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Unformatted text preview: CSE 355 Theory of Computing ID: ___________ Spring 2009  Colbourn Midterm # 1 Page 1 of 8 19 February 2009 NAME Sample Solution ASU ID either 9 or 10digit is fine You have one hour and 15 minutes to complete the exam. Do not open the exam until instructed to do so. No notes, texts, computers, calculators, or communication devices are permitted. Write all answers on the examination paper itself. BUDGET YOUR TIME WELL! SHOW ALL WORK! Question 1 [15] Question 2 [15] Question 3 [10] Question 4 [10] Question 5 [10] Total [60] 26.8 raw average Sorted Grades out of 60 are 57 56 53 48 46 44 44 43 42 41 38 37 34 31 30 30 30 29 27 27 27 27 26 26 26 25 25 25 25 24 24 24 22 22 21 21 20 20 20 18 17 17 16 16 16 15 15 14 13 12 11 11 10 9 8. This midterm is worth 15% of your final grade. These grades will be scaled upwards as follows to determine what you get out of 15. If you received g/60, then compute 5 + (g/5) to get the grade out of 15. The new average is then 10.36/15 = 69.1%. The grade distribution out of 15 becomes 6.6 6.8 7 7.2 7.2 7.4 7.6 7.8 8 8 8.2 8.2 8.4 8.4 8.6 9 9 9.2 9.2 9.4 9.4 9.8 9.8 9.8 10 10 10 10 10.2 10.2 10.4 10.4 10.4 10.4 10.8 11 11 11 11.2 11.8 12.4 12.6 13.2 13.4 13.6 13.8 13.8 14.2 14.6 15.6 16.2 16.4 CSE 355 Theory of Computing ID: ___________ Spring 2009  Colbourn Midterm # 1 Page 2 of 8 Question 1. [15 marks total] Let G be the grammar S  aSb  SS  aAb A  aAb  S (a) [3 marks] Give two leftmost derivations to show that G is ambiguous. S SS S S These are two leftmost derivations of the same string in the language. Note that we must start with the start variable, and end with no variables (just terminals). (a) [7 marks] Give an unambiguous grammar that is equivalent to G. S  E E T  TE T ab  aEb Alternatively here is an even more compact solution that one student found: S  aSbS If we think of a as `(` and b as `)`, the language is the set of all strings with balanced parentheses....
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 Fall '08
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