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"An overview of current developments in research on feasible computations; and a consideration of this area of research in relation to provable properties of complexity of computations. The author begins by defining and discussing efficient reductions between problems and considers the families and corresponding complete languages of NL, DCSL, CSL, P, NP, PTAPE, EXPTIME, and EXPTAPE. Definitions and results are uniformly extended to computationally simpler natural families of languages such as NL, P, and CSL by using Log n-tape bounded reductions. The problem of determining what can and cannot be formally proven about running times of algorithms is discussed and related to the problem of establishing sharp time bounds for one-tape Turing machine computations, and the inability to formally prove running times for algorithms is then related to the presence of gaps in the hierarchy of complexity classes."

"Focuses on finding the minimum number of arithmetic operations needed to perform the computation and on finding a better algorithm when improvement is possible. The author concentrates on that class of problems concerned with computing a system of bilinear forms. Results that lead to applications in the area of signal processing are emphasized, since (1) even a modest reduction in the execution time of signal processing problems could have practical significance; (2) results in this area are relatively new and are scattered in journal articles; and (3) this emphasis indicates the flavor of complexity of computation."

"This book constitutes the refereed proceedings of the 14th International Workshop of Descriptional Complexity of Formal Systems 2012, held in Braga, Portugal, in July 2012. The 20 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 33 submissions. The topics covered are automata, grammars, languages and related systems, various measures and modes of operations (e.g., determinism and nondeterminism), trade-offs between computational models and/or operations, succinctness of description of (finite) objects, state explosion-like phenomena, circuit complexity of Boolean functions and related measures, resource-bounded or structure-bounded environments, frontiers between decidability and undecidability, universality and reversibility, structural complexity, formal systems for applications (e.g., software reliability, software and hardware testing, modeling of natural languages), nature-motivated (bio-inspired) architectures and unconventional models of computing, and Kolmogorov complexity."

"Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. "

"The goal of this book is to uncover techniques that will aid in overcoming complexity and enable us to produce reliable, dependable computer systems that will operate as intended, and yet are produced on-time, in budget, and are evolvable, both over time and at run time. We hope that the contributions in this book will aid in understanding the nature of software complexity and provide guidance for the control or avoidance of complexity in the engineering of complex software systems."