Suppose L is a subset of {a, b}*. If xo, x1,... is a sequence of distinct strings in {a, b}* such that forevery n20, xn and xn+1 are L-distinguishable, does it follow that the strings xo, X1,... are pairwise L-distinguishable?

INTRODUCTION: A subset of a, b* is the language L. Take a look at the succession of unique strings…

Answered: Suppose L is a subset of {a, b}". If…

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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Let E={0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 4 symbols, that is, the length of w is at least 4) and (the first symbol of w is different from the last symbol of w) and (interior(w) is vorpal according to the following two definitions)}. For any string y containing at least 4 symbols, let interior (y) be the substring of y obtained by removing the first two symbols and the last two symbols of y. A string x over Σ is called vorpal if x satisfies one or more of the following conditions: • x is made up of exactly k 0-symbols where k modulo 4 is 3 (and no 1-symbols) ● x is made up of at least two 1-symbols (and no 0-symbols) ● x contains 011
Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N}is uncountable. We will show that F = {X ⊆ N | |X| < ∞} is countable, with an onto functiong : N → F that is computable.Write a program/function (e.g., in Python) that runs forever and prints every element of F,e.g., if run it would print something like{0}{1}{0,2}{3}{0,2}{0,5,7}{1}{0,1}{}{2}...(Note that you must prove that the program works, i.e., it prints every element of F, and onlyelements of F.)
Let ∑ = {a, b}. Given the language L = {b^n a^m: m,n≥0}, find the regular expression r such that L(r) = L.
No hand written and fast answer with explanation
Prove that L2 = {w = {0,1}+ | w starts and ends with the same symbol} is regular. string of length 1 (e.g., w = 0) starts and ends with the same symbol.
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.
Given a list of rational numbers,find their product. ConceptThe reduce() function applies a function of two arguments cumulatively on a list of objects in succession from left to right to reduce it to one value. Say you have a list, say [1,2,3] and you have to find its sum. >>>reduce(lambdax,y:x+y,[1,2,3])6 You can also define an initial value. If it is specified, the function will assume initial value as the value given, and then reduce. It is equivalent to adding the initial value at the beginning of the list. For example: >>>reduce(lambdax,y:x+y,[1,2,3],-3)3>>>fromfractionsimportgcd>>>reduce(gcd,[2,4,8],3)1 Input Format First line contains , the number of rational numbers.The of next lines contain two integers each, the numerator( ) and denominator( ) of the rational number in the list. Constraints Output Format Print only one line containing the numerator and denominator of the product of the numbers in the list…
Let Σ={0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 2 symbols, that is, the length of w is at least 2) and (the first symbol of w is different from the last symbol of w) and (centre (w) is mimsy according to the following two definitions)}. For any string y containing at least 2 symbols, let centre (y) be the substring of y obtained by removing the first symbol and the last symbol of y. A string x over Σ is called mimsy if x is made up of either • at least two 0-symbols (and no 1-symbols), or an even number of 1-symbols (and no 0-symbols).
Let E= {0,1}. Give a regular expression r over Σ such that L(r) = { w in Σ* | (w contains at least 2 symbols, that is, the length of w is at least 2) and (the first symbol of w is different from the last symbol of w) and (centre (w) is mimsy according to the following two definitions)}. For any string y containing at least 2 symbols, let centre (y) be the substring of y obtained by removing the first symbol and the last symbol of y. A string x over Σ is called mimsy if x is made up of either • at least two 0-symbols (and no 1-symbols), or • an even number of 1-symbols (and no 0-symbols).
Recall a set A is countable if |N| ≥ |A|. Recall that Cantor’s theorem shows that P(N) = {X ⊆ N}is uncountable. Prove this.Show that F = {X ⊆ N | |X| < ∞} is countable, with an onto functiong : N → F that is computable. Write a program/function (e.g., in Python) that runs forever and prints every element of F,e.g., if run it would print something like{0}{1}{0,2}{3}{0,2}{0,5,7}{1}{0,1}{}{2}...(Note that you must prove that the program works, i.e., it prints every element of F, and onlyelements of F.)
a) Determine which of the following sets have valid/invalid alphabets:Σ1= {a, ab, b, d, be}Σ2= {a, bc, ce, da} b) Consider Σ= {a, bac, ca, de, f} to find the length of the string s=bacdeacadef by tokenizing. Give its reverse Rev (s).

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Suppose L is a subset of {a, b}". If xo,x1,... is a sequence of distinct strings in {a, b}* such that for every n> 0, xn and xn+1 are L-distinguishable, does it follow that the strings xo, x1,... are pairwise L- distinguishable?