Regular Canonical Systems
In chapter 4 we have generalized finite automata to a wider class of structures, finite transition systems, and we have extended the run method to extend the notion of behavior. Via subset construction we showed this larger class of structures to still have periodic behavior only. Such results are useful; they provide additional freedom to describe periodic sets, that is, automata behavior. Stated differently, to show that an event is periodic it suffices to show it to be definable by a transition system. We made use of this freedom in section 4.4, to show that regular events are periodic. In this chapter we will find a large extension of finite transition systems to structures we call regular canonical systems. To extend the notion of behavior adequately, we will have to abandon the run idea. Its place will be taken by the notion of a formal deduction (or proof), which plays a central role in modern logic and linguistics.
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