We study decidability and complexity questions related to a continuous analogue of the
Skolem-Pisot problem concerning the zeros and nonnegativity of a linear recurrent …

We consider the Membership and the Half-Space Reachability problems for matrices in
dimensions two and three. Our first main result is that the Membership Problem is decidable …

Most computational problems for matrix semigroups and groups are inherently difficult to
solve and even undecidable starting from dimension three. The questions about the …

A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by
two pieces of input:(i) a mathematical program (an objective function f: R n→ R and a …

We study the decidability of three well-known problems related to integer matrix
multiplication: Mortality (M), Zero in the Left-Upper Corner (Z), and Zero in the Right-Upper …

We introduce two generalizations of synchronizability to automata with transitions weighted
in an arbitrary semiring K=(K,+,*, 0, 1).(or equivalently, to finite sets of matrices in K^ nxn.) …

This paper studies the linear recurrence automata model in which multiple linear
recurrences can be used to generate sequences of numbers. We parameterised the model …

We study reachability problems for various nondeterministic polynomial maps in Z n. We
prove that the reachability problem for very simple three-dimensional affine maps (with …

In the reachability problem for polynomial iteration, we are given a set of polynomials over
integers and we are asked whether a particular integer can be reached by a non …

In this thesis we explore decision problems for linear dynamical systems, which are a
fundamental model in theoretical computer science, software verification and control theory …