Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In automata theory, an alternating finite automaton (AFA) is a nondeterministic finite automaton whose transitions are divided into existential and universal transitions. A basic theorem tells that any AFA is equivalent to an non-deterministic finite automaton (NFA) by performing a similar kind of powerset construction as it is used for the transformation of an NFA to a deterministic finite automaton (DFA). This construction converts an AFA with k states to an NFA with up to 2k states.An alternative model which is frequently used is the one where Boolean combinations are represented as clauses. For instance, one could assume the combinations to be in Disjunctive Normal Form so that {{q1},{q2,q3}} would represent q_1 vee (q_2 wedge q_3). The state tt (true) is represented by {{}} in this case and ff (false) by varnothing. This clause representation is usually more efficient.

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