Abstract
Zero-one exclusion is a family of distributed tasks indexed by n-bit Boolean signatures b[0], …b[n − 1]. We are interested in asynchronous computations where at most n + 1 asynchronous processes participate. They communicate with one another by reading and writing a shared memory, and halt after choosing a Boolean value. If m < n + 1 processes participate, then they must not all choose the value b[m − 1]. If all n + 1 processes participate, then they must not all choose the same value.
It is easy to show that some instances of zero-one exclusion are computationally difficult, in the sense that they cannot be solved by any algorithm in which asynchronous processes communicate by reading and writing a shared memory. Can we characterize the Boolean signatures for which zero-one exclusion does have an asynchronous read-write algorithm? We give a partial answer, which we feel is interesting because of the way it ties together distributed computability, combinatorial topology, and elementary number theory.
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Gafni, E., Herlihy, M. (2014). Sporadic Solutions to Zero-One Exclusion Tasks. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_1
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DOI: https://doi.org/10.1007/978-3-662-43948-7_1
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