Question

If M is a nondeterministic finite automaton over Σ and every state of M is an accepting state, then L(M)= Σ*

false
true

Answer 1

It is true that if an NFA called M over an alphabet Σ has every state as an accepting state, then the language it accepts, L(M), is equivalent to Σ*, which represents all possible strings over the alphabet.

Step-by-step explanation:

If M is a nondeterministic finite automaton (NFA) over Σ and every state of M is an accepting state, then it is true that L(M)= Σ*. This is because, in an NFA with all accepting states, any sequence of transitions on any string from Σ* will eventually lead to an accepting state, since every state is accepting. By definition, Σ* represents the set of all possible strings over the alphabet Σ, including the empty string. Given that every possible string will be accepted by the automaton, the language accepted by M, denoted as L(M), is indeed Σ*.