Journal ArticleDOI
On digital nondeterminism
Felipe Cucker,Martín Matamala +1 more
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This article is published in Theory of Computing Systems \/ Mathematical Systems Theory.The article was published on 1996-12-01. It has received 34 citations till now. The article focuses on the topics: Theory of computation.read more
Citations
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A graph-constructive approach to solving systems of geometric constraints
TL;DR: A graph-constructive approach to solving systems of geometric constraints capable of effeciently handling well-constrained, overconstraining, and under Constrained configurations is presented.
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Dynamical recognizers: real time language recognition by analog computers
TL;DR: A model of analog computer which can recognize various languages in real time by composing iterated maps, which can be seen as a real-time, constant-space, off-line version of Blum, Shub, and Smale's real-valued machines.
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Logical Approaches to Computational Barriers
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Exotic Quantifiers, Complexity Classes, and Complete Problems
Peter Bürgisser,Felipe Cucker +1 more
TL;DR: It turns out that infinitesimal and generic quantifiers can be eliminated, so that the relevant complexity classes can be described in terms of the usual quantifiers only.
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Logics which capture complexity classes over the reals
Felipe Cucker,Klaus Meer +1 more
TL;DR: This paper adapts the approach of descriptive complexity theory for this model of computation introduced by Blum, Shub, and Smale and extend it to capture some further complexity classes over the reals by logical means.
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Neural networks and physical systems with emergent collective computational abilities
TL;DR: A model of a system having a large number of simple equivalent components, based on aspects of neurobiology but readily adapted to integrated circuits, produces a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size.
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Neural computation of decisions in optimization problems
John J. Hopfield,David W. Tank +1 more
TL;DR: Results of computer simulations of a network designed to solve a difficult but well-defined optimization problem-the Traveling-Salesman Problem-are presented and used to illustrate the computational power of the networks.
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On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines
Book
Structural Complexity I
TL;DR: This volume is written for undergraduate students who have taken a first course in Formal Language Theory and presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory.
Journal ArticleDOI
Analog computation via neural networks
TL;DR: It is noted that these networks are not likely to solve polynomially NP-hard problems, as the equality “ p = np ” in the model implies the almost complete collapse of the standard polynomial hierarchy.