1. [10 points] Consider the following language: L-(z E {a, b) * 1 x has both ab and ba as substrings) Construct a deterministic finite automaton accepting the language L. You may give its 5-tuple for- mal definition or its transition diagram. Give the idea of your construction, or brief and precise interpretations of the states of your machine. Give a regular expression denoting the language L. Annotate your regular expression or provide brief explanation for your