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1) Consider the language L = L1 ∩ L2, where L1 = {ww^R : w ∈ {a, b}* and L2 = {a^n b*a^n: n ≥ 0}.
a) List the first four strings in the lexicographic enumeration of L?
b) Write a context-free grammar to generate L.
c) Show a natural pda for L.
d) Prove that L is not regular.
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
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 some examples of declarative knowledge. Write some examples of procedural knowledge. Then, compare examples, highlighting the similarities & differences.
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.
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.
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.
Dynamic programming algorithm to compute a shortest superstring.
Redundant sequence identi cation
Give a construction that assumes you are given a DFA for L and show how to construct an NFA (with or without ε-moves) to recognize sort(L).
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
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