Pls. repharse this notations and concept.Thank you. This is precisely the Nonogram-type description a1, a2, . .., a, for a line (rowor column). Note that it has length 2r + 1 and can also be written as0*1ª o+1®°0+ ...1ªro*.We denote the set of all Nonogram-type descriptions by Dnonogram C D. In thesequel we will concentrate on this type of description.Let s be a finite string over r. If zero or more occurrences of x are replacedwith elements from E, the resulting string is called a specification of s. Aspecification to a string over E (i.e., no longer containing any “x" symbols) iscalled a fir. If a string s has a fix that adheres to a given description d, s iscalled fixable with respect to d. By definition, the boolean function Fiæ(s, d)is true if and only if s is fixable with respect to d. In a somewhat differentcontext, we also use the term fixing a pixel to indicate that a pixel has onlyone possible value, and can therefore be assigned that value.An m x n Nonogram description N consists of m > 0 row descriptionsr1, r2, ...,"m € Dnonogram and n > 0 column descriptions c, C2, . .. , Cn E Dnonogram-A partial filling is an m x n matrix over I. The set of all partial fillings is de-noted by Imxn; its elements can also be considered as strings of length m x n.If a partial filling contains no occurrences of x, it is called a full fix. A full fixF€ Emxn adheres to the Nonogram description N if the ith row of F adheresto r; (for all i = 1,2, ..., m) and the jth column of F adheres to c; (for allj = 1,2, ..., n). We generalize the concepts of specification and fixable thatdefined for single lines in the natural way to mxn Nonograms.|were We now define notation for a single line (i.e., row or column) of a Nonogram.After that, we combine these into rectangular puzzles.Let E be a finite alphabet. Its elements are referred to as pixel values. Inthis paper we focus on the case E = {0, 1}, but most concepts apply to setsconsisting of more than two elements as well. The symbols 0 and 1 representthe white (0) and black (1) pixels in the puzzle. In addition, we introduce aspecial symbol, x ¢ E, indicating that a pixel is not decided yet. Put I' =EU {x}. For l > 0, let E' (resp. I*) denote the set of all strings over E (resp.T) of length l.For describing a Nonogram, we introduce more general concepts of row andcolumn descriptions, such that Nonograms are in fact a special case. Most ofthe concepts in this paper can be applied to all logic problems that follow themore general definitions.A description d of length k > 0 is an ordered series (d, d2, ..., dr) with d; =o;{a,, b;}, where o; e £ and a;, b, € {0, 1, 2, ...} with a; < b; (j = 1,2, ...,k).The curly braces are used here in order to stick to the conventions from regularexpressions; so, in o;{a;, b;} they do not refer to a set, but to an ordered pair.Any such d, will correspond with between a, and b; characters o,, as definedbelow. Without loss of generality we will assume that consecutive characterso; differ, so o; # Oj+1 for j = 1,2, ..., k – 1. Let Dr denote the (infinite) setof all descriptions of length k, and put D = U,Dk, where Do consists of theempty description e. A single d; = o;{a;,b;} is called a segment description.We will sometimes write o* as a shortcut for o{0, } (for o e E) and o+as a shortcut for o{1,00}, where ∞ is suitably large number. We use oª asa shortcut for o{a, a} (a € {0, 1, 2, ...}), and we sometimes omit parenthesesand commas; also oº is omitted.A finite string s over E adheres to a description d (as defined above) if s =of o..o, where a; < c; < b; for j = 1,.,k. As an example, considerthe following description for E = {0, 1}:d = (0{0, 0}, 1{a1, a1}, 0{1, 0}, 1{a2, a2},0{1, 0}, ..., 1{a,, a, }, 0{0, ∞}).

Due to bartleby guidelines and multiple pages i was able to do only single and it is to complex to…

This is precisely the Nonogram-type description a1, a2, ...,a, for a line (row or column). Note that it has length 2r +1 and can also be written as oʻ1ª*o+1®°0+ ...1ªo*. We denote the set of all Nonogram-type descriptions by Daonogran C D. In the sequel we will concentrate on this type of description. Let s be a finite string over I. If zero or more occurrences of x are replaced with elements from E, the resulting string is called a specification of s. A specification to a string over E (i.e., no longer containing any "x" symbols) is called a fir. If a string s has a fix that adheres to a given description d, s is called firable with respect to d. By definition, the boolean function Fir(s,d)

This is precisely the Nonogram-type description a1, a2, ...,a, for a line (row or column). Note that it has length 2r +1 and can also be written as oʻ1ªo+1®°0+ ...1ªo. We denote the set of all Nonogram-type descriptions by Daonogran C D. In the sequel we will concentrate on this type of description. Let s be a finite string over I. If zero or more occurrences of x are replaced with elements from E, the resulting string is called a specification of s. A specification to a string over E (i.e., no longer containing any "x" symbols) is called a fir. If a string s has a fix that adheres to a given description d, s is called firable with respect to d. By definition, the boolean function Fir(s,d)

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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