This paper tries to fully characterize the properties and relationships
of space classes defined by Turing machines that use less than
logarithmic space - may they be deterministic,
nondeterministic or alternating (DTM, NTM or ATM).

We provide several examples of specific languages ... more >>>

Deterministic k-tape and multitape Turing machines with one-way,
two-way and without a separated input tape are considered. We
investigate the classes of languages acceptable by such devices with
time bounds of the form n+r(n) where r in o(n) is a sublinear
function. It is shown that there ... more >>>

We show necessary and sufficient conditions that
certain algebraic functions like the rank or the signature
of an integer matrix can be computed in GapL.

more >>>

Polynomial factorization is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity theory classifies polynomials into complexity classes based on their perceived `hardness'. This raises a natural question: Do ... more >>>

We show that algebraic formulas and constant-depth circuits are \emph{closed} under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then all its factors can be computed by small constant-depth circuits or formulas ... more >>>