In algorithmic information theory, the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory.
The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary that are valid according to the language's syntax. The linguist Noam Chomsky theorized that four different classes of formal grammars existed that could generate increasingly complex languages. Each class can also completely generate the language of all inferior classes.
In formal language theory, a context-free language (CFL), also called a Chomsky type-2 language, is a language generated by a context-free grammar (CFG).
In formal language theory, a context-free grammar, G, is said to be in Chomsky normal form if all of its production rules are of the form:
The star height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions of limited star height, i.e. with a limited nesting depth of Kleene stars. Specifically, is a nesting depth of one always sufficient? If not, is there an algorithm to determine how many are required? The problem was first introduced by Eggan in 1963.
Richard Edwin Stearns is an American computer scientist who, with Juris Hartmanis, received the 1993 ACM Turing Award "in recognition of their seminal paper which established the foundations for the field of computational complexity theory". In 1994 he was inducted as a Fellow of the Association for Computing Machinery.
In computer science, computational learning theory is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms.
Ray Solomonoff was an American mathematician who invented algorithmic probability, his General Theory of Inductive Inference, and was a founder of algorithmic information theory. He was an originator of the branch of artificial intelligence based on machine learning, prediction and probability. He circulated the first report on non-semantic machine learning in 1956.
Solomonoff's theory of inductive inference is a mathematical theory of induction introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory.
Tree-adjoining grammar (TAG) is a grammar formalism defined by Aravind Joshi. Tree-adjoining grammars are somewhat similar to context-free grammars, but the elementary unit of rewriting is the tree rather than the symbol. Whereas context-free grammars have rules for rewriting symbols as strings of other symbols, tree-adjoining grammars have rules for rewriting the nodes of trees as other trees.
In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule. A language that only admits ambiguous grammars is called an inherently ambiguous language. Deterministic context-free grammars are always unambiguous, and are an important subclass of unambiguous grammars; there are non-deterministic unambiguous grammars, however.
The generalized star-height problem in formal language theory is the open question whether all regular languages can be expressed using generalized regular expressions with a limited nesting depth of Kleene stars. Here, generalized regular expressions are defined like regular expressions, but they have a built-in complement operator. For a regular language, its generalized star height is defined as the minimum nesting depth of Kleene stars needed in order to describe the language by means of a generalized regular expression, hence the name of the problem.
In formal language theory, a noncontracting grammar is in Kuroda normal form if all production rules are of the form:
Marcel-Paul "Marco" Schützenberger was a French mathematician and Doctor of Medicine. He worked in the fields of formal language, combinatorics, and information theory. In addition to his formal results in mathematics, he was "deeply involved in [a] struggle against the votaries of [neo-]Darwinism", a stance which has resulted in some mixed reactions from his peers and from critics of his stance on evolution. Several notable theorems and objects in mathematics as well as computer science bear his name. Paul Schützenberger was his great-grandfather.
Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects, such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" the relations or inequalities found in information theory. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously."
Indexed languages are a class of formal languages discovered by Alfred Aho; they are described by indexed grammars and can be recognized by nested stack automata.
In formal grammar theory, the deterministic context-free grammars (DCFGs) are a proper subset of the context-free grammars. They are the subset of context-free grammars that can be derived from deterministic pushdown automata, and they generate the deterministic context-free languages. DCFGs are always unambiguous, and are an important subclass of unambiguous CFGs; there are non-deterministic unambiguous CFGs, however.
Dana Angluin is a professor emeritus of computer science at Yale University. She is known for foundational work in computational learning theory and distributed computing.
Giovanni Pighizzini is an Italian theoretical computer scientist known for his work in formal language theory and particularly in state complexity of two-way finite automata. He earned his PhD in 1993 from the University of Milan, where he is a full professor since 2001. Pighizzini serves as the Steering Committee Chair of the annual Descriptional Complexity of Formal Systems academic conference since 2006.
Murray Eden, was an American physical chemist and academic. He was a professor in electrical engineering, a lecturer, a visiting professor and adjunct professor at institutions including at the Massachusetts Institute of Technology and the National Institutes of Health.
