Computing functions on asynchronous anonymous networks

In an “anonymous” network the processors have no identity numbers. We investigate the problem of computing a given functionf on an asynchronous anonymous network in the sense that each processor computesf(I) for any inputI = (I(v1),...,I(vn)), whereI(vi) is the input to processorvi,i = 1, 2,...,n. We address the following three questions: (1) What functions are computable on a given network? (2) Is there a “universal” algorithm which, given any networkG and any functionf computable onG as inputs, computesf onG? (3) How can one find lower bounds on the message complexity of computing various functions on anonymous networks?

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