Theory of Semi-Feasible Algorithms (EATCS Series: Monographs in Theoretical Computer Science)

Hardcover, x + 148 pages, NOT ex-library. Clean and bright throughout with unmarked text, free of inscriptions and stamps, firmly bound. Boards show minor handling wear. Issued without a dust jacket. -- -- Theory of Semi-Feasible Algorithms is a comprehensive academic work within the field of theoretical computer science, focusing on the study of computational complexity, particularly the concept of semi-feasibility in algorithms. The book dives deeply into the properties and implications of semi-feasible sets, which are closely linked to selectivity in computational problems. It systematically analyses P-selective and nondeterministic selective sets, the role of advice in computational complexity, and the significance of lowness within complexity classes. The authors discuss P-selectivity as a measure of the ease with which membership in a set can be decided when given partial information, and how this concept extends to nondeterministic selectivity. The work explores the practical boundaries of these theoretical models, including advice strings, which provide additional information that can be used to solve problems, offering both upper and lower bounds for such advice in P-selective sets. Additionally, the book addresses key questions in complexity theory, such as whether P-selective sets can be hard for other complexity classes, like NP and PSPACE, or whether they can be truth-table or Turing-hard for these classes. An important component of the book is its investigation of the lowness properties of P-selective and nondeterministically selective sets, exploring how these sets can be placed within larger complexity hierarchies, such as the polynomial hierarchy, and their implications for computational power. The work also examines the closure properties of selectivity under various reductions and operations, including Boolean closures, self-reducibility, and equivalence classes, providing detailed insights into how these sets behave under specific computational transformations. Hemaspaandra and Torenvliet further generalize selectivity through weaker forms, such as multiselectivity and probabilistic selector functions, and introduce refinements to P-selectivity like P-semi-rankability and associative P-selectivity. These generalizations provide a more nuanced understanding of the relationship between selectivity and computational complexity. The monograph is aimed at researchers and students in theoretical computer science, particularly those interested in computational complexity theory, semi-feasibility, and algorithmic efficiency. It offers foundational concepts, advanced theorems, and rigorous proofs that contribute to the understanding of how semi-feasible algorithms fit into the broader landscape of computational complexity. -- "This book presents a consolidated survey of the vibrant field of research known as the theory of semi-feasible algorithms. This research stream perfectly showcases the richness of, and contrasts between, the central notions of complexity: running time, nonuniform complexity, lowness, and NP-hardness. Research into semi-feasible computation has already developed a rich set of tools, yet is young enough to have an abundance of fresh, open issues. Being essentially self-contained, the book requires neither great mathematical maturity nor an extensive background in computational complexity theory or in computer science in general. Newcomers are introduced to the field systematically and guided to the frontiers of current research. Researchers already active in the field will appreciate the book as a valuable source of reference.".…