A Turing machine computing the reverse function(Figure 7.11)

JianSyuan Wong

q0∆aabb

q0∆aabb Ⱶ ∆q1aabb

q0∆aabb Ⱶ ∆q1aabb Ⱶ ∆Aq2abb

q0∆aabb Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb

q0∆aabb Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆ Ⱶ ∆BBAq9A

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆ Ⱶ ∆BBAq9A Ⱶ ∆BBq9Aa

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆ Ⱶ ∆BBAq9A Ⱶ ∆BBq9AaⱵ ∆Bq9Baa

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆ Ⱶ ∆BBAq9A Ⱶ ∆BBq9AaⱵ ∆Bq9Baa Ⱶ ∆q9Bbaa

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆ Ⱶ ∆BBAq9A Ⱶ ∆BBq9AaⱵ ∆Bq9Baa Ⱶ ∆q9Bbaa Ⱶ q9∆bbaa

q0∆aabb

Ⱶ ∆q1aabb Ⱶ ∆Aq2abb Ⱶ ∆Aaq2bb Ⱶ ∆Aabq2b Ⱶ ∆Aabbq2∆ Ⱶ ∆Aabq3b Ⱶ ∆Aaq7bA Ⱶ ∆Aq7abA Ⱶ ∆q7AabA Ⱶ ∆Bq1abA Ⱶ ∆BAq2bA Ⱶ ∆BAbq2A Ⱶ ∆BAq3bA Ⱶ ∆Bq7AAA Ⱶ ∆Bq7AAAⱵ ∆BBq1AA Ⱶ ∆BBAq8A Ⱶ ∆BBAAq8∆ Ⱶ ∆BBAq9A Ⱶ ∆BBq9AaⱵ ∆Bq9Baa Ⱶ ∆q9Bbaa Ⱶ q9∆bbaa Ⱶ ha∆bbaa accept

q0∆aabb