Week 1:
Lecture 1
1.
Languages, Machines, Functions
2.
Languages
Regular Languages,
Context Free Language
Context Sensitive Languages
Recursively Enumerable Languages
How to define?
Grammars: Regular Grammars, CFG, CSG etc.
Grammar G = (V,
Σ
, P, S), where
V is a finite set called the variables
Σ
is a finite set, disjoint from V, called the variables
P is a set of productions (rules), where each production has a form of
α
->
β
and
α
,
β
∈
(V
∪
Σ
)
*
S is the start symbol.
Regular grammar
CFG, …
Example:
Even parity strings
({S, A}, {0,1}, P, S), where
P is:
S -> 1A
,
S ->
0S,
S -> 0
A -> 0A,
A -> 1,
A -> 1S
3.
Machines: Computability
Finite State Automata (DFA)
M = (Q,
Σ
,
δ
, q0, F), where
Q: a finite set called states
Σ
: a finite set called the alphabet
δ
: Q
×
Σ
→
Q is the transition function
q0
∈
Q is the start state
F
⊆
Q is the set of accept states
Example:
Even parity language
M1 = (Q,
Σ
,
δ
, q0, F), where
Q = {q0, q1}
Σ
= {0,1}
δ
:
0
1
q0
q0
q1
q1
q1
q0