# Automaton Theory and Modeling of Biological Systems by M.L. Tsetlin (Eds.)

By M.L. Tsetlin (Eds.)

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28) Finite Automata and Modeling the Simplest Forms of Behavior 29 The coefficients A , B, C, D, in ( 2 8 ) are found from the equations for R, and R,,, in the system (23). Then we find the expressions for Rk = (ri*),r i 2 ) ) for k = I , 2,. . , n: I n these expressions d is the normalization constant, and x is either root of the quadratic equation (27). The expressions for R l l f k= rj&, rAyk) are found from the equalities Upon using Eq. (21), we arrive at the following expression for the expectation value of a nonpenalty for an automaton with a linear tactic, L,,,,2,in the composite medium K , specified by formulas ( 2 2 ) and ( 2 2 ' ) : W(L,n,,* K ) =(A - 1)2 { 2 n s / ( l - 26)}(A where cash y = + I), cash - 1 cosh ny (A + ( 1 - A ) Z ~1 -s 2A 1 - 26 - coth y / 2 sinh ny' (32) I.

33) In these formulas 0 5 g< 1 ; it is not hard to check that the matrix remains stochastic. The behavior of automata with an evolving structure in random media can be described by a nonhomogeneous Markov chain. For automata whose structures evolve as described by Eqs. (33), there exist stationary values of the transition probabilities, and one can speak of the final probabilities of the states of the system. , the simplest automaton with an evolving structure having only two states is equivalent to an automaton with a linear tactic having an infinite number of states.

In the final part of this section we shall give an example of a system whose functioning is largely similar to the behavior of automata in stationary random media and possesses a naturally defined expediency. Suppose there are n books K , , K2,. . , K,, lying in a stack on a desk. The books in the stack may be used in various ways-for example, one can choose the desired book and put it back in the same location after use. It is, however, often preferred not to search for the original location of the book chosen, but to simply put it on top of the stack.