A new thesis concerning synchronised parallel computing  Simplified parallel ASM thesis
Authors 
Flavio Ferrarotti KlausDieter Schewe Loredana Tec Qing Wang 
Editors 

Title  A new thesis concerning synchronised parallel computing  Simplified parallel ASM thesis 
Booktitle  CoRR  Computing Research Repository, abs/1504.06203 
Type  misc 
Month  April 
Year  2015 
Abstract  A behavioural theory consists of machineindependent postulates characterizing a particular class of algorithms or systems, an abstract machine model that provably satisfies these postulates, and a rigorous proof that any algorithm or system stipulated by the postulates is captured by the abstract machine model. The class of interest in this article is that of synchronous parallel algorithms. For this class a behavioural theory has already been developed by Blass and Gurevich, which unfortunately, though mathematically correct, fails to be convincing, as it is not intuitively clear that the postulates really capture the essence of (synchronous) parallel algorithms. In this article we present a much simpler (and presumably more convincing) set of four postulates for (synchronous) parallel algorithms, which are rather close to those used in Gurevich's celebrated sequential ASM thesis, i.e. the behavioural theory of sequential algorithms. The key difference is made by an extension of the bounded exploration postulate using multiset comprehension terms instead of ground terms formulated over the signature of the states. In addition, all implicit assumptions are made explicit, which amounts to considering states of a parallel algorithm to be represented by metafinite firstorder structures. The article first provides the necessary evidence that the axiomatization presented in this article characterizes indeed the whole class of deterministic, synchronous, parallel algorithms, then formally proves that parallel algorithms are captured by Abstract State Machines (ASMs). The proof requires some recourse to methods from finite model theory, by means of which it can be shown that if a critical tuple defines an update in some update set, then also every other tuple that is logically indistinguishable defines an update in that update set. 