power + operator for binary

Question

What is the specific definition for power $+$ operator in automata theory? For example, when $x$ is a binary what does it mean that $x = 0^+$. Does it mean that x is a string with at least one $0$?

Answer 1

Given an alphabet $\Sigma$ the Kleene star $\Sigma^*$ is defined as the language containing all words that can be constructed from $\Sigma$.

The Kleene plus is defined as $\Sigma^*$ without the empty word:

$\Sigma^+ := \Sigma^* \setminus \{\varepsilon\}$