Question

Construct a reduced dfa for the following extended regular expression over the alphabet {0, 1, 2} (not {0, 1}!): [(0*1)* Intersection 0(0*1)*]*

Answer 1

To construct a reduced DFA for the given expression, we need to understand the language it represents, formulate the initial DFA from the expression components, and then reduce it by merging equivalent states and eliminating redundancies.

Step-by-step explanation:

To construct a reduced deterministic finite automaton (DFA) for the given extended regular expression over the alphabet {0, 1, 2}: [(0*1)* Intersection 0(0*1)*]*, we should first understand the language described by this expression. The expression can be broken down into segments for clarity:

• (0*1)*: A sequence of 0s followed by a 1, repeated any number of times, including none.
• 0(0*1)*: A single 0 followed by any number of sequences of 0s followed by a 1.
• The entire expression inside the brackets is repeated any number of times, including none, due to the * outside the bracket.
• Intersection operation implies that only strings that satisfy both conditions will be considered.

The resulting DFA must accept strings that contain sequences starting with a 0 followed by any number of 0s, optionally followed by a 1, and this pattern can repeat. To reduce the DFA, we would combine equivalent states and remove unnecessary/redundant states.