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. (d) L = {0, 1}* - L1, where L1 is the language {1010010001…10n-110n1 : n n ≥ 1}.
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
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...
Question 3 Give a context-free grammar for each of the following languages over = {a,b,c}. 1. {a^jen: n >0}. 2. {animck : k=n+m} 3. Strings of a's and b's that contain twice as many a's as b's (for example, aba).
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0 < n < m} is not context-free.
2. (6 pts) Use the pumping lemma for context-free languages and the string s = ap + 1 bpcP+1 to show that L (amb"cm | 0
construct a push down automata that recognises each of the
following languages.
D = {0m1rom+n | m, n >0} b. E = {xc" | x € {a,b}", n > 0, and x has na's or n b’s} Hint: Ę is the union of two simpler context-free languages. IT
Can someone use pumping Lemma to show if these are regular
languages or not
c) Is L regular? give a finite automaton or prove using pumping lemma. (d) Is L context-free? give a context-free grammar or pushdown automaton, otherwise pr using pumping lemma. (16 pts)Given the set PRIMES (aP | p is prime (a) Prove that PRIMES is not regular. (b) Prove that PRIMES is not context-free. (c) Show if complement of PRIMES (PRIMES ) is regular or not. d)...