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An Introduction to the Theory of Computation, Chapter 4, Post's Correspondence Problem. A proof of the undecidability of PCP based on Chomsky type-0 grammars. Dong, Jing. "The Analysis and Solution of a PCP Instance." 2012 National Conference on Information Technology and Computer Science.
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 ...
In theoretical computer science, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory , computability theory and computational complexity theory .
Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: [1]
Martin Davis makes a persuasive argument that Turing's conception of what is now known as "the stored-program computer", of placing the "action table"—the instructions for the machine—in the same "memory" as the input data, strongly influenced John von Neumann's conception of the first American discrete-symbol (as opposed to analog) computer—the EDVAC.
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. [1]
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability.
Giunti calls the models studied by computation theory computational systems, and he argues that all of them are mathematical dynamical systems with discrete time and discrete state space. [ 13 ] : ch.1 He maintains that a computational system is a complex object which consists of three parts.