Generalized cryptographic semi-regular sequences: A variant of Fröberg conjecture and a simple complexity estimation for Gröbner basis computation

In this paper, we study generalized cryptographic semi-regular sequences, which are expected to generic in the space of homogeneous polynomial sequences on which the coordinate rings have Krull dimension one. We provide an upper-bound on the complexity of the Gr\"{o}bner basis computation for such a sequence.