|
Query (complexity)
In descriptive complexity, a query is a mapping from structures of one signature to structures of another vocabulary. Neil Immerman, in his book Descriptive Complexity, "use the concept of query as the fundamental paradigm of computation" (p. 17). Given signatures \sigma and \tau, we define the set of structures on each language, \mboxsigma/math> and \mboxtau/math>. A query is then any mapping I : \mboxsigma\to \mboxtau/math> Computational complexity theory In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by ... can then be phrased in terms of the power of the mathematical logic necessary to express a given query. Order-independent queries A query is order-independent if the ordering of objects in the structure does not affect the results of the query. In databases, these queri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Descriptive Complexity
''Descriptive Complexity'' is a book in mathematical logic and computational complexity theory by Neil Immerman. It concerns descriptive complexity theory, an area in which the expressibility of mathematical properties using different types of logic is shown to be equivalent to their computability in different types of resource-bounded models of computation. It was published in 1999 by Springer-Verlag in their book series Graduate Texts in Computer Science. Topics The book has 15 chapters, roughly grouped into five chapters on first-order logic, three on second-order logic, and seven independent chapters on advanced topics. The first two chapters provide background material in first-order logic (including first-order arithmetic, the BIT predicate, and the notion of a first-order query) and complexity theory (including formal languages, resource-bounded complexity classes, and complete problems). Chapter three begins the connection between logic and complexity, with a proof that th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signature (logic)
In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an algebraic structure. In model theory, signatures are used for both purposes. They are rarely made explicit in more philosophical treatments of logic. Definition Formally, a (single-sorted) signature can be defined as a 4-tuple , where ''S''func and ''S''rel are disjoint sets not containing any other basic logical symbols, called respectively * ''function symbols'' (examples: +, ×, 0, 1), * ''relation symbols'' or ''predicates'' (examples: ≤, ∈), * ''constant symbols'' (examples: 0, 1), and a function ar: ''S''func \cup ''S''rel → \mathbb N which assigns a natural number called ''arity'' to every function or relation symbol. A function or relation symbol is called ''n''-ary if its arity is ''n''. Some authors define a nullary (0-ary) function symbol as ''constant s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neil Immerman
Neil Immerman (born 24 November 1953, Manhasset, New York) is an American theoretical computer scientist, a professor of computer science at the University of Massachusetts Amherst.Faculty directory: Neil Immerman Computer Science Department, , retrieved 2010-01-23. He is one of the key developers of , an approach he is currently applying to research in model checking, database theory, and computational complexity theory. Professor Immerman is an ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure (mathematical Logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a ''semantic model'' when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as " interpretations", whereas the term "interpretation" generally has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generic Query
Generic or generics may refer to: In business * Generic term, a common name used for a range or class of similar things not protected by trademark * Generic brand, a brand for a product that does not have an associated brand or trademark, other than the trading name of the business providing the product * Generic trademark, a trademark that sometimes or usually replaces a common term in colloquial usage * Generic drug, a drug identified by its chemical name rather than its brand name In computer programming * Generic function, a computer programming entity made up of all methods having the same name * Generic programming, a computer programming paradigm based on method/functions or classes defined irrespective of the concrete data types used upon instantiation ** Generics in Java In linguistics *A pronoun or other word used with a less specific meaning, such as: ** generic ''you'' ** generic ''he'' or generic ''she'' ** generic ''they'' * Generic mood, a grammatical mood used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
