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The Complexity Of Boolean Functions

The Complexity of Boolean Functions PDF

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Author: Ingo Wegener
Publisher: Wiley
ISBN: 9780471915553
Size: 19.98 MB
Format: PDF, ePub, Docs
Category : Computers
Languages : en
Pages : 470
View: 7520

Book Description: Presents a large number of recent research results previously unavailable in book form. Initially deals with the wee-known computation models, and goes on to special types of circuits, parallel computers, and branching programs. Includes basic theory as well recent research findings. Each chapter includes exercises.


Boolean Function Complexity

Boolean Function Complexity PDF

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Author: Stasys Jukna
Publisher: Springer Science & Business Media
ISBN: 3642245080
Size: 60.67 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 620
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Book Description: 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 book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.


Average Time Complexity Of Decision Trees

Average Time Complexity of Decision Trees PDF

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Author: Igor Chikalov
Publisher: Springer Science & Business Media
ISBN: 3642226612
Size: 23.15 MB
Format: PDF, ePub, Docs
Category : Computers
Languages : en
Pages : 104
View: 354

Book Description: Decision tree is a widely used form of representing algorithms and knowledge. Compact data models and fast algorithms require optimization of tree complexity. This book is a research monograph on average time complexity of decision trees. It generalizes several known results and considers a number of new problems. The book contains exact and approximate algorithms for decision tree optimization, and bounds on minimum average time complexity of decision trees. Methods of combinatorics, probability theory and complexity theory are used in the proofs as well as concepts from various branches of discrete mathematics and computer science. The considered applications include the study of average depth of decision trees for Boolean functions from closed classes, the comparison of results of the performance of greedy heuristics for average depth minimization with optimal decision trees constructed by dynamic programming algorithm, and optimization of decision trees for the corner point recognition problem from computer vision. The book can be interesting for researchers working on time complexity of algorithms and specialists in test theory, rough set theory, logical analysis of data and machine learning.


Complexity Theory

Complexity Theory PDF

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Author: Ingo Wegener
Publisher: Springer Science & Business Media
ISBN: 3540210458
Size: 65.96 MB
Format: PDF, ePub, Mobi
Category : Computers
Languages : en
Pages : 308
View: 407

Book Description: Reflects recent developments in its emphasis on randomized and approximation algorithms and communication models All topics are considered from an algorithmic point of view stressing the implications for algorithm design


The Complexity Of Valued Constraint Satisfaction Problems

The Complexity of Valued Constraint Satisfaction Problems PDF

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Author: Stanislav Zivny
Publisher: Springer Science & Business Media
ISBN: 3642339735
Size: 21.39 MB
Format: PDF, Kindle
Category : Computers
Languages : en
Pages : 170
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Book Description: The topic of this book is the following optimisation problem: given a set of discrete variables and a set of functions, each depending on a subset of the variables, minimise the sum of the functions over all variables. This fundamental research problem has been studied within several different contexts of discrete mathematics, computer science and artificial intelligence under different names: Min-Sum problems, MAP inference in Markov random fields (MRFs) and conditional random fields (CRFs), Gibbs energy minimisation, valued constraint satisfaction problems (VCSPs), and, for two-state variables, pseudo-Boolean optimisation. In this book the author presents general techniques for analysing the structure of such functions and the computational complexity of the minimisation problem, and he gives a comprehensive list of tractable cases. Moreover, he demonstrates that the so-called algebraic approach to VCSPs can be used not only for the search for tractable VCSPs, but also for other questions such as finding the boundaries to the applicability of certain algorithmic techniques. The book is suitable for researchers interested in methods and results from the area of constraint programming and discrete optimisation.


