The language Balanced over E = {(,)} is defined recursively as follows 1. ЛЕ Вalanced. 2. Vx, y € Balanced, both xy and (x) are elements of Balanced. A prefix of a string x is a substring of x that occurs at the beginning of x. Prove by induction that a string x belongs to this language if and only if (iff) the statement B(x) is true. B(x): x contains equal numbers of left and right parentheses, and no prefix of x contains more right than left.

Q: If L is a formal language that contains finitely many strings, the language L,* , which contains…

A: Concatenation of Language P and Q The set of strings that may be generated by combining any string…

Q: Consider a set of symbols = {abc}. (1) Find all strings in E* shorter than 3. (2) Let L = {1, b,…

A: set of symbols = {a,b,c}

Q: S is a set of strings over the alphabet {a, b}* recursively defined as: Base case: λ ∈ S, a ∈ S, b…

A: Base case: λ ∈ S, a ∈ S, b ∈ S Recursive rules: If x ∈ S, then Rule 1: axb ∈ S Rule 2: bxa ∈ S

Q: En is the language that contains all and only strings that, in turn, contain nothing but the letter…

A: By definition, a language is regular if some finite automata recognizes it. So if we can prove that…

Q: Show that L= {a": n>4} is regular. Show that the language L= {a": n> 0,n± 4} is regular.

A: ANSWER:-

Q: the first b. 3.The last symbol of the string is d. 4.Each a is immediately fo

A: Let L be the language over {a, b,c,d} accepting all strings so that: 1.All c’s occur before the…

Q: Consider the language L of strings over the alphabet Σ = {a, b} which contain an equal number of a’s…

A: CFG is a formal grammar which is used to generate the all possible strings in given formal…

Q: Give a recursive definition for the set of all strings of 0’s and 1’s that contain exactly two and…

A: Here have to determine about math problem about recursive definition.

Q: Give a recursive definition for the language STRANGE which is defined over the alphabet Σ = {a, b}…

A: The language STRANGE is defined over the alphabet Σ = {a, b} and encompasses strings with an even…

Q: Let L be the language defined by the following regular expression 0(0 | 1)∗1(0 | 1)∗ Write 3…

A: The regular phrase 0(0 | 1)*1(0 | 1)* defines the language L. A group of strings with particular…

Q: a. Correctness of dynamic programming algorithm: Usually, a dynamic programming algorithm can be…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Let ANTIPALINDROME be the language of all even-length strings over the alphabet {a,b} such that, for…

A: Given:  Let ANTIPALINDROME be the language of all even-length strings over the alphabet {a,b} such…