Generalized Nondeterministic Finite Automaton

Generalized Nondeterministic Finite Automaton

In the theory of computation, a generalized nondeterministic finite automaton (GNFA), also known as expression automaton or generalized nondeterministic finite state machine is a variation of NFA where each transition is labeled with any regular expression. The GNFA reads blocks of symbols from the input which constitute a string as defined by the regular expression on the transition. There are several differences between a standard finite state machine and a generalized nondeterministic finite state machine. A GNFA must have only one start state and one accept state, and these cannot be the same state, whereas a NFA or DFA both may have several accept states, and the start state can be an accept state. A GNFA must have only one transition between any two states, whereas a NFA or DFA both allow for numerous transitions between states. In a GNFA, a state has a single transition to every state in the machine, although often it is a convention to ignore the transitions that are labelled with the empty set when drawing generalized nondeterministic finite state machines.

Read more about Generalized Nondeterministic Finite Automaton:  Formal Definition

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Generalized Nondeterministic Finite Automaton - Formal Definition
5-tuple, (S, Σ, T, s, a), consisting of a finite set of states (S) a finite set called the alphabet (Σ) a transition function (T (S ∖ {a}) × (S ∖ {s}) → R) a start state (s ∈ S) an accept ... This differs from other finite state machines, which take as input a single state and an input from the alphabet (or the empty string in the case of nondeterministic finite state machines) and outputs the ...
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... Nondeterministic algorithms, on the other hand, do not have such specific paths, allowing for the same inputs to result in different outputs ... Deterministic analysis is often considered safer than nondeterministic methods since it explores all possible system states in an exhaustive and thorough way ... Nondeterministic analysis, however, may only explore a subset of the entire state space, and thereby miss some of the possible faults ...
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... Nondeterministic Turing machines have only bounded nondeterminism. 1976 paper on powerdomains Now the set of initial segments of execution sequences of a given nondeterministic program P, starting from a given state, will form a tree ... each choice point, the branching factor of the tree is always finite ...
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