Interactive Computation
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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. Informally, it m ...
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. 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 for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ...
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Game Semantics
Game semantics (german: dialogische Logik, translated as ''dialogical logic'') is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes. History In the late 1950s Paul Lorenzen was the first to introduce a game semantics for logic, and it was further developed by Kuno Lorenz. At almost the same time as Lorenzen, Jaakko Hintikka developed a model-theoretical approach known in the literature as ''GTS'' (game-theoretical semantics). Since then, a number of different game semantics have been studied in logic. Shahid Rahman (Lille) and collaborators developed dialogical logic into a general framework for the study of logical and philosophical issues related to logical pluralism. Beginning 1994 this triggered a kind of renaissance with lasting consequences. This new philosophical impulse experienced a pa ...
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Peter Wegner
Peter A. Wegner (August 20, 1932 – July 27, 2017) was a computer scientist who made significant contributions to both the theory of object-oriented programming during the 1980s and to the relevance of the Church–Turing thesis for empirical aspects of computer science during the 1990s and present. In 2016, Wegner wrote a brief autobiography for ''Conduit'', the annual Brown University Computer Science department magazine.Wegner, Peter
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Super-recursive Algorithm
In computability theory, super-recursive algorithms are a generalization of ordinary 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. Turing machines and other mathematical models of conventional algorithms allow researchers to find properties of recursive algorithms and their computations. In a similar way, mathematical models of super-recursive algorithms, such as inductive Turing machines, allow researchers to find properties of super-recursive algorithms and their computations. Burgin, as well as other researchers (including Selim Akl, Eugene Eberbach, Peter Kugel, Jan van Leeuwen, Hava Siegelmann, Peter Wegner, and Jiří Wiedermann) who studied different kinds of super-recursive algorithms and contributed to the theory of super-recursive algorithms, have argued that super-recursive algorithms can be used ...
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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 o ...
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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 empiricism (see Penelope Maddy) with mathematics, issues related to realism, the importance of culture, necessity of 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 mathematical practice in either field, this would nonetheless be insufficient to disprove alternate approaches. Eugene Wigner (1960) noted that this culture need not be restricted to mathematics, physi ...
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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 intui ...
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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 ad ...
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Hypercomputation
Hypercomputation or super-Turing computation refers to models of computation that can provide outputs that are not Turing-computable. Super-Turing computing, introduced at the early 1990's by Hava Siegelmann, refers to such neurological inspired, biological and physical realizable computing; It became the mathematical foundations of Lifelong Machine Learning. Hypercomputation, introduced as a field of science in the late 1990s, is said to be based on the Super Turing but it also includes constructs which are philosophical. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that can 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 computa ...
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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 ...
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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 a formula 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 probl ...
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Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used 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). 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, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ...
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