The.Algorithm.Design.Manual.Springer-Verlag.1998

Finite State Machine Minimization
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Finite State Machine Minimization
Input description: A deterministic finite automaton M.
Problem description: The smallest deterministic finite automaton M' such that M' behaves identically to
M.
Discussion: Problems associated with constructing and minimizing finite state machines arise repeatedly
in software and hardware design applications. Finite state machines are best thought of as pattern
recognizers, and minimum-size machines correspond to recognizers that require less time and space.
Complicated control systems and compilers are often built using finite state machines to encode the
current state and associated actions, as well as the set of possible transitions to other states. Minimizing
the size of this machine minimizes its cost.
Finite state machines are best thought of as edge-labeled directed graphs, where each vertex represents
one of n states and each edge a transition from one state to the other on receipt of the alphabet symbol
that labels the edge. The automaton above analyzes a given sequence of coin tosses, with the dark states
signifying that an even number of heads have been observed. Automata can be represented using any
graph data structure (see Section ), or by using an transition matrix, where is the size of the
alphabet.
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