1. Context Sensitive Grammar & Turing Machines
Akram Salah

2. Language L is a set of strings, w, over an alphabet S
A grammar G(V, T, S, P) in which P is a set of rules.
Strings generated, or accepted, by G, L(G), is a language
An automaton is a machine that accepts, or acts upon, a set of strings.
Strings that are generated, or accepted, by an automaton defines a language.

3. Regular Languages Simple Nested patterns
We need a higher level languages
Regular grammars
Production rules are restricted
LHS must be a single variable
RHS is either left linear or right linear
Automata associated with regular languages are finite.

4. Context free Languages
A level higher than regular languages
Grammars
Production rules
RHS constraints are relaxed
Parsing is tree like, ambiguity
Automata
Push down automata
Stack, in addition to finite automata

5. Context Sensitive Grammar
A grammar G = (V, T, S, P) is said to be context-sensitive if production rules in P have the form
x -> x, where
x& y e (V u T)+ and |x| < |y|
Non-contracting
A language L is said to be context sensitive iff there is a context sensitive grammar G such that L = L(G) u L.
We have relaxed the constraints on RHS & LHS
Note that a regular and context free languages, are also context sensitive.

6. Context sensitive G = ({A, B, S}, {a, b, c}, S, P), where P
S -> abc|aAbc,,
Ab -> bA,
Ac -> Bbcc,
bB -> Bb,
aB -> aa|aaA.
S => aAbc => abAc => abBbcc
=> aBbbcc => aaAbbbb => aabBbcc
=> aabbAcc => aabbBbccc
=> aabBbbccc => aaBbbbccc
=> aaabbbccc. a3b3c L= {anbncn : n > 1}

7. Control Unit
Read-write head
Tape

8. Turing Machine A Turing machine M is
M = (Q, S, G, d, q0, [], F), where
Q finite set of internal states of control unit,
S input alphabet,
G finite set of symbols called tape alphabet,
d: Q x G -> Q x G x {L, R} is a transition function,
[] e G is a special symbol called blank,
q0 e Q is the initial state of the control unit,
F subset Q is the set of final states.

9. Turing Machine Design a Turing machine that accepts
L = {an bn : n > 1}

10. Turing Machine Q = {q0, q1, q2, q3, q4} F = {q4}, S = {a, b}
G = {a, b, x, y, []}.

11. Turing Machine d(q0, a) = (q1, x, R), d(q1, a) = (q1, a, R),
d(q1, y) = (q1, y, R),
d(q1, b) = (q2, y, R),
d(q2, y) = (q2, y, L),
d(q2, a) = (q2, a, L),
d(q2, x) = (q0, x, R),
d(q0, y) = (q3, y, R),
d(q3, y) = (q3, y, R),
d(q3, []) = (q4, [], R).

12. Turing Machine
There are several models that follow Turing machine

13. Universal Turing Machine
Control Unit of Mu
Internal State of M
Description of M
Tape content of M

14. Universal Turing Machine
A universal Turing machine (reprogrammable Turing machine) Mu
An automaton that, given as input a description of any Turing machine M and a string w, can simulate the computation of M on w

15. The Chomsky Hierarchy
Type 0: languages generated by unrestricted grammars
Recursively enumerable languages (LRE)
Type 1: languages generated by context sensitive grammars (LCS).
Type 2: languages generated by context-free grammars (LCF).
Type 3: languages generated by regular grammars (LREG)
Each language family type i is proper subset of the family type i-1.
deterministic context-free (LDCF), recursive languages (LREC)

16. The Chomsky Hierarchy RE CS CF
REG