The Context Free Grammar below is given: G=( {S,a,b}, {0,1}, S, {S⇒0b|1a, a→0|0s|1aa|ɛ, b→1|1s|Obb}) Which string(s) could belong to the language generated by this grammar? 101110111 ☐ 10010100 0100101110 0000100001
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- Define a NPDA for the language L= {uv € {a, b}*||u|l = |v| and u # v*}. Another way to interpret L is that it is the set of all cven length strings that are not a palindrome.Using Java, a program that reads as input an arbitrary context-free grammar from a text file and then derives/enumerates five strings from the grammar. The file cfg.txt can be used to test your program. The grammar represented in cfg.txt is the following grammar for non-palindromes (from input alphabet {a,b}): S -> aSa | bSb | XX -> aYb | bYaY -> aY | bY | lambdaThis is formatted in cfg.txt as follows: S aSaS bSbS XX aYbX bYaY aYY bYY *An asterisk is used for lambda. Assume that the first state listed in the input file is the start state. Read the grammar into a map (aka hash or dictionary) where the key is a variable and the value is a list of right-hand sides. If you are using Java, you could use Hashtable by declaring a Hashtable of the following type:Hashtable<String, ArrayList<String>>Do not write the program specific to this grammar in cfg.txt. Further, assume that the test file will have more than three variables, and productions on the right hand side can…The language composed of all strings over the alphabet {a,b} of the form: zero or more a's followed by zero or more b's, i.e., {"", a, b, aa, ab, bb, aaa, aab, abb, bbb, ...}, where "" is the empty string, is a regular language: show why this is. Note that you may use any line of argument on regular languages, e.g., by showing that it can be constructed using the properties ("Regular Language: a formal definition"), or by drawing the finite state automaton (FSA), or giving its description.
- Build a DPDA that accepts the language L ={(ab)" (aab)b²n |n≥0Assumptions. • Alphabet E = {a, b} • L = {a"b" : n 20 An mod 3 = 0} To do in this exercise. Find a context-free grammar G such that L(G) = L. Save your context-free grammar as a JFLAP jff file, and submit that .jff file to Canvas as your solution to this exercise.subject theory of computer science Consider the following grammar G = {S, A}, S = {S}, ∑ = {a, b}, P : S → aS | aA; A → bA | b; Which of the following regular expression denotes L(G)? A.a(ab)*b B.a*b* C.aa*bb D.a*ab*b
- Build a TM over the alphabet Σ = {a,b} that accepts the language where each word has twice asmany b’s as a’s.Formal language Let’s define languages: L1 = {wan | w is an arbitrary string containing a’s and b’s, of length n}, Σ = {a, b} L2 = {w | 01∗0(11 + 00)∗} , Σ = {0, 1} Find out if the language is regular or not?Create a Deterministic Finite Automaton (DFA) for the language L that is defined over the input alphabet E = {a, b} and has all of the following properties: i. Second and third letters of its words are the same, ii. Its words are longer than four letters, and iii. Its last letter cannot be the letter b. My answer is true or wrong? If it is wrong can you fix it? 96 91 92 a a. 95 9. 96
- 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 ɛ € 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.Using Java, write a program that reads as input an arbitrary context-free grammar from a text file and then derives/enumerates five strings from the grammar. The file cfg.txt can be used to test your program. The grammar represented in cfg.txt is the following grammar for non-palindromes (from input alphabet {a,b}): S -> aSa | bSb | XX -> aYb | bYaY -> aY | bY | lambdaThis is formatted in cfg.txt as follows: S aSaS bSbS XX aYbX bYaY aYY bYY *An asterisk is used for lambda. Assume that the first state listed in the input file is the start state. Read the grammar into a map (aka hash or dictionary) where the key is a variable and the value is a list of right-hand sides. If you are using Java, you could use Hashtable by declaring a Hashtable of the following type:Hashtable<String, ArrayList<String>>Do not write the program specific to this grammar in cfg.txt. Further, assume that the test file will have more than three variables, and productions on the right hand side…Construct a PDA that matches all strings in the language over {x.y} such that each string has at least twice as many y's as x's. Editor Below, give a short description of the set of strings associated with each state of your PDA.