Note that due to the universal quantification a run is represented by a run tree. A accepts a word w, if there exists a run tree on w such that every path ends in an accepting state.
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 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 DNF so that would represent . The state tt (true) is represented by in this case and ff (false) by . This clause representation is usually more efficient.
An alternating finite automaton (AFA) is a 6-tuple, , where
Publication No. WO/2010/018710 Published on Feb. 18, Assigned to NEC for Finite Automaton Generation Device, Pattern Matching Device, Finite Automaton Circuit Generation Method, Program (Japanese Inventor)
Feb 19, 2010; GENEVA, Feb. 23 -- Akihiro Motoki Japan, has developed a finite automaton generating device, pattern matching device, method for...
US Patent Issued to Juniper Networks on March 8 for "Network Attack Detection Using Partial Deterministic Finite Automaton Pattern Matching" (California Inventors)
Mar 09, 2011; ALEXANDRIA, Va., March 9 -- United States Patent no. 7,904,961, issued on March 8, was assigned to Juniper Networks Inc....