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In computer science and mathematical logic, an infinite-tree automaton is a state machine that deals with infinite tree structures. It can be seen as an extension of top-down finite-tree automata to infinite trees or as an extension of infinite-word automata to infinite trees.
A finite automaton which runs on an infinite tree was first used by Michael Rabin[1] for proving decidability of S2S, the monadic second-order theory with two successors. It has been further observed that tree automata and logical theories are closely connected and it allows decision problems in logic to be reduced into decision problems for automata.
- ^ Rabin, M. O.: Decidability of second order theories and automata on infinite trees,Transactions of the American Mathematical Society, vol. 141, pp. 1–35, 1969.