Nondeterministic finite automatonIn 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. A nondeterministic finite automaton (NFA), or nondeterministic finite-state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is not a DFA, but not in this article.
Alan TuringAlan Mathison Turing (ˈtjʊərɪŋ; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence.
Primitive recursive functionIn computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop can be determined before entering the loop). Primitive recursive functions form a strict subset of those general recursive functions that are also total functions. The importance of primitive recursive functions lies in the fact that most computable functions that are studied in number theory (and more generally in mathematics) are primitive recursive.
Abstract machineIn computer science, an abstract machine is a theoretical model that allows for a detailed and precise analysis of how a computer system functions. It is similar to a mathematical function in that it receives inputs and produces outputs based on predefined rules. Abstract machines vary from literal machines in that they are expected to perform correctly and independently of hardware. Abstract machines are "machines" because they allow step-by-step execution of programmes; they are "abstract" because they ignore many aspects of actual (hardware) machines.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
Halting problemIn computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine.
Computer scientistA computer scientist is a scholar who specializes in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (although there is overlap). Although computer scientists can also focus their work and research on specific areas (such as algorithm and data structure development and design, software engineering, information theory, database theory, computational complexity theory, numerical analysis, programming language theory, computer graphics, and computer vision), their foundation is the theoretical study of computing from which these other fields derive.
Markov algorithmIn theoretical computer science, a Markov algorithm is a string rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete, which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation. Markov algorithms are named after the Soviet mathematician Andrey Markov, Jr. Refal is a programming language based on Markov algorithms.
Nondeterministic algorithmIn computer programming, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm. There are several ways an algorithm may behave differently from run to run. A concurrent algorithm can perform differently on different runs due to a race condition. A probabilistic algorithm's behaviors depends on a random number generator.
Linear bounded automatonIn computer science, a linear bounded automaton (plural linear bounded automata, abbreviated LBA) is a restricted form of Turing machine. A linear bounded automaton is a nondeterministic Turing machine that satisfies the following three conditions: Its input alphabet includes two special symbols, serving as left and right endmarkers. Its transitions may not print other symbols over the endmarkers. Its transitions may neither move to the left of the left endmarker nor to the right of the right endmarker.
