<p>Traditional models of computation on finite strings can accept strings or produce a result of a computation. However, when a computation continues for an indefinite (infinite) period a different model of computation is needed. Büchi automata provide such a model of computation. Büchi automata are finite automata operating on infinite strings. A computation is successful (or accepted) by a Büchi automaton if, given a set of favorable states, a favorable state (or states) occur(s) infinitely often. However, there is no accounting for non-favorable states also occurring infinitely often. Hence, the meaning of a successful computation of Büchi automata can have lower than acceptable accuracy. In this paper, the new paradigm of the infinite unit axiom and grossone are applied to extend the computational accuracy of Büchi automata and leads to a more accurate meaning of a successful computation on an infinite string.</p>