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Space complexity in polynomial calculus [PDF]
SIAM Journal on Computing, 2015 During the last decade, an active line of research in proof complexity has been to study space complexity and time-space trade-offs for proofs. Besides being a natural complexity measure of intrinsic interest, space is also an important issue in SAT ...
Filmus, Yuval +4 more
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Circuit complexity, proof complexity, and polynomial identity testing [PDF]
2014 IEEE 55th Annual Symposium on Foundations of Computer Science, 2014 We introduce a new algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have ...
Grochow, Joshua A., Pitassi, Toniann
core +4 more sources
Logical Methods in Computer Science, 2013 This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is applicable in two ...
Martin Avanzini, Georg Moser
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Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 Nondeterministic polynomial-time Blum-Shub-Smale Machines over the reals give rise to a discrete complexity class between NP and PSPACE. Several problems, mostly from real algebraic geometry / polynomial systems, have been shown complete (under many-one ...
Christian Herrmann +2 more
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Leonardo's bivariate and complex polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2022 Given the purpose of mathematical evolution of Leonardo's sequence, we have the prospect of introducing complex polynomials, bivariate polynomials and bivariate polynomials around these numbers. Thus, this article portrays in detail the insertion of the variable x, y and the imaginary unit i in the sequence of Leonardo.
Mangueira, Milena +3 more
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Zeros of complex random polynomials spanned by Bergman polynomials [PDF]
Involve, a Journal of Mathematics, 2021 We study the expected number of zeros of $$P_n(z)=\sum_{k=0}^n _kp_k(z),$$ where $\{ _k\}$ are complex-valued i.i.d standard Gaussian random variables, and $\{p_k(z)\}$ are polynomials orthogonal on the unit disk. When $p_k(z)=\sqrt{(k+1)/ } z^k$, $k\in \{0,1,\dots, n\}$, we give an explicit formula for the expected number of zeros of $P_n(z)$ in a ...
Landi, Marianela +3 more
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A polynomial local optimality condition for the concave piecewise linear network flow problem
AIMS Mathematics, 2021 This paper studies the local optimality condition for the widely applied concave piecewise linear network flow problem (CPLNFP). Traditionally, for CPLNFP the complexity of checking the local optimality condition is exponentially related to the number of
Zhibin Nie, Shuning Wang, Xiaolin Huang
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A new search direction for full-Newton step infeasible interior-point method in linear optimization
Croatian Operational Research Review, 2023 In this work, we investigate a full Newton step infeasible interior-point method for linear optimization based on a new search direction which is obtained from an algebraic equivalent transformation of the central path system.
Behrouz Kheirfam
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A predictor-corrector path-following algorithm for symmetric optimization based on Darvay's technique [PDF]
Yugoslav Journal of Operations Research, 2014 In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique.
Kheirfam Behrouz
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New complexity analysis of full Nesterov-Todd step infeasible interior point method for second-order cone optimization [PDF]
Yugoslav Journal of Operations Research, 2018 We present a full Nesterov-Todd (NT) step infeasible interior-point algorithm for second-order cone optimization based on a different way to calculate feasibility direction. In each iteration of the algorithm we use the largest possible barrier parameter
Kheirfam Behrouz
doaj +1 more source