Turing Machines


12rd lecture, June 24, 2016

Language Theory and Compilers


Martin J. Dürst


© 2005-15 Martin J. Dürst 青山学院大学

Today's Schedule


Summary of Previous Lecture


Example Solution for bison Homework

(paper only)


Formal Language Hierarchy

(Chomsky hierarchy)

Grammar Type Language (family) Automaton
phrase structure grammar (psg) 0 phrase structure language Turing machine
context-sensitive grammar (csg) 1 context-sensitive language linear bounded automaton
context-free grammar (cfg) 2 context-free language pushdown automaton
regular grammar (rg) 3 regular language finite state automaton


Historic Background


Automata Commonalities


Automata Differences


How a Turing Machine Works


Turing Machine Example


Turing Machine Definition



Techniques and Tricks for Programming



It can be shown that all these extensions can be simulated on a plain Turing machine


Universal Turing Machine


Computability is Everywhere

It turns out that there are many other mechanisms that can simulate an (universal) Turing machine:

All these mechanisms can simulate each other and have the same power.


Church-Turing Thesis

It is unclear whether this applies to Physics in general.


Other Contributions





Deadline: June 30, 2016 (Thursday), 19:00

Where to submit: Box in front of room O-529 (building O, 5th floor)

Format: A4 single page (using both sides is okay; NO cover page, staple in top left corner if more than one page is necessary), easily readable handwriting (NO printouts), name (kanji and kana) and student number at the top right

For the Turing machine given by the following state transition table:

Current state Current tape symbol New tape symbol Movement direction Next state
→1 0 1 L 1
→1 1 0 L 2
→1 _ _ L 4*
2 0 0 L 2
2 1 1 L 2
2 _ _ R 3
3 0 _ R 3
3 1 1 L 4*
  1. Draw the state transition diagram for this machine
  2. Show in detail how this machine processes the input ..._1100100_...
  3. Guess and explain what kind of calculation this machine does if the tape contains only a single contiguous sequence of '0'es and '1'es with at least one '1' (surrounded by blanks)

(The Turing machine always starts on the rightmost non-blank symbol)



universal turing machine