  A behavioural theory consists of machine-independent 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 meta-finite
first-order 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.
