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autonomy, adaptability, knowledge, mobility, collaboration, and persistence. These features exist in
different types of agent systems such as collaborative agents, interface agents, reactive agents, mobile
agents, information agents, heterogeneous agents, and economic agents. The concurrency and automa-
tion of agents require that the modeling language does not have any sequential bias and global control
structure. In addition, the dynamic nature and non-determinism of interaction between an agent and its
environment are suited to a computation model with a loose mechanism for specifying the underlying
data structure. For example, data, which move around the Internet, can be well modeled by chemical
solution; and mobile agents, which are created dynamically and transferred from clients to servers, can
be represented as molecules containing γ-abstractions that transfer among solutions. This provides a
mechanism for describing inter-agent communications and agent migration in a single framework. It
is worthwhile to note that CRM specifications separate architectures from nonessential features of the
system effectively. For example, it catches the way program units interact with one another and leaves
nonessential specifications, such as the number of program units, connection links for communications,
and organizations of data, to the subsequent design phases.
We refer the readers to (Lin, 2004) and (Lin & Yang, 2006) for detailed justifications for the appro-
priateness of using the CRM to model MAS. Here we give the summary of our findings. The benefits
of using the CRM to model MAS include: (1) The architectural design of the system can be separated
from the design of individual units that have to deal with proprietary features of the underlying com-
puting resources, because CRM allows us to treat each node in the distributed networking systems
as an element of a multi-set data structure, which in-turn can be an active program to be defined in
a lower level of the program structure. (2) Parallelism can be easily achieved without extra efforts in
designing communication and synchronization mechanism because CRM express them implicitly. (3)
Concurrency and dynamic nature of MAS can be easily reflected by CRM's non-determinism feature.
(4) Autonomy can be expressed naturally by CRM's locality of reaction feature. (5) It provides a frame-
work for combining different programming technologies because no assumptions are made about the
way for implementing each node in the system hierarchy. (6) The reusability of the agent systems can
be promoted by higher-order CRM languages because the existing agents can be combined by using
higher-order operations defined in those languages.
Progra M synthesis for gaMMa
A barrier to make an automatic software design system practical is that there is no a straightforward
way to bridge descriptive specifications and operational ones. For example, first-order logic formulas,
unless in some elaborately arranged recursive forms (e.g., as those studied in learning systems (Shapiro,
1981)), is hard to be mapped to programs directly.
In Gamma language, the classical method proposed by Banatre and Le Metayer (1990) is to de-
compose the specification into an invariant and a termination condition. The program is synthesized
by deduction to meet the termination condition while keeping the invariant satisfied. The program is
designed under the guidance of the invariant and the variant rather than derived out directly from the
specification. And much skill is need in figuring out the invariant and variant.
We propose a method for constructing programs from first-order specifications (Lin & Chen, 1998).
The method constructs a semantic verification program for a specification. Few syntactic derivations are
needed in constructing the program. In addition, the target programs, which are in Gamma language, are
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