Search results
Results from the WOW.Com Content Network
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 ...
To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via Thompson's construction, powerset construction, and DFA minimization. If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree.
Therefore, it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine. This can be performed using the powerset construction, which may lead to an exponential rise in the number of necessary states. For a formal proof of the powerset construction, please see the Powerset construction article.
An example that can be used to demonstrate the powerset construction reducing NFAs to equivalent DFAs. The corresponding DFA is Image:DFA-powerset-construction-example.svg. Created by Derrick Coetzee in Adobe Illustrator based on the same source as en:Image:NFA-powerset-construction-example.png, which this replaces. Date
An example that can be used to demonstrate the powerset construction reducing NFAs to equivalent DFAs. The corresponding NFA is Image:NFA-powerset-construction-example.svg. Created by Derrick Coetzee in Adobe Illustrator based on the same source as en:Image:DFA-powerset-construction-example.png, which this replaces. Date
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 ...
Given a DFA, the problem of determining if it has a synchronizing word can be solved in polynomial time [2] using a theorem due to Ján Černý. A simple approach considers the power set of states of the DFA, and builds a directed graph where nodes belong to the power set, and a directed edge describes the action of the transition function.
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.