In computer science, mutual exclusion refers to the requirement of ensuring that no two concurrentprocesses are in their critical section at the same time; it is a basic requirement in concurrency control, to prevent race conditions. Here, a critical section refers to a period when the process accesses a shared resource, such as shared memory. The requirement of mutual exclusion was first identified and solved by Edsger W. Dijkstra in his seminal 1965 paper titled Solution of a problem in concurrent programming control, and is credited as the first topic in the study of concurrent algorithms.
A simple example of why mutual exclusion is important in practice can be visualized using a singly linked list (See Figure 1). In such a linked list, the removal of a node is done by changing the "next" pointer of the preceding node to point to the subsequent node (e.g., if node i is being removed then the "next" pointer of node i − 1 will be changed to point to node i + 1). In an execution where such a linked list is being shared between multiple processes, two processes may attempt to remove two different nodes simultaneously, resulting in the following problem: let nodes i and i + 1 be the nodes to be removed; furthermore, let neither of them be the head nor the tail; the next pointer of node i − 1 will be changed to point to node i + 1 and the next pointer of node i will be changed to point to node i + 2. Although both removal operations complete successfully, node i + 1 remains in the list since i − 1 was made to point to i + 1, skipping node i (which was the node that reflected the removal of i + 1 by having its next pointer set to i + 2). This can be seen in Figure 1. This problem (normally called a race condition) can be avoided by using the requirement of mutual exclusion to ensure that simultaneous updates to the same part of the list cannot occur.
In logic and probability theory, two propositions (or events) are mutually exclusive or disjoint if they cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.
In the coin-tossing example, both outcomes are, in theory, jointly exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (both cannot happen at the same time) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6).
Logic
In logic, two mutually exclusive propositions are propositions that logically cannot be true in the same sense at the same time. To say that more than two propositions are mutually exclusive, depending on context, means that one cannot be true if the other one is true, or at least one of them cannot be true. The term pairwise mutually exclusive always means that two of them cannot be true simultaneously.
It is also evident that economic ties with China and the US do not have to be mutually exclusive ... China and Australia should therefore enhance mutual understanding and trust to promote common development through mutually beneficial cooperation.
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It's the witching hour in Salem. Democrats in the Massachusetts city are vowing to producer a challenger to Rep ... Pictured ... Pictured ... These two ideas are not mutually exclusive, and we can even disagree on them ... New York TimesDemocratsMassachusetts. .
South Carolina officials announced today that a new "Recycle Here SC" app is available to help state residents access recycling tips from their phones ...Lt. Gov ... Evette said she believes sustainability and profitability are "not mutually exclusive.".
Eric Schmidt told an audience ... Schmidt later retracted his statement, claiming he “misspoke” ... Socially beneficial intelligence ... And technological progress and social progress are not mutually exclusive. In fact, they can be mutually strengthening ... .
Ty B. Kerley. DMin... Or so it would seem. Drs. Newburg and D’Aquili eventually reached a point in their research where science could take them no further saying; “we were left with two mutually exclusive possibilities ... And THAT is Why God Won’t Go Away ... ....
... for other timeless hits of his including “With You” and “Take You Down” from 2007’s Exclusive ... These two things are not mutually exclusive,” she wrote.
Rep.Seth Moulton (D-Mass.) doubled down on his recent comments about transgender athletes, saying the response to them proves his point... These two ideas are not mutually exclusive, and we can even disagree on them.”.
“It’s interesting because traditionally for Black women, there's been this sense that there are certain hardships that they have encountered [and therefore] marriage and education have been seen as being mutually exclusive.” ...
Lockhart Post-Register
13 Nov 2024
Lockhart Post-Register
13 Nov 2024