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# UW-Madison CS 536 - practice, f18 midterm

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CS 536 Practice Midterm Exam Fall 2018 1. (a) Is the set of strings that contain no duplicate characters regular? Why? (b) Write a regular expression for comments that begin with << and end with >>. The body of the comment may contain any character sequence except >> (so that >> always marks the end of the comment). 2. Let S = { [i ]j | i ≠ j }. S is the set of all unbalanced brackets; that is, a number of left brackets followed by a different number of right brackets. Is S a regular set? If it is, give a regular expression or finite automaton that defines it. If S isn’t a regular set, explain carefully why. 3. Give JLex regular expression definitions that match the following strings (a) The four characters: "\n" (b) Any odd number of backslash characters (e.g., \ or \\\ or \\\\\, etc.). (c) A CSX multi-line comment, delimited by { and }, that is allowed to contain no more than two new-line characters. That is, the comment may appear entirely on one line, or it may span two or three lines, but no more than three lines. !! 4. Below is a context-free grammar for a language of assignments that includes arrays: 1. stmtList → stmt stmtList 2. | λ 3. stmt → ID = exp ; 4. array → [ rowList ] 5. rowList → nonEmpty 6. | λ 7. nonEmpty → row moreRows 8. moreRows → ; nonEmpty 9. | λ 10. row → exp more 11. more → , row 12. | λ 13. exp → term tail 14. tail → + term tail 15. | λ 16. term → ID 17. | INTLIT 18. | array Here are the FIRST and FOLLOW sets for all of the non-terminals: Non-terminal X FIRST(X) FOLLOW(X) stmtList ID EOF stmt ID ID EOF array [ + , ; ] rowList ID INTLIT [ ] nonEmpty ID INTLIT [ ] moreRows ; ] row ID INTLIT [ ; ] more , ; ] exp ID INTLIT [ , ; ] tail + , ; ] term ID INTLIT [ + , ; ] (a) Recall that terminal t is in FOLLOW(X) if in some partial parse tree with the start non-terminal at the root, X is one leaf of the tree and t is the next non-lambda leaf immediately to the right. For example, the following partial parse tree justifies the fact that for the CFG given above, terminal ID is in FOLLOW(stmt):! Complete the partial parse tree below to justify the fact that terminal ; is in FOLLOW(term).! (b) Fill in the parse table below using the numbers of the grammar rules rather than the rules themselves. Is the grammar LL(1)? !ID INTLIT = + ; , [ ] EOF stmtList !!!!!!!!!stmt !!!!!!!!!array !!!!!!!!!rowList !!!!!!!!!nonEmpty !!!!!!!!!moreRows !!!!!!!!!row !!!!!!!!!more !!!!!!!!!exp !!!!!!!!!tail !!!!!!!!!term !!!!!!!!!! 5. Consider the following grammar where File is the start non-terminal, and symbols in bold are terminals. (a) Apply the transformations learned in class to left factor the grammar above and write the results below. Give the entire grammar, not the just the transformed rules. (b) If the grammar you wrote above has any immediate left recursion, apply the transformation learned in class to remove it and write the result below. You do not need to give the entire grammar; you can just give the transformed

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