Computation Over Abstract Structures: Serial and Parallel Procedures and Friedman's Effective Definitional Schemes

Abstract A general form of parallel procedure is defined for computation over abstract relational structures. These procedures are compared over both total and partial structures with Friedman's effective definitional schemes [12]. Various kinds of serial procedure are considered, also conditions under which parallel procedures are equivalent to serial (e.g. over total structures). Comparisons are made with the classical theory of partial recursive functionals with partial functions as arguments. The effects of different assumptions about the times taken by processors are explored, also the effect of asynchronous operation.

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