By Oded Goldreich
This publication deals a accomplished standpoint to fashionable issues in complexity thought, that's a significant box of the theoretical foundations of desktop technological know-how. It addresses the looming query of what could be completed inside a constrained period of time without or with different restricted typical computational assets. can be utilized as an advent for complicated undergraduate and graduate scholars as both a textbook or for self-study, or to specialists, because it offers expositions of a number of the sub-areas of complexity conception corresponding to hardness amplification, pseudorandomness and probabilistic evidence structures.
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Extra info for Computational Complexity: A Conceptual Perspective
So far we have focused on the time complexity of computational tasks, while relying on the natural association of efficiency with time. However, time is not the only resource one should care about. Another important resource is space: the amount of (temporary) memory consumed by the computation. The study of space complexity has uncovered several fascinating phenomena, which seem to indicate a fundamental difference between space complexity and time complexity. For example, in the context of space complexity, verifying proofs of validity of assertions (of any specific type) has the same complexity as verifying proofs of invalidity for the same type of assertions.
Furthermore, even when specific computational problems are studied, this study is (explicitly or at least implicitly) aimed at understanding the computational limitations of certain resource bounds. The aforementioned general perspective seems linked to the significant role of conceptual considerations in the field: The rigorous study of an intuitive notion of efficiency must be initiated with an adequate choice of definitions. , a specific algorithmic schema). Indeed, the definitions attempt to capture any possible reality, which means that the choice of definitions is governed by conceptual principles and not merely by empirical observations.
One aspect that makes Complexity Theory unique is its perspective on the most basic question of the theory of computation, that is, the way it studies the question of what can be efficiently computed. The perspective of Complexity Theory is general in nature. This is reflected in its primary focus on the relevant notion of efficiency (captured by corresponding resource bounds) rather than on specific computational problems. In most cases, complexity theoretic studies do not refer to any specific computational problems or refer to such problems merely as an illustration.