Related papers: Vector Reachability Problem in $\mathrm{SL}(2,\mat…
Reachability in hypergraphs is essential for modeling complex groupwise interactions in real-world applications such as co-authorship, social network, and biological analysis, where relationships go beyond pairwise interactions. In this…
Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two…
Nonlinear matrix equations play a crucial role in science and engineering problems. However, solutions of nonlinear matrix equations cannot, in general, be given analytically. One standard way of solving nonlinear matrix equations is to…
We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of…
We consider a variant of reachability in Vector Addition Systems (VAS) dubbed \emph{box reachability}, whereby a vector $v\in \mathbb{N}^d$ is box-reachable from $0$ in a VAS $V$ if $V$ admits a path from $0$ to $v$ that not only stays in…
Solution discovery asks whether a given (infeasible) starting configuration to a problem can be transformed into a feasible solution using a limited number of transformation steps. This paper investigates meta-theorems for solution…
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…
We investigate the dimension-parametric complexity of the reachability problem in vector addition systems with states (VASS) and its extension with pushdown stack (pushdown VASS). Up to now, the problem is known to be $\mathcal{F}_k$-hard…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…
Equations over linearly ordered semilattices are studied. For any equation $t(X)=s(X)$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in $n$ variables.
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
In PLDI'20, Lee et al. introduced the \emph{promising } semantics PS 2.0 of the C++ concurrency that captures most of the common program transformations while satisfying the DRF guarantee. The reachability problem for finite-state programs…
In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original…
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 Corner (R). Let d and k be positive integers. Define M(k, d x d)…
Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
We study the almost-sure reachability problem in a distributed system obtained as the asynchronous composition of N copies (called processes) of the same automaton (called protocol), that can communicate via a shared register with finite…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…