# Math Help - please help with this Q...... of Finite automaton

1. ## please help with this Q...... of Finite automaton

let L be a regular language of binary strings.

let L* be another language such that (x:x belong to L and x ^ R belong to L) where x ^ R is the reverse

show that L* is also regular

2. The idea here is to make a new automaton which computes $x$ and $x^R$ simultaneously, such that it will enter an accepting state iff both $x$ and $x^R$ enter an accept state at the same point of the computation. You complete the details.