Given a CFG G and a variable A, consider the problem of testing whether A is usable. We say A is usable if it appears in some derivation of some string w ∈ G. Formulate this problem as a language and show that it is decidable.

Draw and formalize a DFA for the language over Σ = {a,b,c} with strings containing an odd number of as, of bs, and of c Hint: try using the intersection construction we discussed in class and label each state with a tuple.

This question is from course Advanced Logic in graduate level. Please give the answer, if yoy know, in a clear and understandable way, as soon as you can.

Please help me with this, I'm stuck...

C-F languages (or see the following figure). In particular..it points out that the language {am,a"b" | m,n = N} is a deterministic C-F language, but not LL(k) for any k Palindromes over {a, b} Non-deterministic C-F {am,a"b" | m.ne N}; Deterministic C-F -LL(K) {ab❘n EN}- Regular To show the language is not LL(k) for any k, note that a grammar for this language is SAB A→ B -> 10 or S-A|B A→ B (you only need to answer one case here, either one). The language contains A as an element. Now consider the case k = 1 and consider the input string ab. When the first symbol is scanned, we get an 'a'. This information alone is not enough for us to make a proper choice. So we don't even know what to do with the first step in | the parsing process. For k = 2, if we consider the input string aabb, we face the same problem. For any k > 2, the input string ab would cause exactly the same problem. So this grammar is not LL(k) for any k. On the other hand, by putting proper instructions into the blanks…

2. Let A be a Turing-recognizable language consisting of descriptions of Turing machines, i.e., A = {(M1), (M2),...}, where every M; is a decider. Prove that some decidable language D is not decided by any decider M, whose description appears in A.

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

Given a regular language L and string w, how can we check if w€ L? Is this a decideable problem?