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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.
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 ...
Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression. In particular, a regular language can match constructs like "A follows B", "Either A or B ...
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.
The system uses a DFA for lexical analysis and the LALR algorithm for parsing. Both of these algorithms are state machines that use tables to determine actions. GOLD is designed around the principle of logically separating the process of generating the LALR and DFA parse tables from the actual implementation of the parsing algorithms themselves.
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 ...
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 ...
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.