Abstract:
######## # ####### # are highly distributed data structures that are used for providing ecient solutions to multiprocessor synchronization problems. Traditionally, balancing networks have been designed to be accessed by ###### # which correspond to ######## # operations. The distribution of tokens on the network's output species the correctness property of the network. However, tokens alone may be inadequate for synchronization problems that require ######## # operations, such as semaphores and critical regions. For such problems, ######### # have been introduced to implement the decrement operation [21]. It has been shown that several kinds of networks that satisfy the ### # ######## # the ######## # ####### # and the ######## # ####### # for tokens alone preserve their properties when antitokens are introduced [2, 5, 21]. Thus, such networks are able to solve synchronization problems that require decrements. A fundamental question that has been left open is to formally characterize all properties of balancing networks that are preserved under the introduction of antitokens. In this work, we provide a simple, combinatorial characterization for all properties warranted by balancing networks which are preserved when antitokens are introduced. This characterization serves as a theoretical tool for identifying the properties that are preserved byantitokens. 2 inputs outputs inputs
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