work on metalinguistic issues in child language, or who could be expected to contribute substantially to the discussion. This book is a direct outcome of that conference, though it is not a complete reflection of the papers presented, or of the discussion that took place.