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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 ...
whether the language recognized by a DFA is included in the language recognized by a second DFA (Inclusion Problem) the DFA with a minimum number of states for a particular regular language (Minimization Problem) DFAs are equivalent in computing power to nondeterministic finite automata (NFAs). This is because, firstly any DFA is also an NFA ...
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 set of all strings accepted by an NFA is the language the NFA accepts. This language is a regular language. For every NFA a deterministic finite automaton (DFA) can be found that accepts the same language. Therefore, it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine.
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.
By definition, the languages accepted by acceptors are the regular languages. The problem of determining the language accepted by a given acceptor is an instance of the algebraic path problem—itself a generalization of the shortest path problem to graphs with edges weighted by the elements of an (arbitrary) semiring. [9] [10] [jargon]
In computer science, a deterministic automaton is a concept of automata theory where the outcome of a transition from one state to another is determined by the input. [1]: 41
TDFA minimization is very similar to DFA minimization, except for one additional restriction: register actions on TDFA transitions must be taken into account. So, TDFA states that are identical, but have different register actions on incoming transitions on the same symbol, cannot be merged.