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ON THE CRITERIA OF THE F5 ALGORITHM
, 2008
"... Faugère’s F5 algorithm is one of the fastest known algorithms for the computation of Gröbner basis. So far only the F5 Criterion is proved, whereas the second powerful criterion, the Rewritten Criterion, is not understood very well until now. We give a proof of both, the F5 Criterion and the Rewrit ..."
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Cited by 3 (0 self)
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Faugère’s F5 algorithm is one of the fastest known algorithms for the computation of Gröbner basis. So far only the F5 Criterion is proved, whereas the second powerful criterion, the Rewritten Criterion, is not understood very well until now. We give a proof of both, the F5 Criterion
THE ALGORITHMIC BEHAVIOUR OF THE F5 ALGORITHM
, 810
"... Abstract. We prove the correctness and termination of Faugère’s F5 algorithm in the homogeneous case without assuming the input to be a regular sequence. Also we discuss the optimized behaviour of F5 in the case the input is a regular sequence and show that then the signature of a polynomial is uniq ..."
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Abstract. We prove the correctness and termination of Faugère’s F5 algorithm in the homogeneous case without assuming the input to be a regular sequence. Also we discuss the optimized behaviour of F5 in the case the input is a regular sequence and show that then the signature of a polynomial
The F5 Algorithm in Buchberger’s Style
 J SYST SCI COMPLEX (2011) 24: 1218–1231
, 2011
"... The famous F5 algorithm for computing Gröbner basis was presented by Faugère in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a Buchberger’s style such that it is easy to understand and ..."
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Cited by 5 (2 self)
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The famous F5 algorithm for computing Gröbner basis was presented by Faugère in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a Buchberger’s style such that it is easy to understand
A new proof of the F5 algorithm
, 1004
"... Abstract. The F5 algorithm is presented by Faugère in 2002. However, Faugère have not provide the rigorous proofs so far. In this paper, we will give a new complete proof and hence reveal the essence of this algorithm. The proof consists of the correctness and termination of the algorithm and the ..."
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Cited by 3 (1 self)
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Abstract. The F5 algorithm is presented by Faugère in 2002. However, Faugère have not provide the rigorous proofs so far. In this paper, we will give a new complete proof and hence reveal the essence of this algorithm. The proof consists of the correctness and termination of the algorithm
Steganalysis of JPEG Images: Breaking the F5 Algorithm
 in 5th International Workshop on Information Hiding
, 2002
"... Abstract. In this paper, we present a steganalytic method that can reliably detect messages (and estimate their size) hidden in JPEG images using the steganographic algorithm F5. The key element of the method is estimation of the coverimage histogram from the stegoimage. This is done by decompress ..."
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Cited by 77 (5 self)
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Abstract. In this paper, we present a steganalytic method that can reliably detect messages (and estimate their size) hidden in JPEG images using the steganographic algorithm F5. The key element of the method is estimation of the coverimage histogram from the stegoimage. This is done
Breaking the F5 Algorithm: An Improved Approach
"... In this paper, we present an improved approach to the “breaking the F5 algorithm”. The key idea is to search for an “optimal” value of β (the probability that a nonzero AC coefficient will be modified) for the image under consideration. Rather than averaging the values of β for 64 shifting steps wo ..."
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In this paper, we present an improved approach to the “breaking the F5 algorithm”. The key idea is to search for an “optimal” value of β (the probability that a nonzero AC coefficient will be modified) for the image under consideration. Rather than averaging the values of β for 64 shifting steps
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
The Viterbi algorithm
 Proceedings of the IEEE
, 1973
"... vol. 6, no. 8, pp. 211220, 1951. [7] J. L. Anderson and J. W..Ryon, “Electromagnetic radiation in accelerated systems, ” Phys. Rev., vol. 181, pp. 17651775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an accelerated system of reference, ” Phys. Reu., vol. 134, pp. A ..."
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Cited by 985 (3 self)
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vol. 6, no. 8, pp. 211220, 1951. [7] J. L. Anderson and J. W..Ryon, “Electromagnetic radiation in accelerated systems, ” Phys. Rev., vol. 181, pp. 17651775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an accelerated system of reference, ” Phys. Reu., vol. 134, pp. A799A804, 1964. [9] T. C. Mo, “Theory of electrodynamics in media in noninertial frames and applications, ” J. Math. Phys., vol. 11, pp. 25892610, 1970.
A Fast Algorithm for Particle Simulations
, 1987
"... this paper to the case where the potential (or force) at a point is a sum of pairwise An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles interactions. More specifically, we consider potentials of whose interactions a ..."
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Cited by 1145 (19 self)
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are Coulombic or gravitational in nature. For a the form system of N particles, an amount of work of the order O(N 2 ) has traditionally been required to evaluate all pairwise interactions, un F5F far 1 (F near 1F external ), less some approximation or truncation method is used. The algorithm of the present
An Algorithm for Tracking Multiple Targets
 IEEE Transactions on Automatic Control
, 1979
"... Abstract—An algorithm for tracking multiple targets In a cluttered algorithms. Clustering is the process of dividing the entire environment Is developed. The algorithm Is capable of Initiating tracks, set of targets and measurements into independent groups accounting for false or m[~clngreports, and ..."
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Cited by 586 (0 self)
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Abstract—An algorithm for tracking multiple targets In a cluttered algorithms. Clustering is the process of dividing the entire environment Is developed. The algorithm Is capable of Initiating tracks, set of targets and measurements into independent groups accounting for false or m
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