Characterizing Valiant's algebraic complexity classes
Journal of Complexity
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UC '08 Proceedings of the 7th international conference on Unconventional Computing
On defining integers in the counting hierarchy and proving arithmetic circuit lower bounds
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
VPSPACE and a transfer theorem over the reals
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the arithmetic complexity of euler function
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Valiant's model: from exponential sums to exponential products
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On certain computations of Pisot numbers
Information Processing Letters
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Let 驴(n) be the minimum number of arithmetic operations required to build the integer $$n \in \mathbb{N}$$ from the constants 1 and 2. A sequence xn is said to be "easy to compute" if there exists a polynomial p such that $$\tau (x_n ) \leq p(\log n)$$ for all It is natural to conjecture that sequences such as $$\left\lfloor {2^n \ln 2} \right\rfloor $$ or n! are not easy to compute. In this paper we show that a proof of this conjecture for the first sequence would imply a superpolynomial lower bound for the arithmetic circuit size of the permanent polynomial. For the second sequence, a proof would imply a superpolynomial lower bound for the permanent or P 驴 PSPACE.