Complexity Properties of Recursively Enumerable Sets
Author | : Ivan da Costa Marques |
Publisher | : |
Total Pages | : |
Release | : 1973 |
Genre | : |
ISBN | : |
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Author | : Ivan da Costa Marques |
Publisher | : |
Total Pages | : |
Release | : 1973 |
Genre | : |
ISBN | : |
Author | : Paul Henry Morris |
Publisher | : |
Total Pages | : 160 |
Release | : 1974 |
Genre | : |
ISBN | : |
Author | : Juris Hartmanis |
Publisher | : SIAM |
Total Pages | : 69 |
Release | : 1978-01-01 |
Genre | : Mathematics |
ISBN | : 9781611970395 |
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. The concluding discussion is on the possibility that the famous P=NP? problem is independent of the axioms of formal mathematical systems such as set theory.
Author | : Robert I. Soare |
Publisher | : Springer Science & Business Media |
Total Pages | : 460 |
Release | : 1999-11-01 |
Genre | : Mathematics |
ISBN | : 9783540152996 |
..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
Author | : Victor Lawrence Bennison |
Publisher | : |
Total Pages | : 166 |
Release | : 1976 |
Genre | : Recursive functions |
ISBN | : |
Author | : G. Lolli |
Publisher | : Springer Science & Business Media |
Total Pages | : 228 |
Release | : 2011-06-17 |
Genre | : Mathematics |
ISBN | : 364211072X |
S. Homer: Admissible recursion theory.- B.E. Jacobs: Computational complexity and recursion theory.- D. Normann: A survey of set recursion.- G.E. Sacks: Priority arguments in Higgler recursion.- R.I. Soare: Construction in the recursively enumerable degrees.- W. Maass: Recursively invariant recursion theory.
Author | : Anil Nerode |
Publisher | : American Mathematical Soc. |
Total Pages | : 538 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 0821814478 |
Author | : Barry S. Cooper |
Publisher | : Springer Science & Business Media |
Total Pages | : 388 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461507553 |
Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.
Author | : Andrea Sorbi |
Publisher | : CRC Press |
Total Pages | : 384 |
Release | : 1997-02-04 |
Genre | : Mathematics |
ISBN | : 9780824700263 |
"Integrates two classical approaches to computability. Offers detailed coverage of recent research at the interface of logic, computability theory, nd theoretical computer science. Presents new, never-before-published results and provides informtion not easily accessible in the literature."
Author | : Ming Li |
Publisher | : Springer Science & Business Media |
Total Pages | : 655 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475726066 |
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).