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A DFA is defined as an abstract mathematical concept, but is often implemented in hardware and software for solving various specific problems such as lexical analysis and pattern matching. For example, a DFA can model software that decides whether or not online user input such as email addresses are syntactically valid. [4]
Example DFA. If in state , it exhibits the ... DFA minimization is the task of transforming a given deterministic finite automaton (DFA) ...
Because the DFA states consist of sets of NFA states, an n-state NFA may be converted to a DFA with at most 2 n states. [2] For every n, there exist n-state NFAs such that every subset of states is reachable from the initial subset, so that the converted DFA has exactly 2 n states, giving Θ(2 n) worst-case time complexity.
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 ...
A common deterministic automaton is a deterministic finite automaton (DFA) which is a finite state machine, where for each pair of state and input symbol there is one and only one transition to a next state.
For example, in 1981, Sidney Liebson, manager of manufacturing engineering for Xerox, estimated that his company would save hundreds of millions of dollars through the application of DFA. [3] In 1988, Ford Motor Company credited the software with overall savings approaching $1 billion. [ 4 ]
A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value ...
In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is not a DFA, but not in this article. Using the subset construction algorithm, each NFA can be translated to an equivalent DFA; i.e., a DFA recognizing the same formal language. [1] Like DFAs, NFAs only recognize regular languages.