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I am trying to create the regular expression for the automaton named "full closure" in the following diagram using the arden's theorem:

Since, we have 3 accepting states, we would find 3 different regular expression and then just union them up. I was able to find regular expression for q0, q1 but facing issues when trying to find one for q2:

q0 = a*
q1 = a*b* + b*
q2 = a*(ac* + bc* + cc* + b*bc* + b*cc* ) + b*(bc* + cc*) + c*

EDIT: I was able to minimize the final expression that is r = q0 + q1 + q2, to

 r = a*b*c* + a*bc* + b*b + c*

 can we further minimize this expression to "a*b*c*"?

My question is can we further minimize this regular expression for q2 and overall when we union? The "full closure" automata recognizes language "a* b* c*"

I am trying to create the regular expression for the automaton named "full closure" in the following diagram using the arden's theorem:

Since, we have 3 accepting states, we would find 3 different regular expression and then just union them up. I was able to find regular expression for q0, q1 but facing issues when trying to find one for q2:

q0 = a*
q1 = a*b* + b*
q2 = a*(ac* + bc* + cc* + b*bc* + b*cc* ) + b*(bc* + cc*) + c*

EDIT: I was able to minimize the final expression that is r = q0 + q1 + q2, to

 r = a*b*c* + a*bc* + b*c*

 can we further minimize this expression to "a*b*c*"?

My question is can we further minimize this regular expression for q2 and overall when we union? The "full closure" automata recognizes language "a* b* c*"

I am trying to create the regular expression for the automaton named "full closure" in the following diagram using the arden's theorem:

Since, we have 3 accepting states, we would find 3 different regular expression and then just union them up. I was able to find regular expression for q0, q1 but facing issues when trying to find one for q2:

q0 = a*
q1 = a*b* + b*
q2 = a*(ac* + bc* + cc* + b*bc* + b*cc* ) + b*(bc* + cc*) + c*

EDIT: I was able to minimize the final expression that is r = q0 + q1 + q2, to

 r = a*b*c* + a*bc* + b*b + c*

My question is can we further minimize this regular expression for q2 and overall when we union? The "full closure" automata recognizes language "a* b* c*"

I am trying to create the regular expression for the automaton named "full closure" in the following diagram using the arden's theorem:

Since, we have 3 accepting states, we would find 3 different regular expression and then just union them up. I was able to find regular expression for q0, q1 but facing issues when trying to find one for q2:

q0 = a*
q1 = a*b* + b*
q2 = a*(ac* + bc* + cc* + b*bc* + b*cc* ) + b*(bc* + cc*) + c*

EDIT: I was able to minimize the final expression that is r = q0 + q1 + q2, to

 r = a*b*c* + a*bc* + b*b + c* 

 can we further minimize this expression to "a*b*c*"?

My question is can we further minimize this regular expression for q2 and overall when we union? The "full closure" automata recognizes language "a* b* c*"

I am trying to create the regular expression for the automaton named "full closure" in the following diagram using the arden's theorem:

Since, we have 3 accepting states, we would find 3 different regular expression and then just union them up. I was able to find regular expression for q0, q1 but facing issues when trying to find one for q2:

q0 = a*
q1 = a*b* + b*
q2 = a*(ac* + bc* + cc* + b*bc* + b*cc* ) + b*(bc* + cc*) + c*

My question is can we further minimize this regular expression for q2 and overall when we union? The "full closure" automata recognizes language "abc*"

I am trying to create the regular expression for the automaton named "full closure" in the following diagram using the arden's theorem:

Since, we have 3 accepting states, we would find 3 different regular expression and then just union them up. I was able to find regular expression for q0, q1 but facing issues when trying to find one for q2:

q0 = a*
q1 = a*b* + b*
q2 = a*(ac* + bc* + cc* + b*bc* + b*cc* ) + b*(bc* + cc*) + c* 

EDIT: I was able to minimize the final expression that is r = q0 + q1 + q2, to

 r = a*b*c* + a*bc* + b*b + c*

My question is can we further minimize this regular expression for q2 and overall when we union? The "full closure" automata recognizes language "a* b* c*"