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Interactive Computation
In computer science, interactive computation is a mathematical model for computation that involves input/output communication with the external world ''during'' computation. Uses Among the currently studied mathematical models of computation that attempt to capture interaction are Giorgi Japaridze's hard- and easy-play machines elaborated within the framework of computability logic, Dina Q. Goldin's Persistent Turing Machines (PTMs), and Yuri Gurevich's abstract state machines. Peter Wegner has additionally done a great deal of work on this area of computer science . See also * Cirquent calculus * Computability logic *Game semantics * Human-based computation *Hypercomputation * Interactive programming * Membrane computing * Quasi-empiricism *RE (complexity) In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amount of time. Informal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Computability Logic
Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic, which is a formal theory of truth. It was introduced and so named by Giorgi Japaridze in 2003. In classical logic, formulas represent true/false statements. In CoL, formulas represent computational problems. In classical logic, the validity of an argument depends only on its form, not on its meaning. In CoL, validity means being always computable. More generally, classical logic tells us when the truth of a given statement always follows from the truth of a given set of other statements. Similarly, CoL tells us when the computability of a given problem ''A'' always follows from the computability of other given problems ''B1,...,Bn''. Moreover, it provides a uniform way to actually construct a solution (algorithm) for such an ''A'' from any known solutions of ''B1,...,Bn''. CoL formulates computational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Super-recursive Algorithm
In computability theory, super-recursive algorithms are posited as a generalization of hypercomputation: hypothetical algorithms that are more powerful, that is, compute more than Turing machines. The term was introduced by Mark Burgin, whose book ''Super-recursive algorithms'' develops their theory and presents several mathematical models. Burgin argues that super-recursive algorithms can be used to disprove the Church–Turing thesis. This point of view has been criticized within the mathematical community and is not widely accepted. Definition Burgin (2005: 13) uses the term recursive algorithms for algorithms that can be implemented on Turing machines, and uses the word ''algorithm'' in a more general sense. Then a super-recursive class of algorithms is "a class of algorithms in which it is possible to compute functions not computable by any Turing machine" (Burgin 2005: 107) Super-recursive algorithms are also related to algorithmic schemes, another novel concept from B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
RE (complexity)
In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amount of time. Informally, it means that if the answer to a problem instance is 'yes', then there is some procedure that takes finite time to determine this, and this procedure never falsely reports 'yes' when the true answer is 'no'. However, when the true answer is 'no', the procedure is not required to halt; it may go into an " infinite loop" for some 'no' cases. Such a procedure is sometimes called a semi-algorithm, to distinguish it from an algorithm, defined as a complete solution to a decision problem. Similarly, co-RE is the set of all languages that are complements of a language in RE. In a sense, co-RE contains languages of which membership can be disproved in a finite amount of time, but proving membership might take forever. Equivalent definition Equivalently, RE is the class ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quasi-empiricism In Mathematics
Quasi-empiricism in mathematics is the attempt in the philosophy of mathematics to direct philosophers' attention to mathematical practice, in particular, relations with physics, social sciences, and computational mathematics, rather than solely to issues in the foundations of mathematics. Of concern to this discussion are several topics: the relationship of Philosophy of mathematics#Empiricism, empiricism (see Penelope Maddy) with mathematics, issues related to Philosophy of mathematics#Mathematical realism, realism, the importance of Philosophy of mathematics#Social constructivism or social realism, culture, necessity of Philosophy of mathematics#Constructivism, application, etc. Primary arguments A primary argument with respect to quasi-empiricism is that whilst mathematics and physics are frequently considered to be closely linked fields of study, this may reflect human cognitive bias. It is claimed that, despite rigorous application of appropriate empirical methods or mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Membrane Computing
Membrane computing (or MC) is an area within computer science that seeks to discover new computational models from the study of biological cells, particularly of the cellular membranes. It is a sub-task of creating a cellular model. Membrane computing deals with distributed and parallel computing models, processing multisets of symbol objects in a localized manner. Thus, evolution rules allow for evolving objects to be encapsulated into compartments defined by membranes. The communications between compartments and with the environment play an essential role in the processes. The various types of membrane systems are known as P systems after Gheorghe Păun who first conceived the model in 1998. An essential ingredient of a P system is its membrane structure, which can be a hierarchical arrangement of membranes, as in a cell, or a net of membranes (placed in the nodes of a graph), as in a tissue or a neural net. P systems are often depicted graphically with drawings. The intu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Interactive Programming
