# Computational Complexity: Theory, Techniques, and Applications

Language: English

Pages: 3492

ISBN: 1461417996

Format: PDF / Kindle (mobi) / ePub

Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The recognition that the collective behavior of the whole system cannot be simply inferred from an understanding of the behavior of the individual components has led to the development of numerous sophisticated new computational and modeling tools with applications to a wide range of scientific, engineering, and societal phenomena.

Computational Complexity: Theory, Techniques and Applications presents a detailed and integrated view of the theoretical basis, computational methods, and state-of-the-art approaches to investigating and modeling of inherently difficult problems whose solution requires extensive resources approaching the practical limits of present-day computer systems. This comprehensive and authoritative reference examines key components of computational complexity, including cellular automata, graph theory, data mining, granular computing, soft computing, wavelets, and more.

concepts have obvious utility when considering different simulations of the same complex system. One can take diﬀerent points of view in deﬁning a transformation of SDS. One approach is to require that a transformation is compatible with the deﬁning structural elements of an SDS, that is, with the dependency graph, the local update functions, and the update schedule. If this is done properly, then one should expect to be able to prove that the resulting transformation induces a transformation at

has come to fruition over the past decade is micro-mechanical electronic component manufacture, which integrates logic circuits, micro-sensors, actuators, and communication on a single chip. Aggregates of these can be manufactured extremely inexpensively, provided that not all the chips need work correctly, and that there is no need to arrange the chips into precise geometrical conﬁgurations or to establish precise interconnections among them. A decade ago, researchers envisioned smart dust

solution of the equation Ã jCr Â X rC1 [C(r;s) ] i m C [C(r;s) ] i; jCs D ı i; jCs m jC1 mD j (30) ) D ˇ reduces to the pair of (1) (0) i C ˇi (0) (0) iC1 C ˇ i 1) d-Dimensional Rules Both [102,105] discuss the extension from one-dimensional to d-dimensional rules deﬁned on tori. In [102] this discussion uses a formalism of multinomials deﬁned over ﬁnite ﬁelds. In [105], the one-dimensional analysis based on circulant matrices is generalized. The matrix formulism of state transitions is

multi-lingual integration, generics, attributes for including metadata in compiled code, aspects, reﬂection, and dynamic method invocation make it well suited for agent-based model development, particularly on the Microsoft Windows platform. C++ C++ is a widely used object-oriented programming language that was created by Bjarne Stroustrup (Stroustrup [39]) at AT&T. C++ is widely noted for both its object-oriented structure and its ability to be easily compiled into native machine code. C++ gives

computational models of complex systems that take their place. An agent-based simulation, sometimes also called an individual-based or interaction-based simulation (which we prefer), of a complex system is in essence a computer program that realizes some (possibly approximate) model of the system to be studied, incorporating the agents and their rules of interaction. The simulation might be deterministic (i. e., the evolution of agent-states is governed by deterministic rules) or stochastic. The