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Unlike BPP, PP is a syntactic rather than semantic class. Any polynomial-time probabilistic machine recognizes some language in PP.In contrast, given a description of a polynomial-time probabilistic machine, it is undecidable in general to determine if it recognizes a language in BPP.
.ppt, the file format used by Microsoft PowerPoint presentation software; Parts-per notation for parts-per-trillion (more common) or parts-per-thousand (less common) PerlPowerTools, a revitalized of the classic Unix command set in pure Perl; Positive partial transpose, a criterion used in quantum mechanics
A mathematical object is an abstract concept arising in mathematics. [1] Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas.
A stable binary format (called a .ppt file, like all earlier binary formats) that was shared as the default in PowerPoint 97 through PowerPoint 2003 for Windows, and in PowerPoint 98 through PowerPoint 2004 for Mac (that is, in PowerPoint versions 8.0 through 11.0) was finally created. It was based on the Compound File Binary Format.
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Graphs such as these are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
Pure mathematics studies the properties and structure of abstract objects, [1] such as the E8 group, in group theory.This may be done without focusing on concrete applications of the concepts in the physical world.