相关论文: On the complexity of bounded time and precision re…
We study the Poincare-Bendixson theorem for two-dimensional continuous dynamical systems in compact domains from the point of view of computation, seeking algorithms for finding the limit cycle promised by this classical result. We start by…
The notion of compliance in Multiset Rewriting Models (MSR) has been introduced for untimed models and for models with discrete time. In this paper we revisit the notion of compliance and adapt it to fit with additional nondeterminism…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
We show that several reconfiguration problems known to be PSPACE-complete remain so even when limited to graphs of bounded bandwidth. The essential step is noticing the similarity to very limited string rewriting systems, whose ability to…
We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of…
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…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the…
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…
We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…
In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The…
This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems,…
This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
Given a topologically transitive system on the unit interval, one can investigate the cover time, i.e. time for an orbit to reach certain level of resolution in the repeller. We introduce a new notion of dimension, namely the stretched…
We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned…
We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they…
The paper deals with the verification of reachability properties in a commonly used state transition model of communication protocols, which consists of finite state machines connected by potentially unbounded FIFO channels. Although simple…