Automaton theory psychology11/18/2023 Context-free grammars specify programming language syntax. Another formalism mathematically equivalent to regular expressions, Finite automata are used in circuit design and in some kinds of problem-solving. Regular expressions, for example, specify string patterns in many contexts, from office productivity software to programming languages. In addition to the general computational models, some simpler computational models are useful for special, restricted applications. a sequence, or a matrix etc.) by an appropriate huge natural number - unambiguity of both representation and interpretation can be established by number theoretical foundations of these techniques. ![]() The lack of the infinite (or dynamically growing) external store (seen at Turing machines) can be understood by replacing its role with Gödel numbering techniques: the fact that each register holds a natural number allows the possibility of representing a complicated thing (e.g. ![]() only decrementation (combined with conditional jump) and incrementation exist (and halting). In most of them, each register can hold a natural number (of unlimited size), and the instructions are simple (and few in number), e.g. Register machine is a theoretically interesting idealization of a computer. Markov algorithm a string rewriting system that uses grammar-like rules to operate on strings of symbols. The computation terminates only if the final term gives the value of the recursive function applied to the inputs. Some pioneers of the theory of computation were Ramon Llull, Alonzo Church, Kurt Gödel, Alan Turing, Stephen Kleene, Rózsa Péter, John von Neumann and Claude Shannon.īranches Automata theory In the last century, it became an independent academic discipline and was separated from mathematics. Therefore, mathematics and logic are used. The theory of computation can be considered the creation of models of all kinds in the field of computer science. So in principle, any problem that can be solved (decided) by a Turing machine can be solved by a computer that has a finite amount of memory. ![]() It might seem that the potentially infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" model of computation (see Church–Turing thesis). There are several models in use, but the most commonly examined is the Turing machine. ![]() In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?". In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). Turing machines are frequently used as theoretical models for computing. An artistic representation of a Turing machine. For the journal, see Theory of Computing.
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