For each of the following languages over the alphabet E = {0, 1}, either prove that the language is regular (by constructing an appropriate DFA, NFA, or regular expression) or prove that the language is not regular (by constructing an infinite fooling set). Recall that Et denotes the set of all nonempty strings over E. Watch those parentheses! {0ªlw10° | w e E*, (a < \w| +c) and (|w|

Q: . Give a CFG G that generates all odd length strings over {a,b}. B. Give a Push-down Automaton that…

A: Logic to build CFG,PDA for the language that have odd length strings over {a,b} for CFG: -we need to…

Q: Consider the set A of all strings of letters a-f of length 6. A few elements of this set are dcebac,…

A: Set A itself:Cardinality: The cardinality of set A is determined by the number of possible strings…

Q: language L = {a i b j c k | i 6= j, j 6= k, i 6= k}; it is not a context- free language. Show that…

A: Given : L = {a i b j c k | i == j, j== k, i == k};

Q: For E = {a, b}, construct dfa's that accept the sets consisting of (d) all strings with at least one…

A: Below is the answer to above question. I hope tis will be helpful for you...

Q: For Σ= {a, b, c, d, e, ..., z}, consider the set L of words w such that the last symbol of w is a…

A: For Σ= {a, b, c, d, e, ..., z}, consider the set L of words w such that the last symbol of w is a…

Q: Let Σ={a, b}. Let L be the language of all strings that contain two b's in their middle third. In…

A:

Q: Let

A: 1.    The number of subsets of a set with a n  elements is 2n  as  n=2, 22 = 4 , then   2.    n=k,…

Q: 1. Let L be the set of strings in fa, b}* that contain an even number of a's and also an even number…

A: Given Language :  The language L can be expanded as L = { aabb , aabaabbab ,  abababab , .....} The…

Q: For E= {a,b}, onstruct dfa's that accept the sets consisting of (a) all strings with exactly one a,…

A:

Q: u ∈ Σ∗| u ends with aa}. L2 = {u ∈ Σ∗| u ends and begins with different letters }. L3 = {u ∈ Σ∗| u…

A: (a) Given languages are, L1 = {u ∈ Σ∗| u ends with aa}here now L2 = {u ∈ Σ∗| u ends and begins with…

Q: Let E={〈M〉| M is a TM and every string in L(M) has even length}. Argue that the property described…

A: I Have answered this question in step 2.

Q: Computing the intersection of two sets is similar to computing the union; only for this operation we…

A: The code for a CSet class based on a BitArray is shown as follows:

Q: Write an algorithm for addressing the subset-superset problem in string matching. That is, search a…

A: arr[] = {"catgc", "ctaagt", "gcta", "ttca", "atgcatc"} Initialize: temp[] = {"catgc", "ctaagt",…

Q: Consider the language L = {a'b'c* | i # j,j # k, i # k}; it is not a context- free language. Show…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  Never use…

Q: Create a Deterministic finite automaton that takes in binary strings and accepts them which has both…

A: The solution is divided in three parts: 1. Split the given language into two small languages. L1…

Q: Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N} is…

A: To prove that F = {X ⊆ N | |X| &lt; ∞} is countable, we can construct an onto function g : N → F.…

Q: Let M be the language of all binary strings that contain the substring 11 and whose number of 0’s is…

A: AND)A set of pairwise distinct strings:A set of strings is pairwise differentiable with respectinto…

Q: A grid must have a mechanism for numbering the tiles in order to support random-access search. A…

A: Introduction The "tile" which refers to an important enough object in the game of "Memory" that we…

Q: For each of the following languages over the alphabet E = {0, 1}, either prove that the language is…

A: The Answer is

Q: Construct an NFA for the set of all strings w *epsilon* {a,b}*; such that (1) w contains both aa and…

A: Designed the NFA for the given language

Q: For E= {a, b}, construct dfa's that accept the sets consists of (i) All strings with no more than…

A: all dfa are given below:-

Q: orithms to enumerate these sets. (You do not need to discuss the mechanics of constructing Turing…

A: It is defined as a step-by-step procedure that defines a set of instructions that must be carried…

Q: A string w of a's and b's is valid if it satisfies one of the following conditions: • w is the empty…

A: We can implement the program as follows:   Algorithm String_Validity( String a, String b , String…

Q: DFA over {a,b} that accepts all strings of length exactly 5 For each state in your automaton, give…

A: We are asked to give a DFA over inputs  {a,b} such  that it  accepts all strings of length exactly 5…

Q: If A is any language, let A 1/3 – 1/3 be the set of all strings in A with their middle thirds…

A: the answer is given below:-

Q: Use a closure operation to reduce the language L of all even-lengthed strings of as and bs where…

A:

Q: Prove that the following language is non-regular, using the Pumping Lemma. L = {ambcr | m, n, r =…

A: The pumping lemma is a fundamental result in formal language theory that provides a way to prove…

Q: Let Σ be the alphabet {a,b}. Let L be the language describe by                     Σ∗ −…

A: Here in this question, it asks us to draw Finite automata the accepts the   Σ∗ − (ε|Σ∗b)aa(ε|bΣ∗)…

Q: 3) Is aa distinguishable from bb with respect to the set of strings over {a,b} that end with bbb? If…

A: Proved that the distinguishable from aa to bb in the given language

Q: Write an algorithm and implement the same in C to solve weight sub set problem for the following…

A: Algorithm: We can use recursive way to solve the weight sub set problem.  Let's have a last element…

Q: Let Σ={x,y,z} be an alphabet and let S be the set of all finite length strings over Σ. Show that S…

A: Introduction Here ∑={x,y,z} and S is a collection of all strings of finite length over ∑

Q: Give a regular expression for each of the following sets. Set of all strings of 0s and 1s…

A: Set of all strings with at least one 0:Look for any string with the number 0 in it. The expression…

Q: Use the pumping lemma to prove that the following language is not context-free. Show all cases on…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  Never use…

Q: Define function p:cat represents set concatenation ◦, which concatenates every pair of strings from…

A: Two or more sets are used to perform multiple operations as per user requirement Various types of…

Q: NFA 0’s near end or 1 at end: Write a nondeterministic finite automaton with at most 10 states that…

A: A Nondeterministic Finite Automaton (NFA) is a theoretical machine used in the study of…

Q: Væ (Q(x) → ¬P(x))

A: From the given expression said that- For all x, if x is a prime number then it should not be even…

Q: For each of the following languages LS {a, b}*, show that the elements of the infinite set {a"|n 2…

A: Shown that the given language are pairwise distinguishable

Q: For each of the following languages LS {a,b}*, show that the elements of the infinite set {a"|n > 0}…

A: Shown that the given language pairwise distinguishable

Q: Let LPrime = {| the number of strings accepted by M is prime). Classify this language as either (i)…

A: Let LPrime = {| the number of strings accepted by M is {the prime}. Classify this language as either…

Q: Let L = {(D) | D is a DFA over the binary alphabet, which accepts at least one string that has 100…

A:

Q: Show L = { w | w is an element of {0, 1, 2}* and (the number of 0s in w ≥ the number of 1s in w) and…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  Never use…

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r€ RB, let L(r) be the…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…