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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.
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 ...
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 ...
The DFA method, like the AEM method, was originally made available in the form of a handbook where the user would enter data on worksheets to obtain a rating for the ease of assembly of a product. Starting in 1981, Geoffrey Boothroyd and Peter Dewhurst developed a computerized version of the DFA method which allowed its implementation in a ...
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 .
At each step of the simulation, the active set of NFA states forms a new DFA state. If the new state is identical to an existing DFA state, it is discarded and replaced with the existing one, and the current branch of simulation terminates. Otherwise the new state is added to the growing set of DFA states and simulation from this state continues.
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
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.
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