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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.
Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression. In particular, a regular language can match constructs like "A follows B", "Either A or B ...
Therefore, the length of the regular expression representing the language accepted by M is at most 1 / 3 (4 n+1 (6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size.
The system uses a DFA for lexical analysis and the LALR algorithm for parsing. Both of these algorithms are state machines that use tables to determine actions. GOLD is designed around the principle of logically separating the process of generating the LALR and DFA parse tables from the actual implementation of the parsing algorithms themselves.
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.
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running ...
For example, a paper in 1999 described how JFLAP now allowed one to experiment with construction type proofs, such as converting an NFA to a DFA to a minimal state DFA, and as another example, converting NPDA to CFG and vice versa. [6] In 2002 JFLAP was converted to Swing. In 2005-2007 a study was run with fourteen institutions using JFLAP.
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. DFAs recognize the set of regular languages and no other languages. [1]: 52