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Process Algebra as Abstract Data Types
In this paper we introduced an algebraic semantics for process algebra in
form of abstract data types. For that purpose, we developed a particular type
of algebra, the seed algebra, which describes exactly the behavior of a process
within a labeled transition system. We have shown the possibility of
characterizing the bisimulation of two processes with the isomorphism of their
corresponding seed algebras. We pointed out that the traditional concept of
isomorphism of algebra does not apply here, because there is even no one-one
correspondence between the elements of two seed algebras. The lack of this
one-one correspondence comes from the non-deterministic choice of transitions
of a process. We introduce a technique of hidden operations to mask unwanted
details of elements of a seed algebra, which only reflect non-determinism or
other implicit control mechanism of process transition. Elements of a seed
algebra are considered as indistinguishable if they show the same behavior
after these unwanted details are masked. Each class of indistinguishable
elements is called a non-hidden closure. We proved that bisimulation of two
processes is equivalent to isomorphism of non-hidden closures of two seed
algebras representing these two processes. We call this kind of isomorphism a
deep isomorphism. We get different models of seed algebra by specifying
different axiom systems for the same signature. Each model corresponds to a
different kind of bisimulation. By proving the relations between these models
we also established relations between 10 different bisimulations, which form a
acyclic directed graph.Comment: 74page