# Is the langauge of (descriptions of) DFAs that accept $\Sigma^*$ decidable?

Is $L = \{\langle A\rangle\mid A\text{ is a DFA and }L(A) = \Sigma^*\}$ decidable?

I know that $L'=\{\langle A,w\rangle \mid A\text{ is a DFA and }w\in L(A)\}$ is decidable, but I'm not sure if this is related.

Every accessible state $s$
• must have a successor state $\tau (s, \sigma)$ for $\sigma \in \Sigma$, where $\tau$ is the transition function of the DFA.