For the language, draw the corresponding DPDA. L ={x ∈ {a, b}* | na (x) < nb (x)}.

Write a TM (Turing Machine) that accepts the language L = {w | w is a string of 0s and 1s whose decimal equivalent is a power of 3}. Ex. 1, 11, 1001, etc. (Include 1 as 3^0 = 1). You may write only the transitions.

Develop a system/application in Prolog that will allow grader to: load a set of student’s grades (see samples from the Table C below) query student’s final letter grade (A, B, C, etc.) by a given student’s name. query student(s) whose grade matches to the input letter grade (e.g., A). For example, show student(s) whose final letter grade is A. There are 3 types of grades for each student—HWs, Exams, and Project, with a weight of 20%, 40% and 40%, respectively, to the 100-point final. Table A and B show how the final grades (in points and letter) are computed. Table C shows samples of students’ grades. You will define the execution instructions to answer the following questions so that grader can test out your application in Prolog: how to load your source code to Prolog runtime/compiler how to load students’ grades to Prolog runtime/compiler how to query student’s letter grade how to query student(s) whose letter grade matches to an input letter grade Please DO NOT hard code any…

Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s and b’s, and the set of b’s is consecutive in the string, e.g., ab, abba, aabb, abbbaa, aaabbbbbaa, etc. Note that ε ∈ L for completeness (0 number of a’s is equal to 0 number of b’s, which are also consecutive). Show that this language is context-free by giving a context-free grammar. Please make sure to test the answers onhttps://web.stanford.edu/class/archive/cs/cs103/cs103.1156/tools/cfg/

Prove that the following language is regular.L = {x | x ∈ {0, 1}∗, x does not contain five consecutive 0's or five consecutive 1's}Hint: You may take advantage of some closure properties.

This is an Automata and Computation question on Functions/Sets.

Write a classifier algorithm for p(Y |X,α)

Suppose LS {a, b}* is defined as follows: A e L; for every x and y in L, the strings axb, bxa, and xy are in L. Show that L= AE B, the language of all strings x in {a, b}* satisfying na(x) = n¿(x).

Given: Language L2 = {w ϵ {a,b}* | w contains substring aab} Construct the DFA representing the given language L2. Assume the layout of the DFA is as follows: ->A->B->C->D*. That is, the number of states are four (4) and A is the starting state and D is the accepting state. How many self-loop edge/s in the constructed DFA representing the given language L2?