1. Show that the following languages are context-free. You can do this by writing a context free grammar or a PDA, or you can use the closure theorems for context-free languages. For example, you could show that L is the union of two simpler context-free languages.
(d) L = {0, 1}* - L1, where L1 is the language {1010010001…10n-110n1 : n n ≥ 1}.
1. Show that the following languages are context-free. You can do this by writing a context...
1. Show that the following languages are context-free. You can do this by writing a context free grammar or a PDA, or you can use the closure theorems for context-free languages. For example, you could show that L is the union of two simpler context-free languages. (b) L {0, 1}* - {0"1" :n z 0}
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that are pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that arc pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
2. (10 points) Use the pumping lemma for context free grammars to show the following languages are not context-free. (a) (5 points) . (b) (5 points) L = {w ◦ Reverse(w) ◦ w | w ∈ {0,1}∗}. I free grammar for this language L. lemma for context free grammars to show t 1. {OʻPOT<)} L = {w • Reverse(w) w we {0,1}*). DA+hattha follaurino lano
The languages L1 = {anbm | m = n or m = 2n } and L2 = {a n b m | n <= m <= 2n } are context free. a. Choose one of the languages and write a CFG for it. b. Write the PDA that comes from your grammar (part a). Show the first 4 moves it would make on some string in your language (of length at least 4). Be sure to show state, input, and...
Consider the following languages Li and L2, respectively, and construct a context free grammar for it if it is a context free language; if not, using the pumping lemma to disprove it. Let na(w) denote the number if a is w, same notation for to now) and nc(w). • L1 = {w we {a,b}* and na(w) = nb(w)} • L2 = {w I w€ {a,b,c}* and na(w) = n5(w) = nc(w)}
5. Is the following language A context-free? You either show that A is context-free by giving a context-free grammar for A, or prove that A is not context-free language using the context-free language pumping lemma
6.) Is the languages Context Free or not? (prove / disprove using pumping lemma for CFL ) L = {0n 1 0n 10n | n >= 1}