1. Lab Session 1 Turing Machines

2. Install Download and unzip TM.zip on the desktop Start the “Turing Machine” executable File>machine>load COPYING.TM File>tape>load Tape 8.tt Press CTRL-T to display the tape Press the “step” button repeatedly and monitor what is going on until the machine halts

3. First Try Build the following TM File>machine>new (default options ok) A bug in the program might display part of the previous TM. It is not actually there

4. First Try Press CTRL-A to show Alphabet Window Define the alphabet: ◦ Alphabets>Set Input Alphabets ◦ and choose “1” and press IMPORTANT: you have to define the alphabet before you do anything else. You can’t change the alphabet once you start designing the TM

5. First Try Create 3 states: ◦ Click on ◦ And click anywhere on the blank screen to draw the state Create 2 transitions: ◦ Click on ◦ Click on state0 and state1 and then click somewhere in between the two states to draw the transition

6. First Try The dialogue on the right will appear For the 1 st transition ◦ select 1 as scan symbol ◦ L as action For the 2 nd transition ◦ press space in the scan symbol box (results in „ = blank) ◦ 1 as action

7. First Try Press CTRL-T to display the tape Write 111 as a representation of number 2 Set the head of the machine on the first 1 and run the machine step by step and monitor the actions

8. Exercise 1 Select a language from the list below and create a language accepting Turing Machine for it (you can use any variation oneway/twoway, (non)deterministic, single/multitape, terminal state) ◦ (a) {a 2 b n |n  0} ◦ (b) {a 2 b n |n  1} ◦ (c) {a 3 b n |n  2} ◦ (d) {a n b 2 |n  0} ◦ (e) {a n b 3 |n  1} ◦ (f) {a 2 b n a 3 |n  0} ◦ (g) {ba 2 b n |n  0} ◦ (h) {b 2 a 2 b n a|n  0} ◦ (i) {b 2 a 2 b n |n  1} (j) {a 2 b n |n2} (k) {a n b m |n,m0} (l) {a 2 b n |n4} (m) {a 2 b n c n |n0} (n) {(ab) n |n0} (o) {a 2n |n0} (p) {a n b m a n |n,m0} (q) {a n |n prime}

9. Exercise 2 Create a number-theoretic function computing Turing Machine for one of the following functions (you can use any variation oneway/twoway, (non)deterministic, single/multitape, terminal state ) ◦ f(n) = 2n + 3 ◦ f(n) = 3n ◦ f(n) = 3n + 4