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broker
find
publish
requester
services
provider
services
bind
Fig. 1. The SOA triangle
The above described agents (provider, requester, and broker) may be likewise
virtual. Usually there are no corresponding physical or implemented compo-
nents in an SOA. It is the services themselves, that play the role of providers,
requesters, and even brokers.
3
An Algebraic View on Services
Both, the foundational considerations of Sect. 1 and the applied aspects of Sect. 2
jointly establish principles of services. Here we introduce fundamental notions
and their properties, as a nucleus for a rich conceptualization of “services as a
paradigm of computation”, to blossom in the sequel of this paper.
3.1
Composition of Services and “Reasonable” Services
As outlined in Sect. 2, a core aspect of services is their composition: Any two
services P and R may be composed, resulting in a service P
R
is not always a very reasonable service, given “any” P and R .Inparticular,
P
R .Ofcourse, P
R may deadlock or livelock; sent messages may remain in a buffer forever,
etc. Conceiving P
R as a transition system T with initial and final states,
a typical requirement for P
R to be “reasonable” is weak termination of T :
Each computation s 0 s 1 ...s k starting from an initial state s 0 , can be extended
to a computation s 0 ...s k ...s n with a final state s n . A final state does not
necessarily deadlock; it may just indicate that one “round” of computation is
finished and the service is prepared to launch into a new round. Instead of weak
termination, any other predicate may characterize “reasonable” services. Typical
examples are fair termination or strong termination, i.e. each (fair) computation
eventually will reach a terminal state.
Formulated in an abstract setting, on the set
S
of all services under consid-
eration we assume a binary, symmetrical operator
:
S×S→S
to compose services, and a distinguished predicate
τ
⊆S
 
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