# Midterm I - Solution CS164, Spring 2014

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2 or number of 'b's is a multiple of 2. (b) Write a regular expression for this language. [4 points] (a*ba*ba*)* (b*ab*ab*ab*)* a* b* (c) Write an NFA for this language. [4 points] (d) Write a DFA with at most 6 states for this language [4 points] (3) Can we construct a regular expression for a language over the alphabet = {a,b} whose strings have equal number of occurrences of a and b? Explain. [4 points] No. Corresponding state machine requires infinite number of states. Yes/No (1) Reason (3)

3 2 LL Parsing Consider the following grammar with terminals *,!, n, (, and ). E F H H * E F F! G G n (E) (a) The grammar is not LL(1). Explain in one sentence why [2 points] F -> F! is left recursive (b) Fix the grammar to make it LL(1) by filling in the blanks below [4 points] E F H H * E G n (E) F G K K! K! K K (c) Compute the first and the follow set of the fixed grammar [8 points] First Follow E (, n \$, ) F (, n \$, ),* G (, n \$, ),*,! H *, \$, ) K!, \$, ),* (d) Compute LL(1) parsing table [10 points] *! ( ) \$ n E E FH E FH F F GK F GK G G (E) G n H H *E K K!K 3 LR Parsing and Ambiguity Consider the following grammar with terminals - (the negation operator) and int. S E E E - E - - E int (a) Draw all the parse trees for the string int int - int [6 points]

4 (b) Is this grammar ambiguous? Why or why not? [2 point] The grammar is ambiguous because it admits multiple parse trees for string int int - int

5 (reduction labels) state 3: reduce E-> --E on \$/- state 4: reduce E->E-E on \$/- state 6: accept S->E on \$ state 7: reduce E->Int on \$/- (c) Complete the above partial LR(1) DFA for the grammar. [16 points] Fill in items of all states by performing closure operation. (6) Fill in missing transition labels on all edges (4) Write the necessary reduce by on labels on states (2) Add missing transition edges (Hint: State 2 and State 5) (4) (d) For each state with a conflict, list the state, the lookahead token, and the type of conflict (i.e. shift-reduce conflict, or reduce-reduce conflict). [4 points] 3: Lookahead token: -, shift-reduce conflict 4: Lookahead token: -, shift-reduce conflict Suppose we want the string - - int - int - int to have only the following parse tree (call this property P).

6 (e) Describe in English the precedence and associativity rules necessary to ensure property P. [4 points] 1. - is right-associative has higher precedence than - (f) Explain, for each conflict in the LR(1) parsing DFA for this grammar, how it should be resolved to ensure property P. [4 points] State 3: reduce instead of shift on - State 4: shift instead of reduce on - (g) Rewrite the grammar to an equivalent unambiguous grammar to ensure property P. Two grammars are equivalent when they accept the same language. [8 points] S E E T - E T T - - T int (h) The Cool grammar has an ambiguity introduced by let-expression. Give an example illustrating the ambiguity associated with let-expression. [4 point] let in 1 + 2

7 can be parsed as: (let in 1) + 2 or let in (1 + 2) Published by Google Drive Report Abuse Updated automatically every 5 minutes

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