Discrete space for trajectories of diagnostic symptoms

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This report is devoted to design and research of new methods of experiments creation for automata recognition in different automata families. Offered approach to experiments creation problem solving is based on systematization (by geometric tools) of input signals, output signals and automata states changing sequences.
Fundamentally new aspects are is the following implemented ones:
1. Discrete geometric images of finite state machine functioning rules A = (S, X, Y, 5, X), sq e S are built on decomposition
of automata behavior on input sequences with length 1,2,3 … and so on, sequential placing ofthis behavior forms by words length increase. (see fig. 1−3.). Developed:
— discrete dictionary geometry GO with points (p, q), where p eX*, q e Y* and |p| = |q|-
— discrete dictionary geometry G1 with points (p, y), where p eX* and ye Y-
— discrete dictionary geometry G2 with points (p, s), where p e X* and s e S.
Fig. 1. Geometric image y of automatic representation s0
U{(p, Ms0, p))} in geometry Go peX*
Fig. 2. Geometric image y1 of automatic representation
U {(p& gt-prmMs0>- p))}, where m= |p|, in geometry G1 peX*
Fig. 3. Geometric image J of transition function of automata s0
A U{(p, 5(s0,p))}, in geometry G2 *
2. Independent of automata output signals, its states have been given with diagnostic symptoms from set of symptoms
W = {a1,a2,…, ap}using functiony looks like
y: S ^ W. Based on this, states sequence si1'si2'& quot-'-, sik associates with diagnostic symptom sequence (word) y (si1), y (si2y (sik) = P1, p 2,…p k.
Methods of creation of simple unconditional and conditional experiments for automata recognition in different automata families with results interpretation in technical diagnosis are developed. Specific feature of methods is: test patterns are not building in the line of test from mathematic model, but in the line of automata, that are recognizing on this tests, from lack of coincidence of geometric images (that define tests). Trajectory systematization of diagnostic symptoms is used essentially, that correspond to state changing trajectories within functioning of automaton. Diagrams look like graph, in which f — defined paths are marked, where f is function of logical algebra, which has the Post’s property. Function y
looks like y: S ^ {0,1} is defined basing on interpretation of automata as mathematic mode of real technical devices faults.
Basing on classification of differences of geometric images of automata and classification of differences f — definable sequences of diagnostic symptoms, test synthesis procedure variants are considered.
R& amp-I, 2003, Ns 3

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