Editing Alternating Turing machine (section)

=== Informal description ===

The definition of NP uses the ''existential mode'' of computation: if ''any'' choice leads to an accepting state, then the whole computation accepts. The definition of co-NP uses the ''universal mode'' of computation: only if ''all'' choices lead to an accepting state does the whole computation accept. An alternating Turing machine (or to be more precise, the definition of acceptance for such a machine) alternates between these modes.

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.