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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.
The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. [3] More precisely, from a regular expression E , the obtained automaton A with the transition function Δ [ clarification needed ] respects the following properties:
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.
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 ...
The set of all strings accepted by an NFA is the language the NFA accepts. This language is a regular language. For every NFA a deterministic finite automaton (DFA) can be found that accepts the same language. Therefore, it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine.
In computer science, a deterministic acyclic finite state automaton (DAFSA), [1] is a data structure that represents a set of strings, and allows for a query operation that tests whether a given string belongs to the set in time proportional to its length.
ij is at most 1 / 3 (4 k+1 (6s+7) - 4) symbols, where s denotes the number of characters in Σ. Therefore, the length of the regular expression representing the language accepted by M is at most 1 / 3 (4 n+1 (6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there ...
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 ...