W. Dean. Algorithms and the mathematical foundations of computer
... can be justified by a supplemental mathematical proof that the algorithm is correct (i.e. that it computes the function that it is claimed to). I will refer to the view expressed by (A) as algorithmic realism.3 Although it is often not identified as a thesis requiring an explicit statement and defen ...
... can be justified by a supplemental mathematical proof that the algorithm is correct (i.e. that it computes the function that it is claimed to). I will refer to the view expressed by (A) as algorithmic realism.3 Although it is often not identified as a thesis requiring an explicit statement and defen ...
Symbol/Membrane Complexity of P Systems with Symport/Antiport
... P systems / tissue P systems with only one membrane / one cell already reach universal computational power, even with antiport rules of weight two (e.g., see [4] and [8]); yet on the other hand, in these P systems the number of symbols remains unbounded. Considering the generation of recursively enu ...
... P systems / tissue P systems with only one membrane / one cell already reach universal computational power, even with antiport rules of weight two (e.g., see [4] and [8]); yet on the other hand, in these P systems the number of symbols remains unbounded. Considering the generation of recursively enu ...
Cognitive Models for Number Series Induction Problems
... recognition, how to derive rules from these patterns and applying them to continue the given number series. The most known examples are IGOR, ANN, MagicHaskeller and Asolver. Determing the performance of a system it is important to analyze not only given solutions but also the complexity of the test ...
... recognition, how to derive rules from these patterns and applying them to continue the given number series. The most known examples are IGOR, ANN, MagicHaskeller and Asolver. Determing the performance of a system it is important to analyze not only given solutions but also the complexity of the test ...
section home
... Is there any faster way to do multiplication? Yes, and breakthroughs have been reported even in recent years. Do we know that multiplication cannot be done by a linear algorithm? The question is still open. No such algorithms is known but it has not been proved impossible. Anuj Dawar ...
... Is there any faster way to do multiplication? Yes, and breakthroughs have been reported even in recent years. Do we know that multiplication cannot be done by a linear algorithm? The question is still open. No such algorithms is known but it has not been proved impossible. Anuj Dawar ...
The complexity of model checking concurrent programs against
... define a non-deterministic polynomially-space bounded Turing machine T that halts in an accepting state iff ¬ϕ is satisfiable in D (i.e. iff there exists a state s ∈ S s.t. D, s |= ¬ϕ). Based on this, we conclude that the problem of model checking is in co-NPSPACE. From this, considering Corollary 1 ...
... define a non-deterministic polynomially-space bounded Turing machine T that halts in an accepting state iff ¬ϕ is satisfiable in D (i.e. iff there exists a state s ∈ S s.t. D, s |= ¬ϕ). Based on this, we conclude that the problem of model checking is in co-NPSPACE. From this, considering Corollary 1 ...
Random Numbers and Monte Carlo Methods
... Methods which make use of random numbers are often called Monte Carlo Methods after the Casino Monte Carlo in Monaco which has long been famous for games of chance. Monte Carlo methods are useful in: • Simulation: Random numbers are used to simulate natural phenomena. In nuclear physics, neutrons mo ...
... Methods which make use of random numbers are often called Monte Carlo Methods after the Casino Monte Carlo in Monaco which has long been famous for games of chance. Monte Carlo methods are useful in: • Simulation: Random numbers are used to simulate natural phenomena. In nuclear physics, neutrons mo ...
spotz_pytrilinos
... A Quick Detour… • Python lists are not suitable for scientific computing – Flexible but inefficient – Heterogeneous data, noncontiguous memory ...
... A Quick Detour… • Python lists are not suitable for scientific computing – Flexible but inefficient – Heterogeneous data, noncontiguous memory ...
