Answer the following question: Information: - Theoretical computer science, or TCS, is a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects of computing and includes the theory of computation. - Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems. - In mathematics and computer science, an algorithm is a self-contained sequence of actions to be performed. Algorithms perform calculation, data processing, and/or automated reasoning tasks. - A calculation is a deliberate process that transforms one or more inputs into one or more results, with variable change. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people. - Automated reasoning is an area of computer science and mathematical logic dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science, and even philosophy. - In theoretical computer science, more precisely in the theory of formal languages, the star height is a measure for the structural complexity of regular expressions: The star height equals the maximum nesting depth of stars appearing in the regular expression. The concept of star height was first defined and studied by Eggan (1963). - Data processing is, generally, "the collection and manipulation of items of data to produce meaningful information." In this sense it can be considered a subset of "information processing", "the change (processing) of information in any manner detectable by an observer." The term Data processing (DP) has also been used previously to refer to a department within an organization responsible for the operation of data processing applications. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - 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 raised by Eggan ( 1963 ) . - In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element. Monoids are studied in semigroup theory as they are semigroups with identity. Monoids occur in several branches of mathematics; for instance, they can be regarded as categories with a single object. Thus, they capture the idea of function composition within a set. In fact, all functions from a set into itself form naturally a monoid with respect to function composition. Monoids are also commonly used in computer science, both in its foundational aspects and in practical programming. The set of strings built from a given set of characters is a free monoid. The transition monoid and syntactic monoid are used in describing finite state machines, whereas trace monoids and history monoids provide a foundation for process calculi and concurrent computing. Some of the more important results in the study of monoids are the KrohnRhodes theorem and the star height problem. The history of monoids, as well as a discussion of additional general properties, are found in the article on semigroups. - In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics it is more commonly known as the free monoid construction. The application of the Kleene star to a set "V" is written as "V". It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterise certain automata, where it means "zero or more". Given the paragraphs above, decide what entity has the relation 'instance of' with 'theorem'.
Answer:
star height problem