Final answer:
First, construct an NFA using Thompson's construction for the given regular expression. Then, convert this NFA to a DFA using subset construction and record the process in a table. Finally, check and minimize the DFA if possible to achieve the minimal DFA.
Step-by-step explanation:
To convert the regular expression (albb)*a | b*c into a minimal DFA, we must follow several steps, including constructing an NFA, converting it to a DFA, and then minimizing the DFA if necessary.
Step 1: Convert to NFA using Thompson's Construction
We begin by creating an NFA for each elementary regular expression and then combine these step by step following the rules of Thompson's construction. Unfortunately, due to the limitations of this format, we cannot draw the NFA here, but it involves creating states with transitions for each part of the regular expression and using epsilon transitions for the concatenation, the alternation operator '|', and the Kleene star '*'.
Step 2: Convert the NFA to a DFA using Subset Construction
Using subset construction, we transition from the NFA to a DFA by creating states in the DFA that represent sets of NFA states. Again, we would typically use a table to show the work, where each row represents a state in the DFA and each column represents a possible input symbol. The entries in the table show the transitions between the states.
Step 3: Minimize the DFA
After creating the DFA, the next step is to check if it can be minimized. This is done by identifying and merging equivalent states that cannot be distinguished by any input string. If no states can be merged, we declare the DFA as minimal.