Give terms t1,t2,...,t5 such that the following derivation makes sense in the polymorphic lambda-calculus, where X is a type and Γ = x : X,f : (∀Z.X →Z →Z),y : X.

Q: Prove that the following language A is decidable (e.g., give a TM that decides A). A = {⟨M⟩ | M is…

A: We will prove that language A = {⟨M⟩ | M is an NFA and L(M) = B}, where B is a regular language, is…

Q: For each of the following regular expressions find a language (i.e., a set of strings) over A =…

A: Regular expressions are symbolic representations of patterns that define sets of strings. The…

Q: 2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Ax | xFT) OR=…

A: Answer: I have given answered in the handwritten format in brief explanation.

Q: Let A = {1, 2, 3, 4} and B = {a, b, c}. Give an example of a function f: A -> B that is neither…

A: A = {1, 2, 3, 4} and B = {a, b, c}  f: A -> B

Q: Give a recursive definition that defines the language: L = {aibj | i ≤ j}

A: Hey there, I am writing the required solution based on the above given question. Please do find the…

Q: 4. What does the following Lisp function do? (defun myfun (1st) (cond ((null lst) ()) ((equal (car…

A: Defun can be used to define a new function, to install a corrected version of an incorrect…

Q: Describe the following sets by regular expressions,       (a) {abba}     (b) {a, ab} .

A: The Answer is in Below Steps

Q: looking for atom code for the following Trace the function f as demonstrated in class for the…

A: Answer: -------- oN

Q: 4. Find a closed form representation for the function defined recursively by f(0) = 5 and…

A: Answer: We have explain in more details to correct using an inductive arguments

Q: Which functions are one-to-one? Which functions are onto? Describe the inverse function for any…

A: This is a question about one-to-one, onto, and bijective functions and their inverses. The question…

Q: Defined the following Clojure program that deals with primitive lambda logic representation: (ns…

A: The provided Clojure program deals with primitive lambda logic representation, defining basic…

Q: 1. For the function defined recursively by f(0)=5 and f(n)= 4f (n-1)+3, answer the following: a.…

A: General guidance The answer provided below has been developed in a clear step by step manner. First…

Q: Let’s define languages: L1    = {wan | w is an arbitrary string containing a’s and b’s, of length…

A: L1= wa^n/ w is an arbitrary string containing a's and b's, of length n L2= {w/01^*0(11+00)^*}

Q: What does the following lambda expression compute: λ(x)x × x × x

A: Given lambda expression is, λ(x)x × x × x

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: Discrete mathematics applied to computer science: homework question. Let f : A → A be a function in…

A: Here is your solution :

Q: Simplify the following assertions (so that ¬ does not appear).

A: Answer to the above question is given below

Q: Lists – Lists can be encoded in the lambda calculus. A way to do this, is by defining a lambda term…

A: From the above information we have to consider ascons is a lambda term representing list…

Q: normalization, and strong normalization to explain how many normal forms the term ten has, and if…

A: The lambda-term "ten" is defined as "take 10 [0, 1, 2, ...]" which corresponds to the Haskell…

Q: Give an dfa that accepts the language L ((a + b)∗b (a + bb)∗).

A: The DFA for the given language L ((a + b)∗b (a + bb)∗) is shown below:

Q: Let G = ({S,A,B,C,D,E,Z},(0,1),R,S), where R = {S → E | Z; E → A | C; A → 01B | 0A | ; B → 1B |…

A: Introduction: Here we are required to to perform the asked questions on given set G =…

Q: Find DFAs that accept the following languages. 1. L(ab(a + ab) ∗ (a + aa)) 2. L(ab∗a ∗ ) ∪ L((ab)…

A: DFAs An algorithm for navigating or searching through tree and graph data structures is called…

Q: Consider an ADT for the data structure of positive integers called POSITIVE_INTEGER defined over a…

A: Please refer to the following step for the complete solution to the problem above.

Q: A binary operator f on a set X is commutative if f(x, y) = f(y, x)for all x, y ∈ X.State whether the…

A: Given that X=P({1, 2, 3, 4}), the P here represents power set of {1, 2, 3, 4}. The power set is a…

Q: Consider an ADT for the data structure of positive integers called POSITIVE_INTEGER defined over a…

A: Given: Consider an ADT for the data structure of positive integers called POSITIVE INTEGER defined…

Q: For the language, draw the corresponding DPDA. L ={x ∈ {a, b}* | na (x) < nb (x)}.

A: The DPDA for the given language

Q: Which proposition denotes the wff given below over the domain {0,1}? ExVyp(x, y) [p(0, 0) V p(0, 1)]…

A: As per the answering guidelines solving the first question completely.

Q: For the following pairs of expressions, find a unifier for each pair if a unifier exists. If a…

A: For the following pairs of expressions, find a unifier for each pair if a unifier exists. If a…

Q: Show that the following language is decidable by giving a high-level description of a decio L(M) =…

A: ALLDFA = {  | D is a DFA and L(D) = Σ* }   Input: DFA D 1. Find the set of all reachable states from…

Q: Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f =…

A: In this question, we are given two functions f and g. And we have to find out the fog as a set of…

Q: (A) Design in JFLAP a simulator of a deterministic finite automaton (DFA) that (only) recognizes the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the following two variable bindings in Lisp: (setq x ‘(a b c d)) (setq y ‘(4 3 2 1))…

A: General guidance The answer provided below has been developed in a clear step by step manner. First…

Q: 3. Consider a function with polymorphic type f ('a * 'b) -> ( 'b -> 'a) : -> 'a 3.1. What is the…

A: The answer is below for the above given question:

Q: Let A and B be sets. How to show the following?: 1. If A es is countable and there exists a…

A: In the realm of set theory, understanding the relationship between countability and the existence of…

Q: e a python function (sat) that solves the satisfiability of the clause set by running through all…

A: Task : Create python program that solves  the satisfiability of the clause set by running through…

Q: Question that I need help with: 1.49 a. Let B = {1 k y| y ∈ {0, 1} ∗ and y contains at least k 1s,…

A: A regular language is a language that can be recognized by a finite automaton or described by a…

Q: Evaluate the following lambda expressions using eager beta-reduction (use the standard…

A: Note : As per the guidelines , we are supposed to answer 1 question per post please repost the other…

Q: Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF {wct | t ∈…

A: The Answer is in step2

Q: 2. Consider a function with polymorphic type f 'а -> 'а -> 'a. : 2.1. What is the type of f 0 ? 2.2.…

A: Given :- Consider a function with polymorphic type f : 'a -&gt; 'a -&gt; 'a. 2.1. What is the type…