Create a PDA that recognizes the following context free language with terminals {a,b,c} L= {wck | wE {a, b}* and k = |w|} (Hint: It is only asking for the # of c's = total number of a's + b's) (i) Describe your algorithm (ii) Give the description as a complete 7-tuple with a transition diagram (iii) Show configuration sequences on babbcccc leading to acceptance.

I keep getting the wrong answer can you please help me with this: Could you assist me with question 2.7 part C? I'm having difficulty with this problem and would greatly appreciate help in creating a state diagram for the push-down automaton in part C. question for 2.7 2.7 Give informal English descriptions of PDAs for the language. c. {w#x | w R is a substring of x for w, x ∈ {0,1} ∗ }

Show that the following language is context-free by either providing a PDA recognizing the language or a CFG generating the languages:

a) Construct a simplest possible PDA using state transition diagram that accepts the language L over alphabets {0, 1, 2} that precisely contains those strings where, the first, middle and the last letter or symbol in the string are the same. b) Demonstrate by computation that 01020  L(M) and 10201 L(M) to validate the PDA that you have constructed.

(a) Design a PDA P that recognizes the language L = {x#y : x, y ∈{1}∗∧ |x| > |y|} over the alphabet Σ = {1, #}. Draw a state diagram according to the format of the textbook and the slides,i.e., start with an empty stack. Furthermore, ensure that every move either pushes or pops, but not both.(b) Obviously, you can easily create a CFG for such a trivial language like L. Here, you are asked to not just produce any CFG for L, but follow the procedure PDA-to-CFG to obtain such a grammar. Even for such a simple PDA, the grammar would be a bit lengthy. Therefore, we make one modification. You don’t have to write any rules that involve variables that generate the empty language. Such rules would have no effect anyway.

L = {am+n bm cn | m,n ≥ 1} over Σ = {a, b, c}   A. Design PDA for L (with as less as states possible) B. Is L is regular language? C. Verify it by Pumping Lemma

Each of the following languages is the intersection of two simpler languages. Ineach part, construct DFAs for the simpler languages, then combine them using theCartesian Product of the two DFAs and produce a final state diagram (reducingthe number of states where possible) for the complete language. Assume thealphabet Σ = {a,b}.a. {w|w has at least 3 a’s and at least 2 b’s}b. {w|w has an even number of a’s and 1 or 2 b’s}c. {w|w starts with an a and has at most 1 b}

Consider the languages L = {a'bm qlxm|1, m 2 0} and Lo = {a2lym}|1, m 2 0}. (Recall from the previous exercise that we would state that L is non-context-free). Which is the simplest model of computation one may use on the language that is the intersection of L and L? Show your reasoning.

For each of the languages below, draw a transition diagram for a DFA which accepts thatlanguage.(a) Strings over Σ = {a, b, c} which begin with the character a and end with the character c.(b) Strings over Σ = {a, b} in which the characters a and b always alternate. For example, stringsababa, bab, and a are in this language.(c) Strings over Σ = {a, b} which end with either aa or bb.(d) Strings over Σ = {0, 1, 2}, such that the sum of all digits in the string is divisible by 4.For example, the string 02101 is in the language because 0 + 2 + 1 + 0 + 1 = 4, which is divisible by 4;but 1212 is not, because 1 + 2 + 1 + 2 = 6 is not divisible by 4.

Design and draw a Pushdown Automaton for the following language. Explain your PDA in brief (in not more than 3 sentences). L={w∈{a,b,c}^∗: w=(a^p)(b^q)(c^r), p,q, r≥0, p=3q+2r+1}