3) Please construct PDAs that accepts the languages defined by the grammar: (20 Points)
a) S --> aSSSab | λ
3) Please construct PDAs that accepts the languages defined by the grammar: (20 Points) a) S...
3. Construct a push down au gprnerated by a grammar with producti (npda) that accepts the lana B--b b. Show that the npda in part a accepts the language a 0 RE
3. Construct a push down au gprnerated by a grammar with producti (npda) that accepts the lana B--b b. Show that the npda in part a accepts the language a 0 RE
4) For the alphabet S={a, b}, construct an FA that accepts the following languages. (d) L= {all strings with at least one a and exactly two b's} (e) L= {all strings with b as the third letter} (f) L={w, |w| mod 4 = 0} // the cardinality of the word is a multiple of 4
1. (20 points) Given the following Grammar G,
S->ASB
A -> aAS | a | λ
B -> SbS | A|bb
(a) Identify and remove the λ-productions.
(b) Identify and remove unit-productions from the result of
(a).
(c) Convert it to Chomsky Normal Form.
1. (20 points) Given the following Grammar G, S->ASB A -> AS | a 1a B -> Sbs | Albb (a) Identify and remove the -productions. (b) Identify and remove unit-productions from the result of (a)....
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)}
Define a context-free grammar that generates exactly each of the following languages. For consistency, please use S for the start variable in all three grammars 1. A- E 10,1) the middle symbol in is 0 and is odd)
Automata, Languages & Computation
Question: For = {a,b} construct
the DFA that accepts the language consisting of all strings over
the with no more than
one a.
The DFA constructed should be in a form similar to the below but
obviously built using the above language:
We were unable to transcribe this imageWe were unable to transcribe this imageb b b 1,1 2,3 3,2 a a
b b b 1,1 2,3 3,2 a a
1)Convert the following context free grammar to Chomsky Normal Form S → a X | Yb X → S | λ Y → b Y | λ 2)Some languages distinguish between uppercase and lowercase in identifiers. What are the pros and cons of this design decision? 3)Use the pumping lemma to prove that the following languages are not regular. (The alphabet is Σ = {a, b}.) a) L = {an b1 ak: k >= n+ l} b) L = {ww:...
5. (5 points) Give context-free grammar that generate the following languages (1) (w is a binary string, and w starts and ends with the same symbol (2) the empty language (empty set)
Construct a Turing Machine (TM) that accepts the following language, defined over the alphabet Σ = {0,1): at accepts the tollowing language, define [10] Give the transition diagram and explain the algorithm implemented by your TM.
For the following grammar (7 points) 1. B - Ba|A S - ABb A - Aba |A to find a grammar without A productions that generates the same language, we first identify non-terminals that drive A. These non-terminals are: A and B. Then from S - ABb, we construct S from A - Aba, we construct A - from B - Ba, we construct B - So, the grammar without A that generates the same language is: