Finite Automata Fall 2018

∑ = {x,y} L1= set of all strings of size 2 over an alphabet ∑ L2= set of all strings of size 3 over an alphabet ∑ L3= set of all strings start with y.

L1 =? L2= ? L3 = ? S= ab

FA FA With output FA without output Moore Mealy DFA NDFA €-NFA

DFA Example DFA Definition/ Mathematical Model Acceptance of stings Construction of a DFA Practice NDFA Definition NDFA Construction Power of DFA and NDFA Minimization of DFA

DFA Example a,b A B a b C a,b

DFA Definition/ Mathematical Model:

Find smallest string from the language. Construction of a DFA Find smallest string from the language. Construct the DFA for the smallest string. Upgrade the DFA by considering all other strings. L1= set of all stings end with ‘a’ L2= {w | |W|>=2}

Practice L3= set of all strings starts with a L4=set of all strings contains a L5=set of all strings start with ab L6= set of all strings ends with ab L7=set of all strings contains ab L8=set of all strings start with ab L9={w | |W|<=2} L10={w | |W|=2}

NDFA Definition

NDFA Construction L1= set of all stings end with ‘a’ L2= {w | |W|>=2}

Practice: L3= set of all strings starts with a L4=set of all strings contains a L5=set of all strings start with ab L6= set of all strings ends with ab L7=set of all strings contains ab L8=set of all strings start with ab L9={w | |W|<=2} L10={w | |W|=2}

Power of DFA and NDFA DFA ≡ NFA NFA ≡ DFA

NDFA to DFA Conversion

Practice

Practice