Problem 7 - Finite Automata

Answer the following questions concerning formal languages.

1.

Show that the language accepted by the following finite automaton is the set of strings having the same number of 0's and 1's such that in any prefix the difference in occurrences of 0's and 1's is at most one.

2.

Give a context-free grammar generating the set of palindromes (a palindrome is a string whose reverse is itself) over alphabet $\{0,1\}$.

See [HOP79] for a detailed answer to this exercise.