Chat with us, powered by LiveChat

Describe a Turing Machine that accepts if the XOR of the first two binary numbers is equal to the third binary number and rejects otherwise.

Words: 328
Pages: 2
Subject: Computer Science

Consider the problem of conputing the XOR of two binary and determining if the result is equal to a third binary number. Suppose the input tape contains three binary numbers, separated by $ symbols. Each binary number consists of one or more bits with one bit per cell. E.g.,

# 0 1 1 0 $ 0 1 0 1 $ 0 0 1 1 # #

(a) Describe a Turing Machine that accepts if the XOR of the first two binary numbers is equal to the third binary number and rejects otherwise.

Note: You just need to describe how the TM would function as we have done in lectures. You do not need to specify the TM in full. Feel free to describe a multi-tape Turing Machine if that is easier.

(b) [5 marks] Describe a Random Access Machine that accepts if the XOR of the first two

binary numbers is equal to the third binary number and rejects otherwise. Note: You

just need to describe how the RAM would function as we have done in lectures.

  1. Consider the problem of checking if an XOR of n binary numbers is equal to 0. The input

tape contains n binary numbers, separated by $ symbols.

(a) Describe a Turing Machine that accepts if the XOR of the binary numbers

is 0. Note: You just need to describe how the TM would function as we have done in

lectures. You do not need to specify the TM in full. Feel free to describe a multi-tape

Turing Machine if that is easier.

(b) Describe a Random Access Machine that accepts if the XOR of the binary

numbers is 0 and rejects otherwise. Note: You just need to describe how the RAM would

function as we have done in lectures.

Marking Scheme

Marking scheme for Question 1a, 1b, 2a, and 2b.

3 points 2 points 1 points 0 points

Correctness Machine would work as

described

Machine may not work

on some inputs

Reasonable attempt

made No answer provided

Description Description is suffi-

ciently detailed

Some key steps are miss-

ing

Very poor description or

no answer provided