Related papers: On the Computational Complexity of Limit Cycles in…
We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, including complexity, regularity, and algorithms. Specifically, we…
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…
Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
There are a number of results saying that for certain "path-following" algorithms that solve PPAD-complete problems, the solution obtained by the algorithm is PSPACE-complete to compute. We conjecture that these results are special cases of…
The flow of a $k$-cooperative system maps the set of vectors with up to~$(k-1)$ sign variations to itself. Strongly $2$-cooperative systems satisfy a strong \Poincare-Bendixson property: any bounded solution that evolves in a compact set…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
The aim of this paper is to obtain quantitative bounds for solutions to the optimal matching problem in dimension two. These bounds show that up to a logarithmically divergent shift, the optimal transport maps are close to be the identity…
We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely…
In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit…
Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics…
We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…
The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a…
We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous…
Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By…
We analyze a three-dimensional discontinuous piecewise linear system \(Z=(X,Y)\) whose switching manifold \(\Sigma\) contains visible-visible two-fold intersection lines. Assuming that the matrices \(DX\) and \(DY\) each have one nonzero…
The concept of "limit cycle" was introduced by Henri Poincar\'e in his second memoir "On curves defined by a differential equation" in 1882. From the point of view of physics, a stable limit cycle (or attractive) is the representation of…
We consider the problem of finding a near ground state of a $p$-spin model with Rademacher couplings by means of a low-depth circuit. As a direct extension of the authors' recent work [Gamarnik, Jagannath, Wein 2020], we establish that any…