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Boolean functions and computation models
Clote, PeterBerlin ; New York : Springer, c2002.This textbook presents a survey of research on boolean functions, circuits, parallel computation models, function algebras, and proof systems. Its main aim is to elucidate the structure of "fast" parallel computation. The complexity of parallel computation is emphasized through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Nonuniform computation models are studied in the form of boolean circuits; uniform ones in a variety of forms. Steps in the investigation of nondeterministic polynomial time are surveyed as is the complexity of various proof systems. The book will benefit advanced undergraduates and graduate students as well as researchers in the field of complexity theory.

Computational molecular biology : an introduction
Clote, PeterChichester ; New York : John Wiley, c2000.Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology. Provides the background mathematics required to understand why certain algorithms work Guides the reader through probability theory, entropy and combinatorial optimization Indepth coverage of molecular biology and protein structure prediction Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction Includes class tested exercises useful for selfstudy Source code of programs available on a Web site Primarily aimed at advanced undergraduate and graduate students from bioinformatics, computer science, statistics, mathematics and the biological sciences, this text will also interest researchers from these fields.

Arithmetic, proof theory, and computational complexity
New York : Clarendon Press ; Oxford, England ; New York : Oxford University Press, 1993.This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. Issuing from a twoyear NSF and Czech Academy of Sciences grant supporting a monthlong workshop and 3day conference in San Diego (1990) and Prague (1991), the book contains refereed articles concerning the existence of the most general unifier, a special case of Kreisel's conjecture on lengthofproof, propositional logic proof size, a new alternating logtime algorithm for boolean formula evaluation and relation to branching programs, interpretability between fragments of arithmetic, feasible interpretability, provability logic, open induction, Herbrandtype theorems, isomorphism between first and second order bounded arithmetics, forcing techniques in bounded arithmetic, ordinal arithmetic in L D o . Also included is an extended abstract of J P Ressayre's new approach concerning the model completeness of the theory of real closed exponential fields. Additional features of the book include (1) the transcription and translation of a recently discovered 1956 letter from K Godel to J von Neumann, asking about a polynomial time algorithm for the proof in ksymbols of predicate calculus formulas (equivalent to the PNP question), (2) an OPEN PROBLEM LIST consisting of 7 fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references.
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