Make your own own regular expression. Regular languages require that your phrase include all three operators (union, concatenation, Kleene star). Generating an NFA from your regular expression using Kleene's theorem part 1 construction is a viable option. Verify that all operators have properly converted their NFA-protected structural components (with the exception of the elimination of null transitions between the concatenation of single symbol NFAs)

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

Question 34 The correct statements are: Decidable languages are closed under union. Decidable languages are closed under intersection. Decidable languages are closed under complement. Semi-decidable languages are closed under complement.

Is each of the following statements true or false? Please explain.  a. Let σgrp := (·, ()-1, 1) be the signature groups, where · is a binary and ()-1 a unary function symbols, and 1 is a constant symbol. Then every σ-structure G := (G,·G, (()-1)G,1G) is a group with the group operation ·G. b. Let A := (A, σA) and B := (B, σB) be σ-structures. If A ⊆ B, then A is a substructure of B.  c. Let A := (A, σA) and B := (B, σB) be σ-structures. If A is a substructure of B, then the inclusion map a ↦ a from A into B is a σ-embedding.

Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF  {wct | t ∈ {a,b}* ∧ w is a substring of t}

Make a conjecture whether or not it is regular and prove your assertion. When you prove a language is not regular, use the game with demon. Do not apply Pumping Lemma directly.

5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.

Quantifiers are called quantifiers because they express somethingabout the number of elements that satisfy a certain property. Showhow to express the following ‘quantified’ statements in predicatelogic with a unary relation symbol R. You don’t have to introduceany new quantifiers to do this, although you will need to keep inmind that the atomic formula x=yis always considered to be partof the language.(a) Exactly one x satisfies R(x).(b) At least one x satisfies R(x). (c) No more than three x satisfy R(x).(d) All but one x satisfy R(x).

Provide DFA diagrams to recognizes the same languages as each of the regular expressions in a. The set of chess moves, in the formal notation, such as p-k4 or kbp x qn. b. All stings of a’s and b’s that do not contain the substring abb. c. All strings of a’s and b’s that do not contain the subsequence abb.

Set up truth tables for the statementsP ⇒ (P ⇒ Q), (P ⇒ Q) ⇒ Q, P ∧ (∼ Q), (∼ P) ∨ (∼ Q)Are any of these statements equivalent?