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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 ...
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.
Brzozowski's algorithm for DFA minimization uses the powerset construction, twice. It converts the input DFA into an NFA for the reverse language, by reversing all its arrows and exchanging the roles of initial and accepting states, converts the NFA back into a DFA using the powerset construction, and then repeats its process.
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 ...
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time , e.g. power-law decaying autocorrelation function ) or 1/f noise .
Microsoft Graph (originally known as Microsoft Chart) is an OLE application deployed by Microsoft Office programs such as Excel and Access to create charts and graphs. The program is available as an OLE application object in Visual Basic. Microsoft Graph supports many different types of charts, but its output is dated.
An early application of partition refinement was in an algorithm by Hopcroft (1971) for DFA minimization. In this problem, one is given as input a deterministic finite automaton, and must find an equivalent automaton with as few states as possible. Hopcroft's algorithm maintains a partition of the states of the input automaton into subsets ...
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