An alternating Turing machine is a non-deterministic Turing machine whose states are divided into two sets: existential states and universal states. An existential state is accepting if some transition leads to an accepting state; a universal state is accepting if every transition leads to an accepting state. (Thus a universal state with no transitions accepts unconditionally; an existential state with no transitions rejects unconditionally). The machine as a whole accepts if the initial state is accepting.
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“The machine has had a pernicious effect upon virtue, pity, and love, and young men used to machines which induce inertia, and fear, are near impotents.”
—Edward Dahlberg (1900–1977)