R70-36 Maximin Automata

A stationary maximin automaton is a system A = 〈S, U, f, h, F〉, where S and U are finite nonempty sets of states and inputs, respectively; F⊆S is a set of final states; f:S × U × S →[0, 1] can be imagined to be a transition relation which associates with every state s E S and input u E U a measure, 0≤ f(s,u,s´) ≤ 1 that the next state is s´, there being no constraint, for example, that the sum of these measures equals 1 for a given s and u. Similarly, the function h: S → [0, 1] defines something like an initial distribution, again with no constraints on the sum of all of the h(s)´s. What serves to distinguish maximin automata from other better known classes of automata is the manner in which the function f is extended to sequences of inputs x ∈ U*; this is defined as follows: