Abstract. For a tropical prevariety in R n given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of the connected components is less than. On a number of 0-dimensional connected components a better boundis obtained, which extends the Bezout bound due to B. Sturmfels from the case k = n to an arbitrary k ≥ n. Also we show that the latter bound is close to sharp, in particular, the number of connected components can depend on k.
Abstract. We consider gate elimination for linear functions and show two general forms of gate elimination that yield novel corollaries. Using these corollaries, we construct a new linear feebly secure trapdoor function that has order of security 5 4 which exceeds the previous record for linear constructions. We also give detailed proofs for nonconstructive circuit complexity bounds on linear functions.
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