Jan Kyncl: Simple Realizability of Complete Abstract Topological
... def.: Call an AT-graph (G, X ) even (or an even G) if |X | is even, and odd (or an odd G) if |X | is odd. Theorem 3: Every complete AT-graph that is not independently Z2 -realizable has an AT-subgraph on at most six vertices that is not independently Z2 -realizable. More precisely, a complete AT-gr ...
... def.: Call an AT-graph (G, X ) even (or an even G) if |X | is even, and odd (or an odd G) if |X | is odd. Theorem 3: Every complete AT-graph that is not independently Z2 -realizable has an AT-subgraph on at most six vertices that is not independently Z2 -realizable. More precisely, a complete AT-gr ...
Step back and look at the Science
... 1936, Turing came up with proof of impossibility …but Alonzo Church published independent paper also showing that it is impossible 1937 Turing’s "On computable numbers, with an application to the Entscheidungsproblem“ published ...
... 1936, Turing came up with proof of impossibility …but Alonzo Church published independent paper also showing that it is impossible 1937 Turing’s "On computable numbers, with an application to the Entscheidungsproblem“ published ...
Equation Solving in Terms of Computational Complexity
... In the framework of algebraic complexity with unit cost per arithmetical operation, the complexity of solving ax = b seems to be a trivial subject, as one division will suffice, but things become highly nontrivial, if we discuss this problem of equation solving forfinite-dimensionalalgebras over som ...
... In the framework of algebraic complexity with unit cost per arithmetical operation, the complexity of solving ax = b seems to be a trivial subject, as one division will suffice, but things become highly nontrivial, if we discuss this problem of equation solving forfinite-dimensionalalgebras over som ...
document
... to right, and we cannot compute y k unless we know xk , i.e., unless we have processed u1 uk−1 . On the other hand, yk does not depend on uk+1 un . This is a direct consequence of the fact that T has been chosen upper triangular, so that such an ordering of computations is indeed possibl ...
... to right, and we cannot compute y k unless we know xk , i.e., unless we have processed u1 uk−1 . On the other hand, yk does not depend on uk+1 un . This is a direct consequence of the fact that T has been chosen upper triangular, so that such an ordering of computations is indeed possibl ...
Comparing mathematical provers - Institute for Computing and
... The Agda proof by Thierry Coquand proves something still more basic. It does not talk about the number two in the natural numbers, but instead about any element in a commutative monoid that satisfies some conditions. The Otter proof has a similar structure. Most people proved the irrationality of th ...
... The Agda proof by Thierry Coquand proves something still more basic. It does not talk about the number two in the natural numbers, but instead about any element in a commutative monoid that satisfies some conditions. The Otter proof has a similar structure. Most people proved the irrationality of th ...
CS173: Discrete Math
... • At each iteration, 2 comparisons are used • For example, 2 comparisons are used when the list has 2k-1 elements, 2 comparisons are used when the list has 2k-2, …, 2 comparisons are used when the list has 21 elements • 1 comparison is ued when the list has 1 element, and 1 more comparison is used t ...
... • At each iteration, 2 comparisons are used • For example, 2 comparisons are used when the list has 2k-1 elements, 2 comparisons are used when the list has 2k-2, …, 2 comparisons are used when the list has 21 elements • 1 comparison is ued when the list has 1 element, and 1 more comparison is used t ...
Numbers as Data Structures: The Prime
... problems where the use of a placed based notation is often implicit in the definition of the problem. One important lesson from computer science is that different representations of the same abstract object may have different computational consequences. For example, a tree may be represented by many ...
... problems where the use of a placed based notation is often implicit in the definition of the problem. One important lesson from computer science is that different representations of the same abstract object may have different computational consequences. For example, a tree may be represented by many ...
Introduction to mathematical fuzzy logic
... Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, mathematical fuzzy logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on m ...
... Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, mathematical fuzzy logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on m ...
PPT - OptiRisk Systems
... -These solutions are evaluated on the “true” distributions “true” objective values -The true objective values should be similar • In practice: use a very large scenario set generated with an exogenuous SG method as the “true” distribution ...
