![Example
Set of strings over {a,b} that contain “bb”
q2q0 q1
a b
a
b
a
b
d a b
q0 q0 q1
q1 q0 q2
q2 q2 q2
}2{
},{
}2,1,0{
qF
ba
qqqQ
],1[],0[ *
qaabq ](https://image.slidesharecdn.com/finiteautomata-170619174558/85/Finite-automata-8-320.jpg)
Finite automata
- 2. Content • Finite automata • Types of finite automata • Finite state diagram • Deterministic finite automata(DFA) • Example of DFA • Non-deterministic finite automata(NFA) • Example of NFA
- 3. Finite Automata A finite automata (FA) is a simple idealized machine used to recognize patterns within input taken from some character set (or alphabet) C. the job of an FA is to accept or reject a input depending on whether the pattern defined by the FA occurs in the input.
- 4. Types of finite automata Finite automata without output Deterministic finite automata Non-deterministic finite automata Finite automata with output Mealy machine Moore machine
- 5. Finite State Diagram • A graphic representation of a finite automata A finite state diagram is a directed graph, where nodes represent elements in Q (i.e., states) and arrows are characters in such that: qa qb Indicates: transmission between qa to qb with a. The initial state is marked with: > The final state(s) are marked with: a
- 6. Deterministic finite automata For each pair of states and possible input chars, there is a unique next state (as specified by the transitions), then the FA is deterministic finite automata. That means the DFA follow single path with single transmission.
- 7. Deterministic finite automata Q:Finite set of states : Finite Alphabet d: Transition function - a total function from Qx to Q q0:Initial/Start State F :Set of final/accepting state ),,,,( 0 FqQM d
- 8. Example Set of strings over {a,b} that contain “bb” q2q0 q1 a b a b a b d a b q0 q0 q1 q1 q0 q2 q2 q2 q2 }2{ },{ }2,1,0{ qF ba qqqQ ],1[],0[ * qaabq
- 9. Another Example Build a FA to accept strings of even length q1 a,b a,b q0
- 10. Non-Deterministic finite automata For each pair of states and possible input chars, there may be more then one next state (as specified by the transitions), then the FA is non-deterministic finite automata. Conceptually, a nondeterministic FA can follow many paths simultaneously.
- 11. Non-deterministic finite automata (NDFA) or (NFA) M = (Q,, , s, F) where Q= Finite set of states = Input alphabet = Q x 2^Q s = Initial state F = Final state
- 12. Difference between DFA and NFA qi qj qkq qi qj a a a DFA NFA a
- 13. String having alphabet =(a,b) • String accept language start with a and end with a. q0 qf q1 a b a b a b q2
- 14. Another Example Build a FA to accept strings of even length q0 q1 q2 a,b a,b