Concepts inFrom polynomial time queries to graph structure theory
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 which 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.
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Time complexity
In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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Finite model theory
Finite Model Theory (FMT) is a subarea of model theory (MT). MT is the branch of mathematical logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). FMT is a restriction of MT to interpretations of finite structures, i.e. structures with a finite universe. Proofs:Since many central theorems of MT do not hold when restricted to finite structures, FMT is quite different from MT in proof methods.
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Database theory
Database theory encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems.
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Relational database
A relational database is a collection of data items organized as a set of formally described tables from which data can be accessed easily. A relational database is created using the relational model. The software used in a relational database is called a relational database management system (RDBMS). A relational database is the predominant choice in storing data, over other models like the hierarchical database model or the network model.
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Logic
Logic (from the Greek ¿¿¿¿¿¿ logik¿) is the philosophical study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, ontology, epistemology, and ethics.
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Query language
Query languages are computer languages used to make queries into databases and information systems. Broadly, query languages can be classified according to whether they are database query languages or information retrieval query languages. The difference is that a database query language attempts to give factual answers to factual questions, while an information retrieval query language attempts to find documents containing information that is relevant to an area of inquiry. Examples include: .
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