Regular Expression for the language that requires one symbol to occur at least once

I am trying to figure out the simplest way to do this using a regular expression.

• Three symbols a, b, c.

• The sequence length is unlimited, i.e. *.

• The symbol a must be somewhere in the sequence at least once, but can appear more than once.

• The sequence may have only a.

More formally, $\{ w \in \{a,b,c\}^* ~|~ \#_a(w)\ge 1 \}$, where $\#_a(w)$ is the number
of $a$s in $w$.

The best I get is


$( ( b \mid c )^\, a\, ( b \mid c )^ )^+$

Is that the simplest way?

The simplest regular expression I can think of for this is $\left(a \mid b \mid c\right)^ a \left(a \mid b \mid c\right)^$. This is simpler than yours by the following measures of complexity:

• It contains less nesting (and fewer parentheses in general)

• It contains fewer quantifiers

StackExchange Computer Science Q#1017, answer score: 7