【摘要】Complex adaptive systems (cas) are systems with a diverse array of agents that adapt and evolve, or learn, as they interact.Markets, biological cells, ecosystems, immune systems, and language communities are familiar examples. Several difficult questions confront us when we try to understand cas: What are typical steps in the formation of communities of interacting agents (such as niches in an ecosystem, metabolic networks in a biological cell, or 'production lines' in an economy)? What kinds of agent interactions promote robustness in the face of shocks (consider the current worldwide 'banking crisis')? What are the mechanisms that yield complex agent hierarchies with sustainable diversity? To answer such questions and improve our ability to steer cas, we must extract the mechanisms that underpin the origin and development of cas agents.

The human immune system provides a clear example of the difficulty of steering a cas. The immune system acts by parsing the surface signals of invading antigens, such as the flu virus. The flu virus continually adapts to the immune system, changing its surface signals so readily that a new flu vaccine must be provided each year, while staphylococcus finds a permanent home in hospitals. To compensate for these changes the immune system provides continually adapting agents -- antibodies -- that co-evolve with the changing boundaries that encapsulate the antigens. As another example, biological cells use a complex hierarchy of semi-permeable membranes to selectively pass certain protein signals that activate different parts of the cell's metabolic network.

In all cas, we can find semi-autonomous bounded compartments that act as agents -- organisms in an ecosystem, organelles in a biological cell, firms in an economy, and so on. The agent boundaries act as conditional filters that pass certain signals and deny others. The conditions that determine passage through a boundary typically look for tags that characterize the incoming signals that are to be admitted (or denied). Tags are exemplified by headers on internet messages, active sites on proteins in a biological cell's metabolic network, and the like. In all cases, we can find an "alphabet" (e.g.amino acids in the case of proteins) for construction of both tags and the boundaries that recognize them. The object then is to develop a "grammar" that determines how the letters of the "alphabet" can be combined to form useful tags. In more mathematical terms, we are looking for a set of generators (the "alphabet") and a set of rules for combining the generators (the "mechanisms"), much as one would proceed to define a finitely-generated mathematical group.

One way to accomplish this task is to provide a general formal language for defining agents. To be relevant for studying cas, the agents must exhibit three levels of activity: (i) performance -- a program or set of rules that determines the agent?s actions under any current situation; (ii) credit assignment -- determination of which performance rules are helpful and which are harmful, and (iii) rule discovery -- provision of plausible new rules for replacing harmful rules. There are rule systems, called classifier systems, that satisfy these requirements.

It is possible to use a generalization of the urn models of probability theory to illustrate the foregoing points. This generalization will be presented and it will be tied to Markov Processes as a way of proving theorems about the interaction of signals and boundaries.