... -These solutions are evaluated on the “true” distributions “true” objective values -The true objective values should be similar • In practice: use a very large scenario set generated with an exogenuous SG method as the “true” distribution ...
Department for Analysis and Computational Number
... Fibered systems Let B be a set and T : B → B be a transformation. We call the pair (B, T ) a fibered system if the following conditions are satisfied: 1. There exists an at most countable set D, which we call the set of digits. 2. There is an application k : B → D such that the sets B(i) = k −1 ({i} ...
... Fibered systems Let B be a set and T : B → B be a transformation. We call the pair (B, T ) a fibered system if the following conditions are satisfied: 1. There exists an at most countable set D, which we call the set of digits. 2. There is an application k : B → D such that the sets B(i) = k −1 ({i} ...
CS 391L: Machine Learning: Computational
... eventually converge to a correct concept and never make a mistake again. • No limit on the number of examples required or computational demands, but must eventually learn the concept exactly, although do not need to explicitly recognize this convergence point. • By simple enumeration, concepts from ...
... eventually converge to a correct concept and never make a mistake again. • No limit on the number of examples required or computational demands, but must eventually learn the concept exactly, although do not need to explicitly recognize this convergence point. • By simple enumeration, concepts from ...
present perfect simple
... I have written a long letter to my friend. or b) To state quantity (how many) … I have written six letters this evening. ...
... I have written a long letter to my friend. or b) To state quantity (how many) … I have written six letters this evening. ...
ConArg: Argumentation with Constraints
... enhanced the tool with the implementation of the extensions developed in [1,2]. In [1] we extend the Dung AFs in order to deal with coalitions of arguments. The initial set of arguments is partitioned into subsets. Each subset represents a different “line of thought” and can be considered as a coali ...
... enhanced the tool with the implementation of the extensions developed in [1,2]. In [1] we extend the Dung AFs in order to deal with coalitions of arguments. The initial set of arguments is partitioned into subsets. Each subset represents a different “line of thought” and can be considered as a coali ...
Computational Complexity from Learners` Perspective in College
... The time measurements for generating problems are listed in Tabs. V and VI. The machine’s specification is as follows. The adopted software is Worflam Mathematica 9.0 (Windows 8.1, 64 bit, Intel(R) Core i5-4300U CPU 1.9 GHz. The main memory is 8.0 GB.) Tests were conducted generating 1,000 problems ...
... The time measurements for generating problems are listed in Tabs. V and VI. The machine’s specification is as follows. The adopted software is Worflam Mathematica 9.0 (Windows 8.1, 64 bit, Intel(R) Core i5-4300U CPU 1.9 GHz. The main memory is 8.0 GB.) Tests were conducted generating 1,000 problems ...
File - Science for all Students
... the form of DNA molecules. Genes designed world. are regions in the DNA that contain Develop and use a model based on evidence the instructions that code for the to illustrate the relationships between systems formation of proteins, which carry out or between components of a system. (HSmost of the ...
... the form of DNA molecules. Genes designed world. are regions in the DNA that contain Develop and use a model based on evidence the instructions that code for the to illustrate the relationships between systems formation of proteins, which carry out or between components of a system. (HSmost of the ...
PPT (pre) - School of Computer Science
... You can measure “time” as the number of elementary “steps” defined in any other way, provided each such “step” takes constant time in a reasonable implementation. Constant: independent of the length n of the input. ...
... You can measure “time” as the number of elementary “steps” defined in any other way, provided each such “step” takes constant time in a reasonable implementation. Constant: independent of the length n of the input. ...
Full Writeup for Teachers
... the ones that humans inevitably make, while some are introduced by the computer. In general we can say that there are four classes of errors that may plague computations: 1. Blunders or bad t ...
... the ones that humans inevitably make, while some are introduced by the computer. In general we can say that there are four classes of errors that may plague computations: 1. Blunders or bad t ...