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1. Rewrite the productions for each of the following nonterminals as right regular grammars: Identifier, Float.
2. Draw a DFSA for identifiers that contain only letters and digits, where the identifier must have at least one letter, but it need not be the first character. Hint: everything to the left of the leftmost letter must be a digit.
3. Show the moves made using the DFSA for identifiers in accepting the following:
1. a 2. a2 3. a2i 4. abc 4. For C-style / * . . . * / comments, give 1. a right regular grammar 2. a regular expression 3. a DFSA
5. Can a language have no reserved words? That is, suppose every reserved word (such as if and for) were merely predefined identifier, which the programmer is free to redefine. Can such a language exist? Explain.
Consider the following grammar: S S (S) | ε. Construct and DFA or LR(0) items for this grammar. Construct SLR(1) parsing table.
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
Create a standard 1-tape Turing machine M to calculate the function sub3. Specifically, calculate sub3 of a natural number represented in binary.
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
Consider the language L = L1 ∩ L2, where L1 = {ww^R : w ∈ {a, b}* and L2 = {a^n b*a^n: n ≥ 0}. Write the first four strings in the lexicographic enumeration of L?
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
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.
Design in JFLAP a Truing machine that takes as input a tape containing a series of n 1s, Where n >= 0, terminated by an = sign.
Write down a structural induction principle for the PlayTree free type
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.
Discuss the impact of Moore's law on data center costs on such things as servers and communications equipment. List at least 3 steps or recommendations your data center can take to offset some or all of the effect of Moore's law.
We showed to prove that if L can be identified by DFA then the language left half(L) = {x ∈ ∑*|∃y xy ∈ L and |x| = |y|} is also regular; here |x| means length of x.
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