Generalized information-lossless automata of finite order. II
The notion of generalized information-lossless automaton was introduced elsewhere. The mathematical model for our analysis is a structured weakly-initialized minimal Mealy automaton A = (S, X, Y, {delta}, {lambda}, S{sub 0}), where S is the finite state set, X the finite input alphabet, Y the finite output alphabet, {alpha} and {lambda} are the transition and output functions that define the mappings {delta}: S x X{yields}S, {lambda}: S x X{yields}Y, S{sub 0} is the set of allowed initial states (1 {le} {vert_bar} S{sub 0} {vert_bar} {le} {vert_bar} S {vert_bar}). Each symbol {bar x} {element_of} X is a vector (x{sub 1},...,x{sub n}), i.e., X = X{sub 1} x X{sub 2} x ... x X{sub n}, and each symbol {bar y} {element_of} Y is a vector (y{sub 1},...,y{sub m}), Y = Y{sub 1} x Y{sub 2} x ... x Y{sub m}. Suppose that in input word {bar v} is applied to the automaton A which is in one of the states of the set S{sub 0} (the exact state is not known), and the response {bar w} to this word is observed in output channels j{sub 1} < j{sub 2} < ... < j{sub {mu}}, where 1 {le} j{sub i} {le} m. If an integer N(A) exists for the automaton A such that the protection of the initial section of length N(A) of the word {bar w} is always sufficient for unique determination of the projection of the first symbol of the word {bar v} in input channels i{sub 1} < i{sub 2} < ... < i{sub v}, where 1 {le} i{sub j} {le} n, independently of the input sequence and the initial state of the automaton, then A is called a generalized information-lossless automaton of finite order (GILFO). The ensure single-valued determination of the number N(A), we assume that it is the least number among all possible numbers of this kind for the automaton A. As previously, we assume without loss of generality that the automaton response is observed in the first u output channels 1,2,...,{mu}, and the unknown word is reconstructed for the first v input channels 1,2,...,v.
- OSTI ID:
- 457602
- Journal Information:
- Cybernetics and Systems Analysis, Journal Name: Cybernetics and Systems Analysis Journal Issue: 4 Vol. 30; ISSN CYASEC; ISSN 1060-0396
- Country of Publication:
- United States
- Language:
- English
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