What Is an Abstractor?

An abstract automaton is an abstract device capable of recognizing language. It is not a machine with physical entities, but an abstract logical relationship system representing the computing methods of the computer. Such an abstract automaton can be used to check whether the input symbol string is a language. Passing sentence: If it is a qualified sentence, the automaton will accept it, if not, it will not accept it. In mathematical linguistics, the theory that studies abstract automata is called automata theory ^[1] .

An abstract automaton is an abstract device capable of recognizing language. It is not a machine with physical entities, but an abstract logical relationship system representing the computing methods of the computer. Such an abstract automaton can be used to check whether the input string of symbols is A qualified sentence in the language, if it is a qualified sentence, the automaton will accept it, if not, it will not accept it, as shown in the figure:

Automata can be divided into

Automaton theory is a mathematical theory about the function, structure and relationship between automaton. An automaton is a mathematical concept. It is an abstract model of a discrete digital system. The discrete digital system referred to here is a dynamic system. Its variables are digital and time is discrete. For example, digital circuits and algorithms are two typical discrete digital systems. The main research topics of automata theory are analysis and synthesis: give a specific automaton structure and analyze its function; give a functional description of automaton and synthesize the structure of automaton that can realize this function.

Automata theory is an earlier part of theoretical computer science. As early as 1850, British Boole (G.Boole) established logical algebra when studying mathematical problems with mathematical methods. In 1948, American Hungarian mathematician J. von Neumann proposed the general logic theory of establishing automata. In the 1950s, on the basis of switch network theory and Turing machine theory in mathematical logic, the branch of mathematics, the automaton theory, was formed. Since the 1950s, the theory of automata has developed deeply and been widely used. The theory of automata can be roughly divided into the following five sub-disciplines:

1. Finite automaton theory: The main research objects are automata with limited storage such as switch networks, digital circuits, and computers;

2. Infinite automata theory: The main research object is automata with unlimited storage such as algorithms and ideal computers;

3. Probabilistic automata theory: The main research object is automata with random factors in the environment or inside;

4. Cellular automata theory: The main research object is a large automaton formed by the parallel operation of many interconnected small automata;

5. Abstract automaton theory: Use automaton as a mathematical system to study the general mathematical properties of automaton.

Automata theory is related to mathematical branches such as mathematical logic, computability theory, computational complexity theory, formal language theory, and cybernetics, especially it is closely related to formal language theory. On the one hand, automata is used as a main description method of formal language, on the other hand, formal grammar can also be used as a description method of automata recognition set. Automata theory has been widely used in the fields of automatic control, computer and digital communication ^[2] .

American linguist N. Chomsky and others established a connection between formal grammar and automata, and proved that there is a correspondence between formal grammar and automata of language: If a language can use Turing To recognize, it can be generated using O-grams, and vice versa; if a language can be recognized using a linear bounded automaton, it can be generated using context-sensitive grammars, and vice versa; Language can be identified by last-in, first-out automaton, then it can be generated by context free grammar, and vice versa; If a language can be identified by finite automaton, it can be generated by finite state grammar and vice versa Of course.

This relationship between formal grammar and automata. Reflecting the internal connection between language generation and recognition, it has become one of the cornerstones of computer science, which is a clear proof of the impact of linguistics on modern natural sciences ^[3] .