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Started by these guys Kurt and Turing - Coggle Diagram
Started by these guys
LANGUAGES
:star:
Natural Languages: How we talk
Formal Language: Not for human communication :forbidden:
Symbols,Strings :smiley:
Length |w| :red_flag:
Concatenation: XY :red_flag:
Alphabet: Finite set of symbols
Formal Language L: a set of strings from one alphabet :star:
Empty Language
Special Languages: Sigma+ Sigmastar : Sigmastar is a infinite set
All possible languages: P(sigma*)
Concatenation: L1L2
Union: L1 + L2
Kleene closure: L*
Empty Language: LPHI, PHI Remember: PHI* is not empty , it has { A }
Regular Expressions
:star:
Base cases: empty language, empty set , symbols in the alphabet
Recursion: r+s ( Union) , rs ( Concatenation) , r* Kleene Closure
Kleenes Theorem
: :star:
Conversion ( RE -> NFA with e moves ) :warning:
Algorithm :check:
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Conversion ( NFA with e moves -> RE ) :warning:
Algorithm :check:
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Classifying of languages :star:
REGULAR LANGUAGES :star:
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NON REGULAR LANGUAGES :star:
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The Pumping Lemma ???
:red_flag:
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Empty alphabet: :forbidden:
Formal Finite Automaton:
(FA)
: 5 tuple (Q,sigma,qo,T,Transition Function :red_flag:
Nondeterministic Finite Automaton
(NFA)
: M(Q,sigma,qo,T,Transition function:( Q X sigma -> P(Q) :red_flag:
Algorithm to solve: :check:
We consider only the set of states resulting from processing the entire string.
If at least one of those states is an accepting state, then accept the string, otherwise reject.
NFA with e-transitions
: M(Q,sigma,qo,T,(Q X (sigma UNION {e} ) -> P(Q) :red_flag:
E-closure: set of states :warning:
This means that when the automaton enters a state with an outgoing e-transition, the automaton may stay in that state or traverse the e-transition to its destination state.
Conversion(NFA with e-moves to FA)
:warning:
Algorithm (NFA with e -> DFA ) :check:
Same alphabet Lose column e
Loose all nondeterminism
Loose all empty sets
Cell values are now set of states
-> states
Empty string