Abstractions of Finite-State Machines and Immediately-Detectable Output Faults
IEEE Transactions on Computers
SIAM Journal on Computing
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
On a class of optimal abstractions of finite-state machines
Formal Methods in System Design
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
Theories of abstract automata (Prentice-Hall series in automatic computation)
Theories of abstract automata (Prentice-Hall series in automatic computation)
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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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.