Turing machine

Concepts in Computer Science

Pritesh Patel

Computer Scientist & Data Scientist for over 20 years

From Automata to Turing Machines

  • Finite Automata: Limited memory, can handle regular languages.
  • Pushdown Automata: Stack-based memory, handles context-free languages.
  • Turing Machine: Unlimited memory (infinite tape), can solve all computable problems.

An illustration of Alan Turing

Concepts in Computer Science

What is a Turing Machine?

A diagram that shows how a Turing Machine functions

Turing Machine

  • Abstract machine with infinite tape.
  • Reads and writes symbols.
  • Capable of simulating any algorithm.
Concepts in Computer Science

Turning Machines via Analogy

An illustration of a kitchen with a cooking making a recipe as an analogy of a Turing Machine

Kitchen & Cook as Turing Machine

  • The counter is the tape.
  • The sections of the counter are the cells.
  • The ingredients are the symbols.
  • The cook is the head that reads and writes.
  • The recipe book is the program guiding the whole process.
Concepts in Computer Science

Why is a Turing Machine important?

Turing Machine & Computability

  • Capable of simulating any algorithm
  • Defines the boundary of what computers can solve
  • Introduces the concept of undecidable problems (e.g., the Halting Problem)
  • Lays the foundation for modern computing theory
Concepts in Computer Science

The halting problem

  • The Question: Can we predict if a program will halt (stop) or run forever on a specific input?
  • Turing's Insight: No universal algorithm exists to solve this for all programs.
  • Result: The Halting Problem is undecidable, some problems have no algorithmic solution.
  • Implications: Limits in computation affect cryptography & AI

A digram that shows what is the Halting Problem

Concepts in Computer Science

Let's practice!

Concepts in Computer Science

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