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Theory of computation homework solutions 4 15

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Personally I firmly believe that the real learning doesn't happen in lectures, but only when we are wrestling with a concept through a set of problems, designed specifically at the right difficulty so that it is challenging, sometimes frustrating, but rewarding and expands our knowledge and skills after solving them maybe with some help from your colleagues. Therefore it is okay if you find the problems hard; that is by design. We will have problem set coming out every week. Some problems are marked with a star ; these are more challenging and fun problems, and are therefore optional and do not count towards the final grades. However, working on these problems will help you master the materials and skills taught in this class.
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Theory of computation homework solutions 4 15
Theory of computation homework solutions 4 15
Theory of computation homework solutions 4 15
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From a mathematical perspective, limitations on the inherent capability of computers arise from the fact that there are fewer programs than there are problems we would like to solve. Of course, there are an infinite number of programs, but it turns out that infinity comes in different sizes, and the number of programs is a smaller sized infinity than the number of problems we wish to solve. We will start out with a counting argument to show inherent limitations on computers, and end up with examples of specific problems that computers cannot solve. In order to accomplish this, we will need a formal model of what a computer is. We will start out with simpler models, with limited power, and progress to models with greater power.
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The Theory of Computation provides a sound logical foundation to computer science. By comparing various formal models of computation with respect to their capabilities, it identifies both fundamental features and ultimate limitations of contemporary digital computing machinery. Rigorous notions of efficiency are captured by famous complexity classes such as P and PSPACE; and concepts like oracles or polynomial-time reduction permit to compare computational problems with respect to their algorithmic cost: NP-hardness results thus serve as 'beacons' of intractability.
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It serves as an introduction to formal models of languages and computation. Topics covered include finite automata and regular languages, pushdown automata and context-free languages, Turing machines, computability, and NP-completeness. Email: instructor's five-letter last name ccs. Office hours , West Village H Office hours: held in the lounge outside room Thursday 11 -
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