the Thompson construction that is able to recognize the sentences generated by the expression b*(ab|ba)b*. Does the sentence w = "abbb" belong to the language generated regular expression? Justify. Convert it to a DFA using the sub-set construction. Verify that the DFA yields the same out the original NFA for the same input string w.

the Thompson construction that is able to recognize the sentences generated by the expression b(ab|ba)b. Does the sentence w = "abbb" belong to the language generated regular expression? Justify. Convert it to a DFA using the sub-set construction. Verify that the DFA yields the same out the original NFA for the same input string w.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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I actually forgot to type "xw" after "given by" in my question. Consider a text corpus consisting of N tokens of d distinct words and the number of times each distinct word w appears is given by xw.
Answer itthe nfa. L1 = {u ∈ Σ∗| u ends with aa}.L2 = {u ∈ Σ∗| u ends and begins with different letters }.L3 = {u ∈ Σ∗| u contains abba}.L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}. Given the above languages:(a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2.(b) Prove that L5 is regular.(c) Construct an NFA M that accepts L5, and prove its correctness.?
Consider the set Rej™M = {(M, w) : M is a TM such that M rejects on input w}. (a) Describe an element in the set and one not in the set. You should provide pseudocode for any TM you discuss. (b) Prove RejTM is recognisable. Hint: Similar to the proof of Halt™M
Implement algorithm GetExp (s, i) pre-cond: s is a string of tokens, andi is an index that indicates a starting point within s. post-cond: The output consists of a parsing p of the longest substring s[i], s[i + 1], ... , s[j − 1] of s that starts at index i and is a valid expression. The output also includes the index j of the token that comes immediately after the parsed expression.
Is aa distinguishable from the string a with respect to the set of strings over {a,b} that end with aaa? If so, prove it. * What implication does the above result have on the design of an FSA M such that L(M) is the set of strings over {a,b} that end with aaa?
For this problem, please kindly show your work Let ?L be a set of all finite binary strings that representing a binary number divisible by 2 (or 102102). What is a REGEX of ?L? Design an FA ?a such that ?a accepts ?L, i.e., ?=?(?)
Implement the function integrate_3(func, xa, xb, ya, yb, za, zb). xa and xb are the endpoints in the x-axis. ya and yb are the endpoints in the y-axis. za and zb are the endpoints in the z-axis. For example, if we have def h(x, y, z): returnmath.sin(x)+math.cos(y)+math.tan(z) r = integrate_3(h, 0, 3, 0, 2, 0, 1) print("{:.3f}".format(r)) This should print 10.453. Set Δx, Δy, and Δz equal to 0.01. The code above corresponds to the following: (see the attached picture below) The functions should return values, NOT print them. Use python, only import math library nothing else.
Please help me fill in the blanks The reverse of a string x, denoted rev(x), is the string obtained by writing x backwards. For example, if x = abbaaab then rev(x) = baaabba. If A is a subset of Σ*, the reverse of A, denoted rev(A), is the subset of Σ* consisting of all reverses of strings in A: rev(A)={rev(x) | x∈A} For example, rev({a,ab,aab}) = {a,ba,baa}. Suppose you are given a deterministic finite automaton M accepting a set A. Show how to construct a DFA N accepting rev(A). (Kozen would suggest putting pebbles on the final states of M and moving them backwards along transition edges.) Describe N formally (i.e. in terms of Q, δ, etc.) including the definition of acceptance. Hint: the subset construction will be helpful here. You can start with M = (Q, Σ, δ, s, F) and define the components of N in terms of the components of M. 1. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where Q_N = ___ 2. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where δ_N = ___ 3. DFA N = (Q_N, Σ, δ_N, s_N, F_N)…
Prove that F = {ww|w is a string from {0,1}*} is not regular. Consider the string s=0p10p1. Note that {0,1}* is any string (including the empty string) containing any number of 0s and 1s (in any order).
Find all strings in L(ba + ab*a) of length less than four. Find a regular expression for the set { a" bm : n, m are even}.
Prove that the following languages are not regular using the Pumping lemma and/or closure properties. Note: Do not use other methods. a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w) b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}
The language L of strings over alphabet Σ = {0, 1} which (in binary) represent even numbers is a regular language. Show this by giving both a. a regular expression and b. by drawing a finite state automaton (FSA) that recognizes strings from this language.