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Computational complexity
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e-book
This book is about complexity science, data structures and algorithms, intermediate programming in Python, and the philosophy of science: Data structures and algorithms: A data structure is a collection that contains data elements organized in a way that supports particular operations. For example, a dictionary organizes key-value pairs in a way that provides fast mapping from keys to values, but mapping from values to keys is generally slower. An algorithm is a mechanical process for performing a computation. Designing efficient programs often involves the co-evolution of data structures and the algorithms that use them. For example, the first few chapters are about graphs, a data structure that is a good implementation of a graph---nested dictionaries---and several graph algorithms that use this data structure. Python programming: This book picks up where Think Python leaves off. I assume that you have read that book or have equivalent knowledge of Python. As always, I will try to emphasize fundmental ideas that apply to programming in many languages, but along the way you will learn some useful features that are specific to Python. Computational modeling: A model is a simplified description of a system that is useful for simulation or analysis. Computational models are designed to take advantage of cheap, fast computation. Philosophy of science: The models and results in this book raise a number of questions relevant to the philosophy of science, including the nature of scientific laws, theory choice, realism and instrumentalism, holism and reductionism, and Bayesian epistemology. This book focuses on discrete models, which include graphs, cellular automata, and agent-based models. They are often characterized by structure, rules and transitions rather than by equations. They tend to be more abstract than continuous models; in some cases there is no direct correspondence between the model and a physical system. Complexity science is an interdisciplinary field---at the intersection of mathematics, computer science and physics---that focuses on these kinds of models. That's what this book is about.
- Subjects:
- Computing
- Keywords:
- Computational complexity Python (Computer program language) Textbooks
- Resource Type:
- e-book
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e-book
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
- Subjects:
- Computing
- Keywords:
- System analysis -- Mathematical models Computational complexity Textbooks System theory -- Mathematical models
- Resource Type:
- e-book
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Courseware
Computability Theory deals with one of the most fundamental questions in computer science: What is computing and what are the limits of what a computer can compute? Or, formulated differently: “What kind of problems can be algorithmically solved?” During the course this question will be studied. Firstly, the notion of algorithm or computing will be made precise by using the mathematical model of a Turing machine. Secondly, it will be shown that basic issues in computer science, like “Given a program P does it halt for any input x?” or “Given two program P and Q, are they equivalent?” cannot be solved by any Turing machine. This shows that there exist problems that are impossible to solve with a computer, the so-called “undecidable problems”. The book is in English, the recorded lectures and slides however, are in Dutch
- Subjects:
- Computing
- Keywords:
- Machine theory Computational complexity Computable functions
- Resource Type:
- Courseware
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Courseware
This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computational complexity
- Resource Type:
- Courseware