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In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this ...
DFAs have been generalized to nondeterministic finite automata (NFA) which may have several arrows of the same label starting from a state. Using the powerset construction method, every NFA can be translated to a DFA that recognizes the same language. DFAs, and NFAs as well, recognize exactly the set of regular languages. [1]
In the theory of computation and automata theory, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) which recognizes the same formal language.
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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.
Like DFAs, NFAs only recognize regular languages. NFAs were introduced in 1959 by Michael O. Rabin and Dana Scott , [ 2 ] who also showed their equivalence to DFAs. NFAs are used in the implementation of regular expressions : Thompson's construction is an algorithm for compiling a regular expression to an NFA that can efficiently perform ...
Let be the set of words over the alphabet {a,b} whose nth last letter is an .The figures show a DFA and a UFA accepting this language for n=2.. Deterministic automaton (DFA) for the language L for n=2 Unambiguous finite automaton (UFA) for the language L for n=2
This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size. [ 6 ] In practice, the size of the regular expression obtained by running the algorithm can be very different depending on the order in which the states are considered by the procedure, i.e., the ...