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173 CSC Midterm Examination October 25th, 2005 Total: 75 points This is a closed book, closed notes exam. There are a total of 75 points. There is also an additional 5 points of extra credit (as part of your choice in question 5). In all cases, explain how you arrived at your answer. An answer without an explanation will not be considered valid. I have tried to make the questions unambiguous. If you are not sure what a question is asking, make some reasonable assumption and write that assumption down next to your answer. The TA has been instructed not to try to explain questions during the exam. 1. [24 points] Consider the following database consisting of student, course, and grade relations: Table 1 student relation sid sname advisor 1 alpha dwarkadas 2 beta hemaspaandra 3 gamma scott 4 delta allen Table 2 cno 173 252 286 254 290A course relation instructor dwarkadas ding hemaspaandra scott allen sid 1 1 2 3 4 4 cno 173 254 173 173 173 290A Table 3 grade relation cname formal systems prog. lang. des. & impl. formal systems formal systems formal systems dialogue modeling grade A B B C B A (a) What is the relation (attributes and tuples) obtained by performing a natural join on the course and grade relations? (b) What is the relation obtained by projecting the grade relation onto the grade attribute (what are the tuples)? (c) How would you implement each of the relations (what data structure would you choose and what attribute/s would you use to organize the tuples in the data structure in each case)? Explain your answer. (d) What is the relational algebra query you would supply to this database to determine the names of students who take a course from their advisor (for this one, I m interested in the query, not in the result (or answer) of the query)? (e) How would you optimize the query above (what is the optimized query)? Explain your optimization. (f) This database could be better designed. How would you redesign the database to eliminate redundancy while avoiding loss of information? 2. [10 points] Consider the following C code to delete an item in a singly-linked list (each line of code has been numbered for easy reference): 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: struct node { int datum; struct node *next; } struct node *mylist_head = NULL; int del( int data, struct node **head) { struct node *temp = *head; struct node *prev = *head; while (temp) { if (temp->datum == data) { if (temp == *head) list_head = temp->next; else prev->next = temp->next; return(1); } else { prev = temp; temp = temp->next; } } return(0); } main() { ... del(25, mylist_head); } You may assume that prior to the call to del, nodes have been (via added dynamic allocation) to mylist head, and in particular, that a node containing the datum 25 has been added. Please indicate exactly where you would make modi cations in the code for the following: (a) This code has a problem (in that it may not do what you expect). What is the problem and how would you x it? (b) This code also has an additional problem in terms of a memory leak in the del function. How would you x it? 3. [15 points] For the regular expression b(a | b) a (a) Construct an NFA using Thompson s construction algorithm. (b) Convert the NFA to a DFA using the subset construction algorithm. (c) Minimize the DFA (or show that your resulting DFA is minimal) using the partitioning algorithm. 4. [16 points] (a) Your systems administrator has declared that a good password must have at least 3 characters, at least one of them must not be a letter (i.e., at least one character must be a digit or a special character), and at least one of them must be a letter. Construct an NFA (could be a DFA) that recognizes good passwords using the following character classes (which de ne the complete alphabet): letter (a | b | c | ... | z | A | B | C | ... | Z) digit (0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9) special ($ | | #) Don t forget to mark the starting and accepting state(s). You DO NOT have to show construction steps and need not use the regular expression to build the NFA. (b) Write the regular expression for the following language: all strings of 0 s and 1 s that do not contain 2 consecutive 1 s. 5. [10 points] Answer 2 of the following 3 questions. You may do the third question for extra credit, but you should clearly indicate which you want counted as extra credit. Otherwise, the last question answered in the bluebook (from beginning to end) will be considered the extra credit. (a) [5 points] Show that the following context-free grammar (in which E is the start symbol and the only non-terminal, and id, +, (, and ) are terminal symbols) is ambiguous. E --> | | | + E E (E) id (id) (b) [5 points] Write a regular expression that accepts the same language as the following context-free grammar (once again, E is the start symbol and the only non-terminal symbol, and id, op, and num are terminal symbols): E --> E op E | id | num (c) [5 points] We are given an NFA N built from regular expression R that accepts string and does not accept string . A new epsilon transition is added between some two states in N to give a new NFA N ewN . Select exactly one among the list of choices in UPPERCASE letters in each item below and explain your answer in each case. i. N ewN [WILL / MAY OR MAY NOT / WILL NOT] accept . ii. N ewN [WILL / MAY OR MAY NOT / WILL NOT] accept .

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