) Define a color word to be an English word that is the name of a color. So some example color words are red, fuschia, and ochre. Define an animal word to be an English word that is the common name of an animal. So some example animal words are cow, cats, and hippopotamus. Let L = {w : w is a sentence with legal English syntax and the number of color words in w equals the number of animal words in w}. As examples, observe that red cats like catnip ∈ L, but red cats like blue green balls ∉ L. Note that, to be in L, w must satisfy the syntactic rules of English. It is not necessary for w to make sense. So, for example, red red blue red cats like dogs and dogs and dogs ∈ L. Prove that L is not regular. (Be particularly careful if you use the Pumping Theorem. You must choose a w that is actually in L.)
Show that dogs={x∈λ} isn’t regular.1. Assume dogs were regular2. Therefore it has a pumping no. ppp3. But… consider the string 0 10 . Can this string be pumped in its first p pletters?…
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