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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 the following identities hold for regular expressions over any alphabet: epsilon + R*R = R*. These should be done by interpreting the regular expressions as languages.
Consider a logic function with three outputs, A , B , and C , and three inputs, D , E , and F . The function is defined as follows: A is true if at least one input is true, B is true
Design a syntactic analyzer for the language specified by the grammar
Express the following set as a regular expression: The set of all strings of length at least three over {0,1} such that every three consecutive.
Write a program would read two numbers and then print all numbers between the first and the second, inclusive. Design unambiguous grammar to parse expressions
Redundant sequence identi cation
Create a finite-state machine design to turn your FPGA development board into a simple programmable music box.
Write some examples of declarative knowledge. Write some examples of procedural knowledge. Then, compare examples, highlighting the similarities & differences.
Show that the language F = {a^i b^j c^k | i, j, k greater than or equal to 0 and if i = 1 then j = k} is not regular. Show, however, that it satisfies the statement of the pumping lemma
Write down a structural induction principle for the PlayTree free type
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
How the problem would be encountered in attempting to represent the following statements in Predicate logic. it should be possible to: John only likes to see French movies.
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