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assign1 - even(b All strings whose lengths are odd(c All...

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CMPSC 138: Fall 2009 Assignment 1 Date Assigned: September 30, 2009 Date Due: October 9, 2009 by 4:30 PM (in the CS 138 homework box) 1. Show that (1 + ... + n ) 2 = 1 3 + ... + n 3 for all n 1. 2. Show that the number of subsets of a set of n elements is 2 n for n 1. 3. Show that every positive integer can be written as a product of primes. 4. Show that there is an inFnite number of primes. 5. ±or the alphabet Σ = { a, b } , construct D±A’s that accept the languages consisting of (a) All strings whose lengths are
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Unformatted text preview: even . (b) All strings whose lengths are odd . (c) All strings with exactly four a ’s. (d) All strings with at least four a ’s. (e) All strings with at most four a ’s. (f) All strings with at least two a ’s and exactly two b ’s. (g) All strings with at least two a ’s or exactly two b ’s. (h) All strings where every bbb is immediately followed by aa. (i) All strings where the leftmost symbol is identical to the rightmost symbol. 1...
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