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: Let L be any regular language over {a, b, c}. Show how the Pumping Lemma can be used to demonstrate…

A: The Answer is in step2

Q: Given a universal set, U = {a, b, c, e, f, g, h, k, m}, and the the ff. sets: A = {a, b, c} B = {a,…

A: Given:   Universal set = U = {a, b, c, e, f, g, h, k, m}, and the the ff. sets: A = {a,b,c} B = {a,…

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: Give a regular expression for the language of all strings over alphabet {0,1} that have exactly…

A: Given: A regular expression for the language of all strings over alphabet {0,1} that have exactly…

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: Write Algorithm which computes all the orbits of a group, is a simple extension of Algorithm 1.…

A: Algorithm which computes all the orbits of a group, is a simple extension of Algorithm :

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: 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: In the WHILE language, prove that if ⇓ s' then there exists an integer k such that s(y) = s'(y) +…

A: Given data, &lt;while b do y := y-x,s&gt; ⇓ s' then there exists an integer k such that s(y) = s'(y)…

Q: Find which propostin equibalen ce bogic is tave and false 7[(p>72) vs] = [PA2175] 2. 3.

A: 1. Given proposition equivalence is, ¬[(p→¬q)∨s)≡[p∧q∧¬s] Consider, ¬[(p→¬q)∨s) =¬[(¬p∨¬q)∨s) where…

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: Let L be a language over the alphabet Σ = {a,b,c}. Prove that L = {abman for any positive integers n…

A: Regular language is a language which can be expressed using a regular expression or using finite…

Q: Suppose a set of n objects is given, such that the size of the ith object satisfies that 0 < < 1. It…

A: The first-fit heuristic is one of the simplest and most commonly used algorithmic solutions to the…

Q: Give a regular expression for the language L over the alphabet > = {0, 1}, where every string in L…

A: Analysis of the regular expression and its effectiveness in implementing the presence of the…

Q: (b) Rewriting the difference of the two languages from part (a), using set-intersection and…

A: I have answered this question in step 2.

Q: positive integer is the gcd of that integer with its amount of digits. Officially, gcdSum(x)=gcd(x,…

A: Here have to determine about the  gcd sum programming problem statement.

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 the universal set be the set ? of all real numbers and let ? = {x ∈ r |0 < x ≤ 2}, ? = {x ∈ r |1…

A: Lets see the solution.

Q: Design in JFLAP a simulator of a finite deterministic automaton that (only) recognizes Even length…

A: Solution: To designing the finite automata for the even length binary number , We know to that the…

Q: Consider a sequence defined on the set of non-negative integers as follows: an = -2(-1)" for n 2 0.…

A: Recursive function is a function that calls itself in its definition directly.

Q: Let L = (ab,aa, baa; and consider the strings w=ba^5baa,x=abaabaaabaa,y=a^4ba^4, z=ba^5ba^4b. Which…

A: First I consider  w = ba^5baa  means w = baaaaabaa  As I break down the above string " baa aa ab aa"…

Q: Let's call two numbers isomorphic if they have same number of digits and set of places having equal…

A: Note, as you haven't mentioned any programming language I am solving the problem using C++…

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: hyphen denotes set difference and ɛ de- notes the empty string. (Hint: L consists of the strings…

A:

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: 3. Let D = (Q, E, 6, go, I) be a DFA. Construct a new DFA D' from D such that L(D') = {w E*: w3 €…

A: DFA stands for Deterministic Finite Automata. It is a 5-tuple,  ,M= (Q,⅀, δ, q0,F)where Q : finite…

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

A:

Q: Prove by an appropriate reduction that the following set is not recursively enumerable: {⟨M⟩|M(⟨M⟩)…

A: The Turing machine is a mathematical model that manipulates the abstract machine and computing…

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: Let T={〈M1,M2〉 | M1 and M2 are two ΤΜ which accept at least one common string} Show that T is…

A: Let T={〈M1,M2〉 | M1 and M2 are two ΤΜ which accept at least one common string} Show that T is…

Q: Define a function alwaysFollows of type [Integer] -> Bool so that alwaysFollows (x, y, lst) is true…

A: Below is the required code in python and sample output:

Q: Consider nonempty set A such that JA| 2 2. Specify which one of the following statements is true. *…

A: According to the information given;- We have to choose the correct option to satisfy the statement.

Q: Let E={0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 4…

A: A regular expression is a sequence of characters that forms a pattern, which is used to match and…

Q: How about we characterize an augmentation activity between a string an and a positive integer x: a⋅x…

A: Here have to determine about the characterize an augmentation activity programming problem…