Problem 5: Functions and Sets Let Σ denote a finite alphabet, Σ* denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : Σ* → N (where N denotes the natural numbers) [a] Is L partial, total, or both? [b] Is L one-to-one? onto? a bijection? [c] How many words in Σ* have length n? [d] How many words in Σ*   have length ≤ n [e] Explain whether Σ* is finite, countable, or uncountable. [f] Explain whether P(Σ*) - the set of all subsets over Σ* - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).

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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.