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  2. File:DFA example multiplies of 3.svg - Wikipedia

    en.wikipedia.org/wiki/File:DFA_example...

    English: Example of a DFA that accepts binary numbers that are multiples of 3. Čeština: Příklad deterministického konečného automatu , který přijímá binární čísla, která jsou beze zbytku dělitelná třemi.

  3. Deterministic finite automaton - Wikipedia

    en.wikipedia.org/wiki/Deterministic_finite_automaton

    An example of a deterministic finite automaton that accepts only binary numbers that are multiples of 3. The state S 0 is both the start state and an accept state. For example, the string "1001" leads to the state sequence S 0, S 1, S 2, S 1, S 0, and is hence accepted.

  4. Finite-state machine - Wikipedia

    en.wikipedia.org/wiki/Finite-state_machine

    An example of an accepting state appears in Fig. 5: a deterministic finite automaton (DFA) that detects whether the binary input string contains an even number of 0s. S 1 (which is also the start state) indicates the state at which an even number of 0s has been input. S 1 is therefore an accepting state. This acceptor will finish in an accept ...

  5. Thompson's construction - Wikipedia

    en.wikipedia.org/wiki/Thompson's_construction

    Generating an NFA by Thompson's construction, and using an appropriate algorithm to simulate it, it is possible to create pattern-matching software with performance that is ⁠ ⁠, where m is the length of the regular expression and n is the length of the string being matched.

  6. Powerset construction - Wikipedia

    en.wikipedia.org/wiki/Powerset_construction

    A state S of the DFA is an accepting state if and only if at least one member of S is an accepting state of the NFA. [2] [3] In the simplest version of the powerset construction, the set of all states of the DFA is the powerset of Q, the set of all possible subsets of Q. However, many states of the resulting DFA may be useless as they may be ...

  7. Regular expression - Wikipedia

    en.wikipedia.org/wiki/Regular_expression

    The DFA can be constructed explicitly and then run on the resulting input string one symbol at a time. Constructing the DFA for a regular expression of size m has the time and memory cost of O (2 m ), but it can be run on a string of size n in time O ( n ).

  8. Finite-state transducer - Wikipedia

    en.wikipedia.org/wiki/Finite-state_transducer

    Each string-to-string finite-state transducer relates the input alphabet Σ to the output alphabet Γ. Relations R on Σ*×Γ* that can be implemented as finite-state transducers are called rational relations. Rational relations that are partial functions, i.e. that relate every input string from Σ* to at most one Γ*, are called rational ...

  9. DFA minimization - Wikipedia

    en.wikipedia.org/wiki/DFA_minimization

    The state of a deterministic finite automaton = (,,,,) is unreachable if no string in exists for which = (,).In this definition, is the set of states, is the set of input symbols, is the transition function (mapping a state and an input symbol to a set of states), is its extension to strings (also known as extended transition function), is the initial state, and is the set of accepting (also ...