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This is the second volume of a two volume collection on Structural
Complexity. This volume assumes as a prerequisite knowledge about
the topics treated in Volume I, but the present volume itself is
nearly self-contained. As in Volume I, each chapter of this book
ends with a section entitled "Bibliographical Remarks", in which
the relevant references for the chapter are briefly commented upon.
These sections might also be of interest to those wanting an
overview of the evolution of the field, as well as relevant related
results which are not included in the text. Each chapter includes a
section of exercises. The reader is encouraged to spend some time
on them. Some results presented as exercises are occasionally used
later in the text. A reference is provided for the most interesting
and for the most useful exercises. Some exercises are marked with a
* to indicate that, to the best knowledge of the authors, the
solution has a certain degree of difficulty. Many topics from the
field of Structural Complexity are not treated in depth, or not
treated at all. The authors bear all responsibility for the choice
of topics, which has been made based on the interest of the authors
on each topic. Many friends and colleagues have made suggestions or
corrections. In partic ular we would like to express our gratitude
to Richard Beigel, Ron Book, Rafael Casas, Jozef Gruska, Uwe
Schoning, Pekka Orponen, and Osamu Watanabe.
In the six years since the first edition of this book was
published, the field of Structural Complexity has grown quite a
bit. However, we are keeping this volume at the same basic level
that it had in the first edition, and the only new result
incorporated as an appendix is the closure under complementation of
nondeterministic space classes, which in the previous edition was
posed as an open problem. This result was already included in our
Volume II, but we feel that due to the basic nature of the result,
it belongs to this volume. There are of course other important
results obtained during these last six years. However, as they
belong to new areas opened in the field they are outside the scope
of this fundamental volume. Other changes in this second edition
are the update of some Bibliograph ical Remarks and references,
correction of many mistakes and typos, and a renumbering of the
definitions and results. Experience has shown us that this new
numbering is a lot more friendly, and several readers have
confirmed this opinion. For the sake of the reader of Volume II,
where all references to Volume I follow the old numbering, we have
included here a table indicating the new number corresponding to
each of the old ones."
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