In mathematics, model theory is the study of (classes of) mathematical structures using tools from mathematical logic. It has close ties to abstract algebra, particularly universal algebra. Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages.
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Logic synthesis
In electronics, logic synthesis is a process by which an abstract form of desired circuit behavior, typically register transfer level (RTL), is turned into a design implementation in terms of logic gates. Common examples of this process include synthesis of HDLs, including VHDL and Verilog. Some tools can generate bitstreams for programmable logic devices such as PALs or FPGAs, while others target the creation of ASICs. Logic synthesis is one aspect of electronic design automation.
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Example-based machine translation
The example-based machine translation (EBMT) approach to machine translation is often characterized by its use of a bilingual corpus with parallel texts as its main knowledge base, at run-time. It is essentially a translation by analogy and can be viewed as an implementation of case-based reasoning approach of machine learning. At the foundation of example-based machine translation is the idea of translation by analogy.
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3D modeling
In 3D computer graphics, 3D modeling is the process of developing a mathematical representation of any three-dimensional surface of object (either inanimate or living) via specialized software. The product is called a 3D model. It can be displayed as a two-dimensional image through a process called 3D rendering or used in a computer simulation of physical phenomena. The model can also be physically created using 3D printing devices. Models may be created automatically or manually.
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Texture synthesis
Texture synthesis is the process of algorithmically constructing a large digital image from a small digital sample image by taking advantage of its structural content. It is an object of research in computer graphics and is used in many fields, amongst others digital image editing, 3D computer graphics and post-production of films. Texture synthesis can be used to fill in holes in images, create large non-repetitive background images and expand small pictures.
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Optimal substructure
In computer science, a problem is said to have optimal substructure if an optimal solution can be constructed efficiently from optimal solutions to its subproblems. This property is used to determine the usefulness of dynamic programming and greedy algorithms in a problem. Typically, a greedy algorithm is used to solve a problem with optimal substructure if it can be proved by induction that this is optimal at each step (Cormen et al. pp. 381¿2).
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Finite difference
A finite difference is a mathematical expression of the form f(x + b) ¿ f(x + a). If a finite difference is divided by b ¿ a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. Recurrence relations can be written as difference equations by replacing iteration notation with finite differences.
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