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Assignment #3 Consider the Deterministic Finite Automaton M Correct Answers

An assignment analyzing the deterministic finite automaton with correct solutions.

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Assignment #3Considerthe Deterministic Finite Automaton M CorrectAnswers1.ConsiderthedeterministicfiniteautomatonM=({q1,q2,q3},{0,1},δ,q1,{q2})whereδisdefinedasfollows:δ(q1,0)=q1δ(q1,1)=q2δ(q2,0)=q3δ(q2,1)=q2δ(q3,0)=q2δ(q3,1)=q2Writeanequivalentregularexpression.2.Provethatthefollowinglanguagesarenotregularsets:(a)L={aibjck|i=0∨j=k,i,j,k≥0}.Examplestringsincludebccc,abbcc,aaa,etc.+(b)L={ww|w∈{0,1}}.Examplestringsinclude00,11,0101,010010,etc.n(c)L={a2|n≥0}.Examplestringsincludeaaaa,a16,a64,etc.(d)L={w|w∈{0,1}∗,wisoftheform(0i1)n,fori=1,2,...,n,n≥0}.Thestringsofthislanguage areε,01,01001,010010001,....,eachsuccessivestringof0’sbeingonelargerthantheprevious.3.FindtheminimumstatefiniteautomatonforthelanguagespecifiedbythefiniteautomatonM=({q0,q1,q2,q3},{0,1},δ,q0,{q0})whereδisdefinedasfollows:

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