Related papers: The Reachability Problem for Affine Functions on t…
One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…
We analyze affine reachability problems in dimensions 1 and 2. We show that the reachability problem for 1-register machines over the integers with affine updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel et…
Reachability for piecewise affine systems is known to be undecidable, starting from dimension $2$. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine…
We study the following reachability problem for piecewise affine maps: Given two vectors $\mathbf{s}, \mathbf{t} \in \mathbb{Q}^d$ and a piecewise affine map $f \colon \mathbb{Q}^d\rightarrow \mathbb{Q}^d$, does there exist $n\in…
We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved…
An affine model of computation is defined as a subset of iterated immediate-snapshot runs, capturing a wide variety of shared-memory systems, such as wait-freedom, t-resilience, k-concurrency, and fair shared-memory adversaries. The…
We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given…
In this paper we study the fine-grained complexity of the CFL reachability problem. We first present one of the existing algorithms for the problem and an overview of conditional lower bounds based on widely believed hypotheses. We then use…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and conjunctive…
We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.
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…
The decision problems on matrices were intensively studied for many decades as matrix products play an essential role in the representation of various computational processes. However, many computational problems for matrix semigroups are…
We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such as: Given symbolic specifications of allowed inputs and outputs in form of Linear…
We study the problem of \emph{robust satisfiability} of systems of nonlinear equations, namely, whether for a given continuous function $f:\,K\to\mathbb{R}^n$ on a~finite simplicial complex $K$ and $\alpha>0$, it holds that each function…
The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether…
Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…
We consider the reachability problem for higher-order functional programs and study the relationship between reachability games (i.e., the reachability problem for programs with angelic and demonic nondeterminism) and may-reachability…