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Proving lower bounds via pseudorandom generators
 FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science, 25th International Conference, Hyderabad, India, December 1518, 2005, Proceedings, volume 3821 of Lecture
, 2005
"... Abstract. In this paper, we formalize two stepwise approaches, based on pseudorandom generators, for proving P � = NP and its arithmetic analog: Permanent requires superpolynomial sized arithmetic circuits. 1 ..."
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Abstract. In this paper, we formalize two stepwise approaches, based on pseudorandom generators, for proving P � = NP and its arithmetic analog: Permanent requires superpolynomial sized arithmetic circuits. 1
Progress on Polynomial Identity Testing
"... Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress on this ..."
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Polynomial identity testing (PIT) is the problem of checking whether a given arithmetic circuit is the zero circuit. PIT ranks as one of the most important open problems in the intersection of algebra and computational complexity. In the last few years, there has been an impressive progress on this problem but a complete solution might take a while. In this article we give a soft survey exhibiting the ideas that have been useful. 1
Determinant Versus Permanent
"... Abstract. We study the problem of expressing permanent of matrices as determinant of (possibly larger) matrices. This problem has close connections with complexity of arithmetic computations: complexities of computing permanent and determinant roughly correspond to arithmetic versions of the classes ..."
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Abstract. We study the problem of expressing permanent of matrices as determinant of (possibly larger) matrices. This problem has close connections with complexity of arithmetic computations: complexities of computing permanent and determinant roughly correspond to arithmetic versions of the classes NP and P respectively. We survey known results about their relative complexity and describe two recently developed approaches that might lead to a proof of the conjecture that permanent can only be expressed as determinant of exponentialsized matrices.