Erik Jonsson School of Engineering and Computer Science

1. Erik Jonsson School of Engineering and Computer Science CS 4384– 001 Automata Theory http://www.utdallas.edu/~pervin Thursday: Chapter Four Tuesday4-15-14 FEARLESS Engineering

2. A search of Albert Einstein's archived manuscripts last year turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe. Einstein was attempting to make sense of Edwin Hubble's observation that the universe was expanding, but he made a mathematical error. When he discovered his mistake, he set aside the paper, which is now in a digital archive of his papers at the Hebrew University in Jerusalem. Waterford Institute of Technology physicist Cormac O'Raifeartaigh and colleagues found the paper while scouring the archive.

3. Examination II

11. Turing Machines Effective Computability

14. Turing Machine (Alan Turing, 1936) • Post Systems (Emil Post, 1936) • μ-recursive functions (Kurt Gödel) • λ-calculus (Alonzo Church, 1932) • Combinatory logic (Haskell B Curry, 1929) Attempts to define effective computability

15. Alan Matheson Turing

18. Princeton Alumni Magazine

25. As before, there are many slightly different – but equivalent – definitions of a Turing Machine. Our (free) text starts out with a machine with k tapes! I don’t like that and nobody else does that. A one-tape machine is the appropriate way to start. Turing Machines

26. Our (free) text uses an input tape that is infinite in both directions as does our (free) JFLAP. Almost all beginning machines start with a “semi-infinite” tape, i.e., one that has a left beginning cell and unlimited cells to the right. It does not matter – just unusual. Our (free) text allows the tape head to move either left (L) or right (R) along the input tape, but also allows it to not go to a different cell after a move (N). Most do not allow an “N” move (it does not matter – it’s just unusual). Each text uses a different symbol for the “blank” character (and usually allows it to be written). Examples: ̺ , □, ʙ, Δ Other differences

27. Definition

28. Definition

29. Example

35. Palindrome