Consider alphabet Σ = {0,1} and language Lo₁ = {weΣ* : w=0"1" for some nonnegative n€ Z}. Prove or disprove that for each language L over Σ, if L n Lo₁ = 0 and L is regular, then L is finite.

(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.

(For thought) a. A token of a computer language is any sequence of characters, with no intervening characters or white space, that taken as a unit has a unique meaning. Using this definition of a token, determine whether escape sequences, function names, and the keywords listed in Table 2.1 are tokens of the C++ language. b. Discuss whether adding white space to a message alters the message and whether messages can be considered tokens of C++. c. Using the definition of a token in Exercise 4a, determine whether the following statement is true: “Except for tokens of the language, C++ ignores all white space.”