Abstractions of random finite-state machines
Suppose that M is a large complex finite-state system (fsm), and we want to construct a smaller model of it. A way of doing so, independent of any special properties that M might have, is to partition its states, inputs, and outputs into classes, collectively referred to as an abstraction. Since abstractions map many fsms into a non-deterministic machine defining an indistinguishability class, given a particular M, an optimal abstraction will minimize the size of this class. Algorithms for constructing such abstractions have been investigated in previous work. In this paper we are interested in large fsms generated by some random procedure, and want to find abstractions that minimize the expected size of an indistinguishability class. We establish various theoretical properties of abstractions optimal in an average sense, and also investigate experimentally how their characteristics change with the parameters governing the structure of the random machines.
abstraction random finite-state machine non-deterministic indistinguishability expected