355mt2s09sol - CSE 355 Spring 2009 Colbourn Theory of...

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CSE 355 Theory of Computing ID: ___________ Spring 2009 - Colbourn Midterm Examination #2 Page 1 of 7 02 April 2009 NAME Ima Sample ASU ID 9- or 10-digit ok You have 75 minutes to complete the exam. Do not open the exam until you are 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! Grades out of 60 are: 12 13 15 16 16 16 16 18 19 20 21 22 23 23 23 24 25 26 27 27 30 31 31 32 34 35 35 36 39 39 41 41 41 42 43 43 45 45 45 46 46 48 50 50 51 51 52 53 56. 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 4 + (g/5) to get the grade out of 15. The new average is then 10.67/15 = 71.1%. The grade distribution out of 15 becomes 6.4 6.6 7 7.2 7.2 7.2 7.2 7.6 7.8 8 8.2 8.4 8.6 8.6 8.6 8.8 9 9.2 9.4 9.4 10 10.2 10.2 10.4 10.8 11 11 11.2 11.8 11.8 12.2 12.2 12.2 12.4 12.6 12.6 13 13 13 13.2 13.2 13.6 14 14 14.2 14.2 14.4 14.6 15.2 Question 1 [8] 8 Question 2 [21] 21 Question 3 [21] 21 Question 4 [10] 10 Total [60] 60 Raw Average: 33.3
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CSE 355 Theory of Computing ID: ___________ Spring 2009 - Colbourn Midterm Examination #2 Page 2 of 7 [8 in total] Question 1: Give examples (no explanation is needed) of languages A and B so that A is a proper subset of B, and [2 marks] (a) A is regular and B is context-free but not regular. Take B = {0 n 1 n : n 0}. Then B is a CFL but not regular. Every finite language is regular, so take a finite subset of B to form A, for example take A = , or A = { ε }, or A = {01}, or A = {0 n 1 n : 100 n 0}. Many other examples are possible. [2 marks] (b) A is regular and B is recursive but not context-free. Take B = {0 n 1 n 2 n : n 0}. Then B is recursive but not context-free. Every finite language is regular, so take a finite subset of B to form A, for example take A = , or A = { ε }, or A = {012}, or A = {0 n 1 n 2 n : 100 n 0}. Many other examples are possible.
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