For a transition , A nondeterministically chooses to switch the state to either q1 or q2, reading a.
For a transition , A moves to q1andq2, reading a.
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 a NFA to a deterministic finite automaton (DFA). This construction converts an AFA with k states to a NFA with up to 2k states.
The alternating group on the set {1,...,n} is called the alternating group of degree n, or the alternating group on n letters and denoted by A
For instance: {1234, 1342, 1423, 2143, 2314, 2431, 3124, 3241, 3412, 4132, 4213, 4321} is the alternating group of degree 4.
The word "isomorphism" applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where "corresponding" means that the two parts play similar roles in their respective structures.
A finite state machine (FSM) or finite state automaton (FSA) is an abstract machine used in the study of computation and languages that has only a finite, constant amount of memory (the state).
Alternating automata also provide a dual notion, where for acceptance all nondeterministic computations must accept.
Formally, a deterministic finite automaton (DFA) consists of an alphabet (Σ), a set of states (S), one of which is chosen as a start state and zero or more as accepting states, and a transition function (T : S × Σ -> S).
, A nondeterministically chooses to switch the state to either 
, A moves to 
Feeds |
Contact