Interactive programming is the procedure of writing parts of a program while it is already active. This focuses on the program text as the main interface for a running process, rather than an interactive application, where the program is designed in development cycles and used thereafter (usually by a so-called "user", in distinction to the "developer"). Consequently, here, ''the activity of writing a program becomes part of the program itself.'' It thus forms a specific instance of interactive computation as an extreme opposite to batch processing, where neither writing the program nor its use happens in an interactive way. The principle of ''rapid feedback'' in extreme programming is radicalized and becomes more explicit. Synonyms: on-the-fly-programming, just in time programming, conversational programming Application fields Interactive programming techniques are especially useful in cases where no clear specification of the problem that is to be solved can be given in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hypercomputation
Hypercomputation or super-Turing computation is a set of hypothetical models of computation that can provide outputs that are not Turing-computable. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that could correctly evaluate every statement in Peano arithmetic. The Church–Turing thesis states that any "computable" function that can be computed by a mathematician with a pen and paper using a finite set of simple algorithms, can be computed by a Turing machine. Hypercomputers compute functions that a Turing machine cannot and which are, hence, not computable in the Church–Turing sense. Technically, the output of a random Turing machine is uncomputable; however, most hypercomputing literature focuses instead on the computation of deterministic, rather than random, uncomputable functions. History A computational model going beyond Turing machines was introduced by Alan Turing in his 1938 PhD dissertation '' Systems of L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Human-based Computation
Human-based computation (HBC), human-assisted computation, ubiquitous human computing or distributed thinking (by analogy to distributed computing) is a computer science technique in which a machine performs its function by outsourcing certain steps to humans, usually as microwork. This approach uses differences in abilities and alternative costs between humans and computer agents to achieve symbiotic human–computer interaction. For computationally difficult tasks such as image recognition, human-based computation plays a central role in training Deep Learning-based Artificial Intelligence systems. In this case, human-based computation has been referred to as human-aided artificial intelligence. In traditional computation, a human employs a computer to solve a problem; a human provides a formalized problem description and an algorithm to a computer, and receives a solution to interpret. Human-based computation frequently reverses the roles; the computer asks a person or a large g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Game Semantics
Game semantics is an approach to Formal semantics (logic), formal semantics that grounds the concepts of truth or Validity (logic), validity on Game theory, game-theoretic concepts, such as the existence of a winning strategy for a player. In this framework, logical formulas are interpreted as defining games between two players. The term encompasses several related but distinct traditions, including dialogical logic (developed by Paul Lorenzen and Kuno Lorenz in Germany starting in the 1950s) and game-theoretical semantics (developed by Jaakko Hintikka in Finland). Game semantics represents a significant departure from traditional Model theory, model-theoretic approaches by emphasizing the dynamic, interactive nature of logical reasoning rather than static truth assignments. It provides intuitive interpretations for various logical systems, including classical logic, intuitionistic logic, linear logic, and modal logic. The approach bears conceptual resemblances to ancient Socratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cirquent Calculus
Cirquent calculus is a proof calculus that manipulates graph (discrete mathematics), graph-style constructs termed ''cirquents'', as opposed to the traditional tree (graph theory), tree-style objects such as formula (logic), formulas or sequents. Cirquents come in a variety of forms, but they all share one main characteristic feature, making them different from the more traditional objects of syntactic manipulation. This feature is the ability to explicitly account for possible sharing of subcomponents between different components. For instance, it is possible to write an expression where two subexpressions ''F'' and ''E'', while neither one is a subexpression of the other, still have a common occurrence of a subexpression ''G'' (as opposed to having two different occurrences of ''G'', one in ''F'' and one in ''E''). Overview The approach was introduced by Giorgi Japaridze, G. JaparidzeG.Japaridze, �Introduction to cirquent calculus and abstract resource semantics��. Journal of Lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
