Show that DSPACE(O(log log n)) contains non-regular languages Consider the language containing all strings zk of the form Zg = 000...000, 000...001, ..., 111...111 i.e. rk is a concatenation of all k-bit strings, in lexicographic order, separated by commas. Let L-k k>0, and define nkk2. (a) Show that L is not a regular language. (b) Show that L can be decided by a deterministic Turing Machine using O(log log n) space. Show that DSPACE(O(log log n)) contains non-regular languages Consider the language containing all strings zk of the form Zg = 000...000, 000...001, ..., 111...111 i.e. rk is a concatenation of all k-bit strings, in lexicographic order, separated by commas. Let L-k k>0, and define nkk2. (a) Show that L is not a regular language. (b) Show that L can be decided by a deterministic Turing Machine using O(log log n) space