Source of the RE 

>	s1 := "(0 + 1 ) * . (1 . 1 + ( 0 + 1 . ( 0 + 1 ) ) )"; s2 := "(0.0* + (1 + 0.0* .1 ).((0 + 1.1* .0).0 * .1)* .(1.1* + (0 + 1.1* .0).0*))";

 

(17.1.2.1)

 

(17.1.2.1)

 

>	nfa5b:=RE2NFA(s2): nfa5c:=RE2NFA(s1): isEmptyNFA(intersectNFA(nfa5b,complementNFA(nfa5c))); isEmptyNFA(intersectNFA(nfa5c,complementNFA(nfa5b)));

 

>	transitionGraph(simplifyDFA(minimalDFA(NFA2DFA(nfa5b)))); transitionGraph(simplifyDFA(minimalDFA(NFA2DFA(nfa5c))));

 

>	nops(op(1,nfa5b)) * nops(op(1,NFA2DFA(nfa5c)));

 

(17.1.2.2)

 

>

 

Another good example about equivalance of expressions 

>

nfa2 := NFA({q0, q1, q2, q3, q4, q5, q6, q7},{"0", "1"},table([(q2, "0") = {q4, q7}, (q1, "0") = {q2, q6}, (q0, lambda) = {q7}, (q7, lambda) = {q2}, (q5, "0") = {q2, q6}, (q0, "0") = {q2, q3}, (q4, "1") = {q0, q5}, (q2, lambda) = {q4}, (q3, lambda) = {q6}, (q1, lambda) = {q5}, (q0, "1") = {q2, q4, q5}, (q4, "0") = {q4, q7}, (q5, lambda) = {q1}, (q6, lambda) = {q0}, (q3, "0") = {q1, q6}, (q4, lambda) = {q5}, (q1, "1") = {q0, q6}]),q0,{q0, q1, q7});

 

(17.1.2.3)

 

>	transitionGraph(nfa2);

 

>	#NFA2RE(nfa2,result=string); NFA2RE(nfa2);

 

(17.1.2.4)

 

>	dfa2:=simplifyDFA(minimalDFA(NFA2DFA(nfa2))); transitionGraph(dfa2);

 

>	NFA2RE(dfa2,result=string);

 

(17.1.2.5)

 

>	isUniversalNFA(nfa2);

 

(17.1.2.6)