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3. Theory of Computing

  • 2026
  • OriginalPaper
  • Chapter
Published in:
Authors
Osama M. Raisuddin
Suvranu De
Published in
Quantum Computing for Engineers
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the theoretical foundations of computing, starting with various types of automata and their computational limits. It explores combinational logic, finite state automata, and their capabilities, leading up to the introduction of Turing machines. The chapter discusses the Church-Turing thesis, which posits that Turing machines can simulate any algorithmic process, and highlights the halting problem as a notable example of an uncomputable problem. It also covers variants of Turing machines, including non-deterministic and probabilistic Turing machines, and their implications for computational complexity. The chapter concludes by reconciling the differences between Turing machines and Boolean circuits, introducing the concept of uniform circuit families. Readers will gain a deep understanding of the theoretical underpinnings of computing, the limits of computability, and the practical applications of these concepts in modern computing.
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previous chapter Polynomial Approximations
next chapter An Overview of Practical Classical Computing
Title
Theory of Computing
Authors
Osama M. Raisuddin
Suvranu De
Copyright Year
2026
Book
Quantum Computing for Engineers

Print ISBN: 978-3-032-03324-6

Electronic ISBN: 978-3-032-03325-3

Copyright Year: 2026

DOI
https://doi.org/10.1007/978-3-032-03325-3_3
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