Provide a regular expression for the following language called DNA that is defined below:

DNA: The language of all DNA sequences (strings over the alphabet {A,C,G,T}) that do not contain any 4-letter string AGGT or AGTT OR contain at least two disjoint substrings AxC, where x can be any character. Meaning, the DNA sequence cannot contain the strings "AGGT" and "AGTT". However, the sequence can have those strings as long as there are 2 substrings "AxC" (where x is A,C,G or T) in the sequence. The following two strings are in the language: ACGAGCTTAGTC, because it does not contain AGGT nor AGTT; and AACGAGGTTTAGAGCTTAG, because it does contain the two substrings AAC and AGC (so it does not matter that it also contains the substring AGGT). The following string is not in the language because it contains the substring AGGT but contains only one substring AxC: AACGAGGTTTAGAAGGCTTAG.

For the regular expression, you may use . to match any character and character class syntax ([...]) to indicate different options for the same character (e.g., [AG] to match either A or G). Do not use any other extensions beyond the basic regular expression syntax (no repetition constructs other than *, no back references, etc.). Then provide the DFA that decides the language DNA. Provide the DFA in graphical form. You are allowed to label transitions that match any character with . and transitions that match a range of characters using character class syntax.