# Regular expression for odd binary numbers without leading zeros

I have to write a regular expression that accepts any odd binary number not preceded by a 0. the best I can come up with is $1(0\cup1)^*1$, but that doesn't match just 1. The best it matches is 11.

• just add that single $1$ to your expression as an alternative to what you already have! – Hendrik Jan Apr 2 '13 at 23:38
• I had thought of that, but I worried that it would not be the minimum possible. Thanks. – agent154 Apr 2 '13 at 23:42
• Minimal length is not always better than "elegant", or "easy to understand". A short alternative could be $1(0^*1)^*$. That one has nested stars, which is more complex in some respects. – Hendrik Jan Apr 2 '13 at 23:49
• Obligatory hint: build an NFA and convert. Also, any question should contain, well, a question. – Raphael Apr 3 '13 at 7:15

## 1 Answer

First you might just add that single $1$ to your expression as an alternative to what you already have. One obtains $1 \cup 1(0\cup 1)^*1$.

An alternative is $1(0^*1)^*$. That one is shorter, but not necessarily better.

Actually that expression I obtained by starting with the FSA below, and realizing that the rightmost two states could be replaced by iterating $0^*1$.

• sorry for going off-topic here, which tool you have used to draw this beautiful looking DFA ? – avi Apr 3 '13 at 8:05
• The diagram was made in $\LaTeX$ using the package GasTeX – Hendrik Jan Apr 3 '13 at 8:36
• @avi I have been using this script of mine with TikZ. – Raphael Apr 3 '13 at 11:15