CS 342 Lecture -*- Outline -*-

* Turing machines (A. Turing, 1936)
**	Turing's thesis
		(Why we're interested)
		every algorithmic problem solution can be
			represented by program of some Turing machine.
		want to compare langauges, compare them on the same problem.

** Informal presentation
	*draw picture with tape extending to right*
	finite state control, "final state light"
	storage tape (one-way tape of cells), read/write head
		tape is unbounded => can store and retrieve unlimited info.

***	primitive actions:
		read a symbol, write a symbol, move right or left one cell
			(and change state)
		direction and symbol written depend on state and symbol read

***	Example: TM that recognizes 1*
		Input alphabet = {0,1}
		transititions (show *graphically*)
			q0: read 1, write 1, move right, goto q0
			    read 0, write 0, move right, goto error
			    read Blank, write Blank, move right, goto halt

**	Formal def:  T = (K, Sigma, Gamma, delta, q0, F)
		K     is finite set of states
		Gamma is finite set of tape symbols, with B for blank
		Sigma is the input alphabet, a subset of Gamma\{B}
		delta is the next move function
			delta: K\F x Gamma -> K x (Gamma\{B}) x {L,R}
			delta is partial: in particular not defined on final
					states, may not be on others
		q0    is the start state, an element of K
		F     is a set of final states, a subset of K

***	Configuration: (q, alpha, i)
		q     is current state
		alpha is the nonblank portion of the tape
				(a string in (Gamma\{B})* )
		i     is the distance from the left where the tape head is
				(leftmost location is 1)

***	inital configuration: (q0, input-string, 1)
***	halting configuration
		(q, alpha, i) where delta(q,alpha[i]) is not defined
***	accepting configuration: a halting configuration where q in F