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This treatise presents an integrated perspective on the interplay
of set theory and graph theory, providing an extensive selection of
examples that highlight how methods from one theory can be used to
better solve problems originated in the other. Features: explores
the interrelationships between sets and graphs and their
applications to finite combinatorics; introduces the fundamental
graph-theoretical notions from the standpoint of both set theory
and dyadic logic, and presents a discussion on set universes;
explains how sets can conveniently model graphs, discussing set
graphs and set-theoretic representations of claw-free graphs;
investigates when it is convenient to represent sets by graphs,
covering counting and encoding problems, the random generation of
sets, and the analysis of infinite sets; presents excerpts of
formal proofs concerning graphs, whose correctness was verified by
means of an automated proof-assistant; contains numerous exercises,
examples, definitions, problems and insight panels.
This book presents a set of historical recollections on the work of
Martin Davis and his role in advancing our understanding of the
connections between logic, computing, and unsolvability. The
individual contributions touch on most of the core aspects of
Davis' work and set it in a contemporary context. They analyse,
discuss and develop many of the ideas and concepts that Davis put
forward, including such issues as contemporary satisfiability
solvers, essential unification, quantum computing and
generalisations of Hilbert's tenth problem. The book starts out
with a scientific autobiography by Davis, and ends with his
responses to comments included in the contributions. In addition,
it includes two previously unpublished original historical papers
in which Davis and Putnam investigate the decidable and the
undecidable side of Logic, as well as a full bibliography of Davis'
work. As a whole, this book shows how Davis' scientific work lies
at the intersection of computability, theoretical computer science,
foundations of mathematics, and philosophy, and draws its unifying
vision from his deep involvement in Logic.
This treatise presents an integrated perspective on the interplay
of set theory and graph theory, providing an extensive selection of
examples that highlight how methods from one theory can be used to
better solve problems originated in the other. Features: explores
the interrelationships between sets and graphs and their
applications to finite combinatorics; introduces the fundamental
graph-theoretical notions from the standpoint of both set theory
and dyadic logic, and presents a discussion on set universes;
explains how sets can conveniently model graphs, discussing set
graphs and set-theoretic representations of claw-free graphs;
investigates when it is convenient to represent sets by graphs,
covering counting and encoding problems, the random generation of
sets, and the analysis of infinite sets; presents excerpts of
formal proofs concerning graphs, whose correctness was verified by
means of an automated proof-assistant; contains numerous exercises,
examples, definitions, problems and insight panels.
This book presents a set of historical recollections on the work of
Martin Davis and his role in advancing our understanding of the
connections between logic, computing, and unsolvability. The
individual contributions touch on most of the core aspects of
Davis' work and set it in a contemporary context. They analyse,
discuss and develop many of the ideas and concepts that Davis put
forward, including such issues as contemporary satisfiability
solvers, essential unification, quantum computing and
generalisations of Hilbert's tenth problem. The book starts out
with a scientific autobiography by Davis, and ends with his
responses to comments included in the contributions. In addition,
it includes two previously unpublished original historical papers
in which Davis and Putnam investigate the decidable and the
undecidable side of Logic, as well as a full bibliography of Davis'
work. As a whole, this book shows how Davis' scientific work lies
at the intersection of computability, theoretical computer science,
foundations of mathematics, and philosophy, and draws its unifying
vision from his deep involvement in Logic.
An up-to-date and comprehensive account of set-oriented symbolic
manipulation and automated reasoning methods. This book is of
interest to graduates and researchers in theoretical computer
science and computational logic and automated reasoning.
"Set Theory for Computing" provides a comprehensive account of set-oriented symbolic manipulation methods suitable for automated reasoning. Its main objective is twofold: 1) to provide a flexible formalization for a variety of set languages, and 2) to clarify the semantics of set constructs firmly established in modern specification languages and in the programming practice. Topics include: semantic unification, decision algorithms, modal logics, declarative programming, tableau-based proof techniques, and theory-based theorem proving. The style of presentation is self-contained, rigorous and accurate. Some familiarity with symbolic logic is helpful but not a requirement. This book is a useful resource for all advanced students, professionals, and researchers in computing sciences, artificial intelligence, automated reasoning, logic, and computational mathematics. It will serve to complement their intuitive understanding of set concepts with the ability to master them by symbolic and logically based algorithmic methods and deductive techniques.
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Computational Intelligence Methods for Bioinformatics and Biostatistics - 14th International Meeting, CIBB 2017, Cagliari, Italy, September 7-9, 2017, Revised Selected Papers (Paperback, 1st ed. 2019)
Massimo Bartoletti, Annalisa Barla, Andrea Bracciali, Gunnar W. Klau, Leif Peterson, …
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R1,557
Discovery Miles 15 570
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Ships in 10 - 15 working days
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This book constitutes the thoroughly refereed post-conference
proceedings of the 14th International Meeting on Computational.
Intelligence Methods for Bioinformatics and Biostatistics, CIBB
2017, held in Cagliari, Italy, in September 2017. The 19 revised
full papers presented were carefully reviewed and selected from 44
submissions. The papers deal with the application of computational
intelligence to open problems in bioinformatics, biostatistics,
systems and synthetic biology, medical informatics, computational
approaches to life sciences in general.
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