1. For the language below,

a) State whether or not it is regular.

b) If you claim the language is not regular, prove your claim using the Pumping Lemma.

c) If you claim the language is regular,

Give a regular expression that matches exactly the strings in the language,

Give a graphical representation of an NFA that recognizes the language,

Convert the NFA into a DFA that recognizes the language, and

Minimize the DFA, that is, convert it into an equivalent DFA with as few states as possible and present it in graphical form.

All binary strings with at most one 1 in each substring of length four. For example, the string 0001000100 belongs to this language: its substrings of length four are 0001, 0010, 0100, 1000, 0001, 0010, and 0100, none of which contains more than one 1. The string 100010100 does not belong to this language because the underlined substring contains two 1s.