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This chapter introduces fundamental concepts from classical computation, including Turing machines and universal circuit families, along with examples of computable and incomputable problems. A brief introduction to automata is provided with increasing computational capabilities, starting with Boolean circuits and culminating with the all-powerful Turing machine and the limits of computable problems and solutions. The Turing machine is then generalized to universal, probabilistic, and non-deterministic Turing machines. A connection between the uniform computing model of Turing machines and Boolean circuits is then made using universal circuit families.

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Theory of Computing

  • 章节

  • 发表日期：

    2026年

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  • Osama M. Raisuddin,
  • Suvranu De

摘要

This chapter introduces fundamental concepts from classical computation, including Turing machines and universal circuit families, along with examples of computable and incomputable problems. A brief introduction to automata is provided with increasing computational capabilities, starting with Boolean circuits and culminating with the all-powerful Turing machine and the limits of computable problems and solutions. The Turing machine is then generalized to universal, probabilistic, and non-deterministic Turing machines. A connection between the uniform computing model of Turing machines and Boolean circuits is then made using universal circuit families.