Related papers: On the Descriptional Complexity of Operations on S…
A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry,…
We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the…
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…
Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
In a \emph{separability problem}, we are given two sets $K$ and $L$ from a class $\mathcal{C}$, and we want to decide whether there exists a set $S$ from a class $\mathcal{S}$ such that $K\subseteq S$ and $S\cap L=\emptyset$. In this case,…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case…
In this paper, we introduce semi-infinite tensor complementarity problem to provide an approach for considering a more realistic situation of the problem. We prove the necessary and sufficient conditions for the existence of the solution…
HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking.…
Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…