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Problem 3. Let C be the language 0, S, function symbol, and + is a binary...
For a string s ∈ {0, 1} let denote the number represented by in the binary * s2 s numeral system. For example 1110 in binary has a value of 14 . Consider the language: L = {u#w | u,w ∈ {0, 1} , u } , * 2 + 1 = w2 meaning it contains all strings u#w such that u + 1 = w holds true in the binary system. For example, 1010#1011 ∈ L and 0011#100 ∈...
Use a first-order language with two constants “−1” and “1”, the unary function s(x), denoting the “successor of x”, and the binary predicate Less(x, y), representing “x is less than y”. Consider the following Horn database, with two rules labeled A and B and fact C: A. Less(x, y) => Less(x, s(y)) B. Less(s(x), y) => Less(x, y) C. Less(s(−1), 1) Using forward chaining (and substitution), begin enumerating all facts implied by fact C, given rules A and B, until...
3. (30 points) A binary communication system transmits signals s(t) (i 1,2). The receiver samples the received signal r(t) s(t) + n(t) at T and obtain the decision statistic r(T) S (T) n(T) a + n, where the signal component is either an +A or a2-A with A >0 and n is the noise component. Assume that s1 (t) and s2(t) are equally likely to be transmitted and the decision threshold is chosen as zero. If A 1 and the...
1. For a string s e 0, î, 2;" and a symbol d e { 0,1,2} let #(s, d) denote the number of times d appears in s. For example, #(0120012, 0)-3. Consider the language: {0, 1, 2. #(11,0) L- #(w, 1), #(11,2) #(w, 2) } . {utfw #(w, 0), #(11, 1) u, w, e For example, 2021 02#0011222 Construct a TM that decides this language. Provide a formal definition of your TM 1. For a string s e 0,...
IMPLEMENT IN C++ Implement a symbol balance checker function for the Pascal programming language. Pascal allows for the following pairs: {}, (), [], begin end . All programs will begin with the word "begin" and end with the word "end". Your function should receive an ifstream object which is already open and will return true, all of the symbols match, or false, they do not. You do not have to worry about comments in the program but you do have...
et l(a) be the language generated by g(a) - (n, 2, s, p) where 2 - [a, b), n= {s,x) and s->axb ... Question: Let L(a) be the language generated by G(a) - (N, 2, S, P) where 2 - [a, b), N= {S,X) and S->aX... Let L(a) be the language generated by G(a) - (N, 2, S, P) where 2 - [a, b), N= {S,X) and S->aXb X->aX|bX|epsilon (i) (3 marks) Describe the language L(a). (First generate a few...
The moment generating function (MGF) for a certain probability distribution is given by 2 (2 + 2) , M(t) = R. t 2 Suppose Xi, X2, are iid random variables with this distribution. Let Sn -Xi+ (a) Show that Var(X) =3/2, i = 1,2. (b) Give the MGF of Sn/v3n/2. (c) Evaluate the limit of the MGF in (b) for n → 0. The moment generating function (MGF) for a certain probability distribution is given by 2 (2 + 2)...
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropriate matched filter to apply for this signal. Draw the optimum receiver 2. What is the average energy of the constellation, i.., E,? 3. Assume the the received signal is r(t)= s(t) +n(t), where n(t) is AWGN with variance 1. Find the error probability...
(20 pts) To understand the value of recursion in a programming language: implement the binary search algorithm first as a recursive function and again using a conditional loop. Your program should create an array of characters holding the letters ‘A’ – ‘Z’ and find the index in the array where the letter ‘K’ is stored. You may use any programming language that supports recursion. (5pts) Define syntax and semantics and give an example. (5pts) Why is it important for a...
I. Let each of R, S, and T be binary relations on N2 as defined here: R-[<m, n EN nis the smallest prime number greater than or equal to m] S -[< m, n> EN* nis the greatest prime number less than or equal to m] (a) Which (if any) of these binary relations is a (unary) function? (b) Which (if any) of these binary relations is an injection? (c) Which (if any) of these binary relations is a surjection?...