Descriptional Complexity Of Formal Systems

Descriptional Complexity of Formal Systems PDF

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Author: Jürgensen
Publisher: Springer
ISBN: 3642393101
Size: 44.55 MB
Format: PDF, Mobi
Category : Computers
Languages : en
Pages : 289
View: 6507

Book Description: This book constitutes the refereed proceedings of the 15th International Workshop of Descriptional Complexity of Formal Systems, DCFS 2013, held in London, ON, Canada, in July 2013. The 22 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 46 submissions. The topics covered are automata, grammars, languages and other formal systems; various modes of operations and complexity measures; co-operating systems; succinctness of description of objects, state-explosion-like phenomena; circuit complexity of Boolean functions and related measures; size complexity and structural complexity of formal systems; trade-offs between computational models and mode of operation; applications of formal systems; for instance in software and hardware testing, in dialogue systems, in systems modeling or in modeling natural languages; and their complexity constraints; size or structural complexity of formal systems for modeling natural languages; complexity aspects related to the combinatorics of words; descriptional complexity in resource-bounded or structure-bounded environments; structural complexity as related to descriptional complexity; frontiers between decidability and undecidability; universality and reversibility; nature-motivated (bio-inspired) architectures and unconventional models of computing; Kolmogorov-Chaitin complexity, algorithmic information.


Communication Complexity And Parallel Computing

Communication Complexity and Parallel Computing PDF

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Author: Juraj Hromkovič
Publisher: Springer Science & Business Media
ISBN: 9783540574590
Size: 76.50 MB
Format: PDF, ePub, Mobi
Category : Computers
Languages : en
Pages : 336
View: 1110

Book Description: The communication complexity of two-party protocols is an only 15 years old complexity measure, but it is already considered to be one of the fundamen tal complexity measures of recent complexity theory. Similarly to Kolmogorov complexity in the theory of sequential computations, communication complex ity is used as a method for the study of the complexity of concrete computing problems in parallel information processing. Especially, it is applied to prove lower bounds that say what computer resources (time, hardware, memory size) are necessary to compute the given task. Besides the estimation of the compu tational difficulty of computing problems the proved lower bounds are useful for proving the optimality of algorithms that are already designed. In some cases the knowledge about the communication complexity of a given problem may be even helpful in searching for efficient algorithms to this problem. The study of communication complexity becomes a well-defined indepen dent area of complexity theory. In addition to a strong relation to several funda mental complexity measures (and so to several fundamental problems of com plexity theory) communication complexity has contributed to the study and to the understanding of the nature of determinism, nondeterminism, and random ness in algorithmics. There already exists a non-trivial mathematical machinery to handle the communication complexity of concrete computing problems, which gives a hope that the approach based on communication complexity will be in strumental in the study of several central open problems of recent complexity theory.


Coding And Complexity

Coding and Complexity PDF

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Author: G. Longo
Publisher: Springer
ISBN: 3709130085
Size: 56.34 MB
Format: PDF, Docs
Category : Technology & Engineering
Languages : en
Pages : 334
View: 6800

Book Description:


Automata Languages And Programming

Automata  Languages and Programming PDF

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Author: Luca Aceto
Publisher: Springer Science & Business Media
ISBN: 3540705740
Size: 28.98 MB
Format: PDF, Mobi
Category : Computers
Languages : en
Pages : 896
View: 600

Book Description: Annotation The two-volume set LNCS 5125 and LNCS 5126 constitutes the refereed proceedings of the 35th International Colloquium on Automata, Languages and Programming, ICALP 2008, held in Reykjavik, Iceland, in July 2008.The 126 revised full papers presented together with 4 invited lectures were carefully reviewed and selected from a total of 407 submissions. The papers are grouped in three major tracks on algorithms, automata, complexity and games, on logic, semantics, and theory of programming, and on security and cryptography foundations. LNCS 5126 contains 56 contributions of track B and track C selected from 208 submissions and 2 invited lectures. The papers for track B are organized in topical sections on bounds, distributed computation, real-time and probabilistic systems, logic and complexity, words and trees, nonstandard models of computation, reasoning about computation, and verification. The papers of track C cover topics in security and cryptography such as theory, secure computation, two-party protocols and zero-knowledge, encryption with special properties/quantum cryptography, various types of hashing, as well as public-key cryptography and authentication