2. Consider the FUN language, prove the following expression evaluates to 3 with respect to the big-step operational semantics that can handle recursion. let r= 2 in I+1

For LL(1) parsers, the following must happen: Chose the correct anwser below: Grammar can have left recursion but not ambiguous Grammar can be ambiguous but no left recursion Grammar can be ambiguous and have left recursion as well. Grammar must be free of left recursion and not ambiguous

3. (a) Let Σ = {a, b}. Find a regular expression corresponding to the language L = {ba} ∗ ∪ {aa, bb}. (b) Let Σ = {0, 1}. Give the language corresponding to the regular expression 10∗ (0 +.

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

Fill out the table for executing the polynomial-time dynamic programming algorithm for deciding whether the string 1001 is in the context-free language generated by the following CFG. Fill the table completely—do not stop the algorithm early. (Note: This CFG is not quite in Chomsky Normal Form since A appears on the right-hand side of a rule, but the same algorithm still works.) A → BC | CC B → BA | 0 C → AB | BB | 1

2. What is the TG corresponding to the language of strings, over alphabet {a, b}, that are composed exactly of odd repetition of the substring ab, i.e. sample strings of this language are ab, ababab, ababab, etc.

This question is about context-free grammars and parsing, and Turing machines (TM’s) i) Consider the following context-free grammar G over the alphabet Σ = {a, b, c}: S → aSb | ε | acSba | abc where S is the start variable. Using the rules of the grammar G, construct parse trees for thewords aabcb and aacbab.  ii) Give 2 words (from Σ∗) that are not in the language accepted by the grammar G of Question i.Justify your answer, explaining why are the words you give not accepted

Problem 3 Show that the following language is decidable: INFINITECEG = {(G) |G is a context-free grammar such that L(G) is infinite}

Is the language composed of all strings over the alphabet {a,b} that contain an odd number of a's a regular language? If so, show why. Note, again, that you may use any line of argument on regular languages, e.g., by drawing the FSA,or by using Closure properties of regular languages, along with the fact that the language is regular