Computational complexity theoryIn 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.
Computational complexityIn computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.
Complexity classIn computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.
Quantum complexity theoryQuantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two important quantum complexity classes are BQP and QMA.
Anti-realismIn analytic philosophy, anti-realism is a position which encompasses many varieties such as metaphysical, mathematical, semantic, scientific, moral and epistemic. The term was first articulated by British philosopher Michael Dummett in an argument against a form of realism Dummett saw as 'colorless reductionism'. In anti-realism, the truth of a statement rests on its demonstrability through internal logic mechanisms, such as the context principle or intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality.
Parameterized complexityIn computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output. The complexity of a problem is then measured as a function of those parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input.
PropertyProperty is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, redefine, rent, mortgage, pawn, sell, exchange, transfer, give away, or destroy it, or to exclude others from doing these things, as well as to perhaps abandon it; whereas regardless of the nature of the property, the owner thereof has the right to properly use it under the granted property rights.
MetaphysicsMetaphysics is the branch of philosophy that studies the fundamental nature of reality. This includes the first principles of: being or existence, identity, change, space and time, cause and effect, necessity, actuality, and possibility. Metaphysics is considered one of the four main branches of philosophy, along with epistemology, logic, and ethics. It includes questions about the nature of consciousness and the relationship between mind and matter, between substance and attribute, and between potentiality and actuality.
Particle physicsParticle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, although ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos.
LawLaw is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior, with its precise definition a matter of longstanding debate. It has been variously described as a science and as the art of justice. State-enforced laws can be made by a group legislature or by a single legislator, resulting in statutes; by the executive through decrees and regulations; or established by judges through precedent, usually in common law jurisdictions.
Social complexityIn sociology, social complexity is a conceptual framework used in the analysis of society. In the sciences, contemporary definitions of complexity are found in systems theory, wherein the phenomenon being studied has many parts and many possible arrangements of the parts; simultaneously, what is complex and what is simple are relative and change in time. Contemporary usage of the term complexity specifically refers to sociologic theories of society as a complex adaptive system, however, social complexity and its emergent properties are recurring subjects throughout the historical development of social philosophy and the study of social change.
ArgumentAn argument is a series of sentences, statements or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion. Arguments are intended to determine or show the degree of truth or acceptability of another statement called a conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective.
Personal propertyPersonal property is property that is movable. In common law systems, personal property may also be called chattels or personalty. In civil law systems, personal property is often called movable property or movables—any property that can be moved from one location to another. Personal property can be understood in comparison to real estate, immovable property or real property (such as land and buildings). Movable property on land (larger livestock, for example) was not automatically sold with the land, it was "personal" to the owner and moved with the owner.
Kolmogorov complexityIn algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy.
Advice (complexity)In computational complexity theory, an advice string is an extra input to a Turing machine that is allowed to depend on the length n of the input, but not on the input itself. A decision problem is in the complexity class P/f(n) if there is a polynomial time Turing machine M with the following property: for any n, there is an advice string A of length f(n) such that, for any input x of length n, the machine M correctly decides the problem on the input x, given x and A.
Physical constantA physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement. There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e.
Particle Data GroupThe Particle Data Group (PDG) is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. It also publishes reviews of theoretical results that are phenomenologically relevant, including those in related fields such as cosmology. The PDG currently publishes the Review of Particle Physics and its pocket version, the Particle Physics Booklet, which are printed biennially as books, and updated annually via the World Wide Web.
PhysicalismIn philosophy, physicalism is the metaphysical thesis that "everything is physical", that there is "nothing over and above" the physical, or that everything supervenes on the physical. Physicalism is a form of ontological monism—a "one substance" view of the nature of reality as opposed to a "two-substance" (dualism) or "many-substance" (pluralism) view. Both the definition of "physical" and the meaning of physicalism have been debated.
Real propertyIn English common law, real property, real estate, immovable property or, solely in the US and Canada, realty, is land which is the property of some person and all structures (also called improvements or fixtures) integrated with or affixed to the land, including crops, buildings, machinery, wells, dams, ponds, mines, canals, roads, and other things. The term is historic, arising from the now-discontinued form of action, which distinguished between real property disputes and personal property disputes.
Argument mapAn argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises, also called contention and reasons. Argument maps can also show co-premises, objections, counterarguments, rebuttals, and lemmas. There are different styles of argument map but they are often functionally equivalent and represent an argument's individual claims and the relationships between them.
