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The Complexity of the Minimal Polynomial
2001We investigate the computational complexity of the minimal polynomial of an integer matrix. We show that the computation of the minimal polynomial is in AC0(GapL), the AC0-closure of the logspace counting class GapL, which is contained in NC2. Our main result is that the problem is hard for GapL (under AC0 many-one reductions). The result extends to
Thanh Minh Hoang, Thomas Thierauf
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On the polynomial IO-complexity
Information Processing Letters, 1989We want to know the relationship between the class P and NP and the new defined classes P(d(n)) and NP(d(n)). We show that there exists a positive density function d(n) for which P(d(n))\(\neq NP(d(n))\) if and only if \(P\neq NP\). On the other hand, we also show that the existence of a positive density function d(n) for which \(P(d(n))=NP(d(n ...
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Stability and zeros of a complex polynomial
1993 IEEE International Symposium on Circuits and Systems, 2002For real polynomials, a stability test algorithm shown by Y. Bistritz (1984) requires about a half of the operations of the Marden-July table method (1964). His method also gives the number of inside the unit circle (IUC) zeros, outside the unit circle (OUC) zeros and on the unit circle (UC) zeros. However, it doesn't work for complex polynomials.
Kaoru Kurosawa +2 more
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On the Complexity of Polynomial Recurrence Sequences
Проблемы передачи информации, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On polynomial and generalized complexity cores
[1988] Proceedings. Structure in Complexity Theory Third Annual Conference, 1988Recent results on polynomial complexity cores, their complexity, density, and structure and their counterparts on proper hard cores are surveyed and interpreted. An approach to generalized complexity cores that is almost axiomatic in nature is included in the discussion. The purpose is to provide an integrated presentation of this material. >
Ronald V. Book +2 more
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The Complexity of Polynomial-Time Approximation
Theory of Computing Systems, 2007In 1996 Khanna and Motwani proposed three logic-based optimization problems constrained by planar structure, and offered the hypothesis that these putatively fundamental problems might provide insight into characterizing the class of optimization problems that admit a polynomial-time approximation scheme (PTAS).
Liming Cai +3 more
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The Proof Complexity of Polynomial Identities
2009 24th Annual IEEE Conference on Computational Complexity, 2009Devising an efficient deterministic -- or even a non-deterministic sub-exponential time -- algorithm for testing polynomial identities is a fundamental problem in algebraic complexity and complexity at large. Motivated by this problem, as well as by results from proof complexity, we investigate the complexity of _proving_ polynomial identities. To this
Pavel Hrubes, Iddo Tzameret
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2002
This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.
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This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis.
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The polynomial method in circuit complexity
[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference, 2002The basic techniques for using polynomials in complexity theory are examined, emphasizing intuition at the expense of formality. The focus is on the connections to constant-depth circuits, at the expense of polynomial-time Turing machines. The closure properties, upper bounds, and lower bounds obtained by this approach are surveyed. >
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Polynomial Theory of Complex Systems
IEEE Transactions on Systems, Man, and Cybernetics, 1971A complex multidimensional decision hypersurface can be approximated by a set of polynomials in the input signals (properties) which contain information about the hypersurface of interest. The hypersurface is usually described by a number of experimental (vector) points and simple functions of their coordinates.
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