Computational Complexity for Continuous Time Dynamics

Computational Complexity for Continuous Time Dynamics

Dissipative flows model a large variety of physical systems. In this Letter the evolution of such systems is interpreted as a process of computation; the attractor of the dynamics represents the output. A framework for an algorithmic analysis of dissipative flows is presented, enabling the comparison of the performance of discrete and continuous time analog computation models. A simple algorith...

Computational Complexity of Continuous Problems

Robust Consensus for Continuous-Time Multiagent Dynamics

This paper investigates consensus problems for continuous-time multiagent systems with time-varying communication graphs subject to input noise. Based on input-to-state stability and integral input-to-state stability, robust consensus and integral robust consensus are defined with respect to L∞ and L1 norms of the noise function, respectively. Sufficient and/or necessary connectivity conditions...

Regret-based continuous-time dynamics

Regret-based dynamics have been introduced and studied in the context of discrete-time repeated play. Here we carry out the corresponding analysis in continuous time. We observe that, in contrast to (smooth) fictitious play or to evolutionary models, the appropriate state space for this analysis is the space of distributions on the product of the players’ pure action spaces (rather than the pro...

Inference Complexity in Continuous Time Bayesian Networks

The continuous time Bayesian network (CTBN) enables temporal reasoning by representing a system as a factored, finite-state Markov process. The CTBN uses a traditional Bayesian network (BN) to specify the initial distribution. Thus, the complexity results of Bayesian networks also apply to CTBNs through this initial distribution. However, the question remains whether propagating the probabiliti...