1.1
A finite automata is a 5-tuple (state, alphabet, transition function, start state, set of accept states) A language is a regular language if some finite automaton recognizes it Regular Operation:. Union, concatenation, star 1.2 DFA and NFA Theorem : Every Non-Deterministic Automaton Has An Equivalent Deterministic Automaton 1.3 R IS: 1. A for Some A in The Alphabet 2. ε 3. Ø 4. (R1∪r2) WHERE R1, R2 Are Regular Expressions 5. (R1оR2) where R1, R2 are regular expressions 6. R1 *, R1 is a regular expression Theorem:. A language is regular if and only if some regular expression describes it 1.4 Pumping lemma for regular languages If A is a regular language , There, WHERE, IFS ANY STRING IN A OF Length At Least P, Then S Many Be Divided Into Three Pieces, S = XYZ, Satisfying The Following Conditions: 1. for Each i 3 0, xyiz îA 2. | Y |> 0 3. | X Y | £ P
