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Automata theory is closely related to formal language theory. In this context, automata are used as finite representations of formal languages that may be infinite. Automata are often classified by the class of formal languages they can recognize, as in the Chomsky hierarchy, which describes a nesting relationship between major classes of automata.
Finite-state machines are a class of automata studied in automata theory and the theory of computation. In computer science, finite-state machines are widely used in modeling of application behavior (control theory), design of hardware digital systems, software engineering, compilers, network protocols, and computational linguistics.
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and; reading an input symbol is required for each state transition.
Further, clocks can be reset. Timed automata are a sub-class of a type hybrid automata. Timed automata can be used to model and analyse the timing behavior of computer systems, e.g., real-time systems or networks. Methods for checking both safety and liveness properties have been developed and intensively studied over the last 20 years.
Automata-based programming is a programming paradigm in which the program or part of it is thought of as a model of a finite-state machine (FSM) or any other (often more complicated) formal automaton (see automata theory). Sometimes a potentially infinite set of possible states is introduced, and such a set can have a complicated structure, not ...
In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, [1] is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). [2] This NFA can be used to match strings against the regular expression. This algorithm is credited to Ken Thompson.
The theory of computation can be considered the creation of models of all kinds in the field of computer science. Therefore, mathematics and logic are used. In the last century, it separated from mathematics and became an independent academic discipline with its own conferences such as FOCS in 1960 and STOC in 1969, and its own awards such as the IMU Abacus Medal (established in 1981 as the ...
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 ...