# Deterministic Computations Whose History Is Independent of the Order of Asynchronous Updating

## OpenBU

 dc.contributor.author Gacs, Peter en_US dc.date.accessioned 2011-10-20T04:32:21Z dc.date.available 2011-10-20T04:32:21Z dc.date.issued 1995-11-18 en_US dc.identifier.uri http://hdl.handle.net/2144/1577 dc.description.abstract Consider a network of processors (sites) in which each site x has a finite set N(x) of neighbors. There is a transition function f that for each site x computes the next state ξ(x) from the states in N(x). But these transitions (updates) are applied in arbitrary order, one or many at a time. If the state of site x at time t is η(x; t) then let us define the sequence ζ(x; 0); ζ(x; 1), ... by taking the sequence η(x; 0),η(x; 1), ... , and deleting each repetition, i.e. each element equal to the preceding one. The function f is said to have invariant histories if the sequence ζ(x; i), (while it lasts, in case it is finite) depends only on the initial configuration, not on the order of updates. This paper shows that though the invariant history property is typically undecidable, there is a useful simple sufficient condition, called commutativity: For any configuration, for any pair x; y of neighbors, if the updating would change both ξ(x) and ξ(y) then the result of updating first x and then y is the same as the result of doing this in the reverse order. This fact is derivable from known results on the confluence of term-rewriting systems but the self-contained proof given here may be justifiable. en_US dc.description.sponsorship National Science Foundation (CCR-920484) en_US dc.language.iso en_US en_US dc.publisher Boston University Computer Science Department en_US dc.relation.ispartofseries BUCS Technical Reports;BUCS-TR-1995-018 en_US dc.title Deterministic Computations Whose History Is Independent of the Order of Asynchronous Updating en_US dc.type Technical Report en_US