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In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and; reading an input symbol is required for each state transition.
An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types—deterministic finite-state machines and non-deterministic finite-state machines. [2] For any non-deterministic finite-state machine, an equivalent deterministic one can be constructed.
The probabilistic automaton may be defined as an extension of a nondeterministic finite automaton (,,,,), together with two probabilities: the probability of a particular state transition taking place, and with the initial state replaced by a stochastic vector giving the probability of the automaton being in a given initial state.
In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) which recognizes the same formal language. It is important in theory because it establishes that NFAs, despite their ...
In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages. On the one hand, an NFA can be exponentially ...
A deterministic finite automaton without accept states and without a starting state is known as a transition system or semiautomaton. For more comprehensive introduction of the formal definition see automata theory .
The obtained automaton is non-deterministic, and it has as many states as the number of letters of the regular expression, plus one. Furthermore, it has been shown [3]: 215 [4] that Glushkov's automaton is the same as Thompson's automaton when the ε-transitions are removed.
In the theory of computation, a generalized nondeterministic finite automaton (GNFA), also known as an expression automaton or a generalized nondeterministic finite state machine, is a variation of a nondeterministic finite automaton (NFA) where each transition is labeled with any regular expression. The GNFA reads blocks of symbols from the ...