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Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to mathematical logic .
Local automata accept the class of local languages, those for which membership of a word in the language is determined by a "sliding window" of length two on the word. [6] [7] A Myhill graph over an alphabet A is a directed graph with vertex set A and subsets of vertices labelled "start" and "finish".
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. It is important in theory because it establishes that NFAs, despite their ...
The finite-state machine has less computational power than some other models of computation such as the Turing machine. [3] The computational power distinction means there are computational tasks that a Turing machine can do but an FSM cannot. This is because an FSM's memory is limited by the number of states it has. A finite-state machine has ...
A simple approach considers the power set of states of the DFA, and builds a directed graph where nodes belong to the power set, and a directed edge describes the action of the transition function. A path from the node of all states to a singleton state shows the existence of a synchronizing word. This algorithm is exponential in the number of ...
Given a set , define = {} (the language consisting only of the empty string), =, and define recursively the set + = {:} for each >. If is a formal language, then , the -th power of the set , is a shorthand for the concatenation of set with itself times.
An ω-language over Σ is said to be recognized by an ω-automaton A (with the same alphabet) if it is the set of all ω-words accepted by A. The expressive power of a class of ω-automata is measured by the class of all ω-languages that can be recognized by some automaton in the class.
For example, the language L p of even-length palindromes on the alphabet of 0 and 1 has the context-free grammar S → 0S0 | 1S1 | ε. If a DPDA for this language exists, and it sees a string 0 n , it must use its stack to memorize the length n , in order to be able to distinguish its possible continuations 0 n 11 0 n ∈ L p and 0 n 11 0 n +2 ...