On the state complexity of reversals of regular languages

Arto Salomaa, Derick Wood, Sheng Yu
2004 Theoretical Computer Science  
We compare the number of states between minimal deterministic ÿnite automata accepting a regular language and its reversal (mirror image). In the worst case the state complexity of the reversal is 2 n for an n-state language. We present several classes of languages where this maximal blow-up is actually achieved and study the conditions for it. In the case of ÿnite languages the maximal blow-up is not possible but still a surprising variety of di erent growth types can be exhibited.
doi:10.1016/j.tcs.2004.02.032 fatcat:swbz3zzy5jcthm4rnxvgt4cwtq