Computational Complexity of Real Functions

1991 ◽  
pp. 40-70 ◽  
Author(s):  
Ker-I Ko
Keyword(s):  
Computational Complexity ◽  
Real Functions

J. C. Shepherdson. Algorithmic procedures, generalized Turing algorithms, and elementary recursion theory. Harvey Friedman's research on the foundations of mathematics, edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in logic and the foundations of mathematics, vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, pp. 285–308. - J. C. Shepherdson. Computational complexity of real functions. Harvey Friedman's research on the foundations of mathematics, edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in logic and the foundations of mathematics, vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, pp. 309–315. - A. J. Kfoury. The pebble game and logics of programs. Harvey Friedman's research on the foundations of mathematics, edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in logic and the foundations of mathematics, vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, pp. 317–329. - R. Statman. Equality between functionals revisited. Harvey Friedman's research on the foundations of mathematics, edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in logic and the foundations of mathematics, vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, pp. 331–338. - Robert E. Byerly. Mathematical aspects of recursive function theory. Harvey Friedman's research on the foundations of mathematics, edited by L. A. Harrington, M. D. Morley, A. S̆c̆edrov, and S. G. Simpson, Studies in logic and the foundations of mathematics, vol. 117, North-Holland, Amsterdam, New York, and Oxford, 1985, pp. 339–352.

1990 ◽  
Vol 55 (2) ◽  
pp. 876-878
Author(s):  
J. V. Tucker
Keyword(s):  
New York ◽  
Computational Complexity ◽  
Recursive Function ◽  
Function Theory ◽  
Recursion Theory ◽  
Foundations Of Mathematics ◽  
Real Functions ◽  
Pebble Game ◽  
Logics Of Programs

On the computational complexity of the Dirichlet Problem for Poisson's Equation

2016 ◽  
Vol 27 (8) ◽  
pp. 1437-1465 ◽  
Author(s):  
AKITOSHI KAWAMURA ◽  
FLORIAN STEINBERG ◽  
MARTIN ZIEGLER
Keyword(s):  
Dirichlet Problem ◽  
Computational Complexity ◽  
Complexity Theory ◽  
Complexity Class ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Precise Sense ◽  
Real Functions ◽  
Riemann Integration

The last years have seen an increasing interest in classifying (existence claims in) classical mathematical theorems according to their strength. We pursue this goal from the refined perspective of computational complexity. Specifically, we establish that rigorously solving the Dirichlet Problem for Poisson's Equation is in a precise sense ‘complete’ for the complexity class ${\#\mathcal{P}}$ and thus as hard or easy as parametric Riemann integration (Friedman 1984; Ko 1991. Complexity Theory of Real Functions).

scholarly journals Computational complexity of real functions

1982 ◽  
Vol 20 (3) ◽  
pp. 323-352 ◽  
Author(s):  
Ker-I. Ko ◽  
Harvey Friedman
Keyword(s):  
Computational Complexity ◽  
Real Functions

Rational Approximation of Real Functions

1988 ◽  
Author(s):  
P. P. Petrushev ◽  
Vasil Atanasov Popov
Keyword(s):  
Rational Approximation ◽  
Real Functions

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

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