Whenever a minimization technique is applied over the DFA the automata reduces furthera.trueb.false

Analyzing the Statement

1. Understanding DFA: A Deterministic Finite Automaton (DFA) is a theoretical model used in computer science and automata theory to recognize patterns within an input taken from a finite set of symbols.

2. Minimization Technique: The minimization of a DFA involves reducing the number of states while preserving the language recognized by the automaton. The primary goal is to achieve a DFA that has the smallest number of states possible.

Evaluating the Statement

• The given statement claims that "whenever a minimization technique is applied over the DFA the automata reduces further."

3. True or False: The statement implies that minimization can always further reduce a DFA. However, a crucial aspect of automata theory is that if a DFA is already minimized, applying minimization techniques (such as state merging) will not change the automaton.

4. Conclusion: Therefore, the statement is false because a minimized DFA cannot be reduced further.

Final Answer

b. false