Question

(a|bb)*a|b*c

Convert the regular expression above into a minimal DFA by following the steps below using paper and pen:

a. Convert the regular expression into an NFA, using Thompson's construction.
b. Convert the NFA above into a DFA, using subset constructions. Show your work in tabular form and show final DFA.
c. If the DFA you created is not minimal, convert it to a minimum-state DFA. If minimal, state that it is minimal. Show work!

Answer 1

To convert the regular expression (a|bb)*a|b*c into a minimal DFA, you need to follow two steps: converting the regular expression into an NFA using Thompson's construction, and converting the NFA into a DFA using subset constructions.

Step-by-step explanation:

Regular Expression Conversion

In order to convert the regular expression (a|bb)*a|b*c into a minimal DFA, we need to follow two steps: first, convert the regular expression into an NFA using Thompson's construction, and second, convert the NFA into a DFA using subset constructions.

Step 1: Converting the regular expression into an NFA using Thompson's construction

To convert the regular expression (a|bb)*a|b*c into an NFA, we can use the following steps:

1. Create an initial state and connect it to two new states using ε-transitions.
2. For each character in the regular expression, create a new state and connect it to the next state using a transition labeled with that character.
3. Create a final state and connect it to each state that represents the end of a subexpression using ε-transitions.
4. Remove the subexpression operators and add ε-transitions between the states representing the concatenation.

Step 2: Converting the NFA into a DFA using subset constructions

To convert the NFA into a DFA, we can use the subset construction algorithm. The algorithm involves creating a new state for each combination of states that the NFA can be in. We start with the initial state of the NFA and find the states it can reach with ε-transitions and labeled transitions. We repeat this process for each new state we create until no new states can be reached.