The Analytical Engine Online: Theory of Computation

The Turing Machine is an abstract, mathematical model that describes what can and cannot be accomplished with computers. The labs for this module revolve around a Turing Machine (TM) simulator, called ITM. We will use ITM to demonstrate how abstract TMs machines work, how they are defined, how they compute, and how powerful they are.

Lab 8.1: Welcome to ITM

Lab 8.2: What's my Line?

Lab 8.3: Incompleteness and Ambiguity

Lab 8.4: Rolling Your Own

Concentrate on the view of a program as an abstract machine
Consider two ways of looking at abstract machines
Investigate and experiment with a variety of Turing Machines
Describe the expressive power and the limitations of Turing Machines

Module Quiz

Print
References

Our approach so far has been top-down, from applications to hardware, via design, programming, and program translation. Now that we've seen what programs¹ are and how a computer² can be designed to do what a program instructs it to do, this text module goes beyond computers to the nature of computation itself. We ask what a computer is; we ask what computation means; we see what computers can and cannot do - not just today's computers, but anything that we can imagine as a computer.
¹pp. 13, Mod. 2, 234, 273, 285
²pp. 7, 257

The fact that the Turing Machine³ (TM) was invented before there were any such things as modern-day computers should convince you that there is more to computation than hardware. Indeed, TMs - described solely in terms of abstract states, infinite tapes, simple read and write devices, and programs - are equal in computational power to any computer available today. By virtue of their abstract nature, they also help us to articulate the theoretical limits of computing, and so serve as an ideal metaphor for this module.
³pp. 271, 273–277, 280-281

	Print References
Our approach so far has been top-down, from applications to hardware, via design, programming, and program translation. Now that we've seen what programs¹ are and how a computer² can be designed to do what a program instructs it to do, this text module goes beyond computers to the nature of computation itself. We ask what a computer is; we ask what computation means; we see what computers can and cannot do - not just today's computers, but anything that we can imagine as a computer.	¹pp. 13, Mod. 2, 234, 273, 285 ²pp. 7, 257
The fact that the Turing Machine³ (TM) was invented before there were any such things as modern-day computers should convince you that there is more to computation than hardware. Indeed, TMs - described solely in terms of abstract states, infinite tapes, simple read and write devices, and programs - are equal in computational power to any computer available today. By virtue of their abstract nature, they also help us to articulate the theoretical limits of computing, and so serve as an ideal metaphor for this module.	³pp. 271, 273–277, 280-281

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