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hmwk_2_sol

# hmwk_2_sol - Discrete Structures Assignment 2 Due at...

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Discrete Structures Aug 30 2011 Assignment 2: Due at beginning of class Mon, Sept 12 Prof. Hopcroft *******Note: this is the ﬁrst homework that will be subject to the style guide on the website. Points will be deducted for homeworks not following the guidelines.******** 1 Regular Expressions Write a regular expression for the set of all strings of 0’s and 1’s that have two blocks of 1’s. A sample string your regular expression should represent: 000000111111000111000 1.1 Answer +4 for correct notation and regular expression, +2 for each correct element of the regular expression, - 1 for extra 0’s and 1’s in an otherwise correct solution. { 0*11*00*11*0* } 2 Recurrence Relation Find a close form solution for the following recurrence equations: (Also, show that you checked the ﬁrst four values of your solution) Saved for next week. 3 Induction +5 for correct base case, +5 for assuming g ( n ) is true in a correct way, +5 for manipulating g ( n + 1) , and +5 for overall correctness Prove by induction that g ( n ) = 2 n 4 + 2 n 2 + 4 is divisible by 4 for all n 1. Proof. Base Case

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hmwk_2_sol - Discrete Structures Assignment 2 Due at...

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