Barry S. Cooper Knihy

The introduction discusses the necessity of the concept of Computably Enumerable (CiE) sets, followed by various explorations in computational theory. Topics include the Solovay and Strong Weak Truth Table degrees, the Fan Theorem, continuous semantics for strong normalization, and advancements in membrane computing. The text delves into comparing computational models, the implications of recombinant DNA in formal languages, and the principles of quantum computing. It also addresses symbol grounding in connectionist models and the complexity of inductive definability. Further discussions cover a logical approach to abstract algebra, Schnorr dimension, and abstract geometrical computation, emphasizing Turing-computing ability and undecidability. The annotation highlights computability in geometry, a language for sequential real number computation, and the intricacies of Borel ranks. It also examines various aspects of model theory, definability in enumeration degrees, and proof mining in functional analysis. Additional topics include the power of mobility in membrane computing, the complexity of algorithms, and the relationship between approximation problems and PCPs. The text presents insights into the computational complexity of sandpiles, recursion, and formalizing arithmetic in type theory. Lastly, it explores new algorithmic paradigms, computability in discrete dynamical systems, and the transfinite action of Turing mach

In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing . These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work.