Consider the language L = {w |w ∈ {0, 1} ∗ , 2 × #0 (w) = #1 (w)} , here #0(w) and #1(w) means the numbers of 0s and 1s in w respectively. That is, this is the language consisting of all strings with exactly twice as many 1s as 0s: for example, 101 ∈ L, 010 ∈/ L. In this problem we will show how to construct a context-free grammar for it. (a) (2 points) For a length n word x, we define a function f (i) = (2 × number of 0s in locations [1 . . . i]) − (number of 1s in locations [1 . . . i]). Show that we have f(i) = f(j) for some i < j if and only if the substring in indices [i + 1, . . . j] has exactly twice as many 1s as 0s (i. e. xi+1,i+2,...,j ∈ L).

Solution: the categorization of functional and non-functional requirement are as follows: some of the more typical functional requirements include: • business rules• transaction corrections, adjustments and cancellations• administrative functions• authentication• authorization levels• audit tracking• external interfaces• certification requirements• reporting requirements• historical data• legal or regulatory requirementswhile,some typical non-functional requirements are: • performance – for example response time, throughput, utilization, static volumetric• scalability• capacity• availability• reliability• recoverability• maintainability• serviceability• security• regulatory• manageability• environmental• data integrity• usability• interoperability

Answer by alison blake may 14th and 15th of some year in the 2020s

Answerpage pane; i believe this is a correct answer/ plz check first/// good luck;