Chapter 10
Models of Computation
A Model of Computing Agent – The Turing Machine Figure 10.1 A Turing Machine Tape
A Model of Computing Agent – The Turing Machine –
Figure 10.2 A Turing Machine Configuration
A Model of Computing Agent – The Turing Machine –
Figure 10.3 The Next Turing Machine Configuration after
Executing One Instruction
A Model of Computing Agent – The Turing Machine –
The Turing Machine Looks For an Appropriate
Instruction of the Form (2,0,-,-,-) – This Agrees With
Figure 10.3
A Model of Computing Agent – The Turing Machine –
The Turing Machine Looks for an Instruction of the
form (2,1,-,-,-) Instruction 4 Applies
A Model of Computing Agent - The Turing Machine –
Again the Turing Machine looks for Instruction 4
A Model of Computing Agent – The Turning Machine –
The Turing Machine looks to Instruction No 5, Leading
to This Configuration
A Model of Computing Agent – The Turing Machine –
Practice Problems 1, ( a)
A Model of Computing Agent – The Turing Machine –
Practice Problems (b)
A Model of Computing Agent – The Turing Machine –
Practice Problems ©
A Model of Computing Agent – The Turing Machine –
Practice Problems (d)
A Model of Computing Agent – The Turing Machine –
Practice Problems (2)
A Model of An Algorithm –A Turing Machine – A Turing
Machine Halts in a Finite Amount of Time. The Tape
Contains the Single Symbol 1. This is the Initial
Configuration and the Turning Machine Halts
A Model of An
Algorithm – The
Turing Machine –
the second set of
instructions contains
the single symbol
“O” and will
continue to apply,
thus the turing
machine will never
halt
A Model of An Algorithm – Turing Machine Examples – Figure
10.4 –State Diagram for the Bit Inverter Machine
A Model of An Algorithm – Turing Machine Examples – A
Sample Computation Using The Turing Machine Beginning
With the String 1101
A Model of An Algorithm – Turing Machine Examples – A
Sample Computation Using Instruction No. 2
A Model of An Algorithm – Turing Machine Examples – A
Sample Computation Using Instruction No. 2 Again.
A Model of An Algorithm – Turing Machine Examples – A
Sample Computation Using Instruction No. 1
A Model of An Algorithm – Turing Machine Examples – A
Sample Computation Using Instruction No. 2
A Model of An Algorithm – A Parity Bit Machine - Figure 10.5 State
Diagram for the Parity Bit Machine
A Model of An Algorithm – A Parity Bit Machine – The
Initial Configuration
A Model of An Algorithm – A Parity Bit Machine – A
Configuration Using Instruction No. 1
A Model of An Algorithm – A Parity Bit Machine – A
Configuration Using Instruction No. 4
A Model of An Algorithm – A Parity Bit Machine – A
Configuration Using Instruction No. 3
A Model of An Algorithm – A Parity Bit Machine – A
Configuration Using Instruction No. 5 to Write the
Parity Bit, Whereupon the Machine Halts.
A Model of An Algorithm – Machines for Unary
Incrementing –Figure 10.6 State Diagram for Incrementer
A Model of An
Algorithm –
machines for unary
incrementing – A
turing machine does
a quick sample
computation at
which point the
machine halts
A Model of An Algorithm – Machines For Unary Incrementing - If
we apply this algorithm to the same input tape, the computation is
this
A Model of An Algorithm – A Unary Addition Machine –
Figure 10.8 State Diagram for the Addition Machine
A Model of An Algorithm – Unsolvable Problems – Figure 10.10
Hypothetical Turing Machine P Running on T* and t
A Model of An Algorithm – Unsolvable Problems – Figure 10.11
Hypothetical Turing Machine Q Running on T* and t
A Model of An
Algorithm – Unsolvable
Problems – Figure 10.12
Hypothetical Turing
Machine S Running on
S*
A Model of An Algorithm – Challenge Work – Multitrack
Turing Machine – Figure 10.13 A Two-Track Turing
Machine
A Model of An Algorithm – Challenge Work – Multitrack
Turing Machine Figure 10.14 New Configuration for the
Two-Track Machine
A Model of An Algorithm – Unsolvable Problems – It is important to
know that computability has its limits, beyond which lies the Great
Abyss of the Uncomputable