Invariants and Home Spaces in Transition Systems and Petri Nets

This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can be used for extracting invariant properties from a parallel system described by a Labeled Transition System in general and a Petri Net in particular. We endeavor to regroup a number of algebraic results dispersed throughout the Petri Nets literature with the addition of new results around the notions of semiflows and generating sets. Examples are given to illustrate how invariants can be handled to prove behavioral properties of a Petri Net. Some additional thoughts on invariants and home spaces will conclude this note.Comment: 83 page

Modeling the Temperature Bias of Power Consumption for Nanometer-Scale CPUs in Application Processors

We introduce and experimentally validate a new macro-level model of the CPU temperature/power relationship within nanometer-scale application processors or system-on-chips. By adopting a holistic view, this model is able to take into account many of the physical effects that occur within such systems. Together with two algorithms described in the paper, our results can be used, for instance by engineers designing power or thermal management units, to cancel the temperature-induced bias on power measurements. This will help them gather temperature-neutral power data while running multiple instance of their benchmarks. Also power requirements and system failure rates can be decreased by controlling the CPU's thermal behavior. Even though it is usually assumed that the temperature/power relationship is exponentially related, there is however a lack of publicly available physical temperature/power measurements to back up this assumption, something our paper corrects. Via measurements on two pertinent platforms sporting nanometer-scale application processors, we show that the power/temperature relationship is indeed very likely exponential over a 20{\deg}C to 85{\deg}C temperature range. Our data suggest that, for application processors operating between 20{\deg}C and 50{\deg}C, a quadratic model is still accurate and a linear approximation is acceptable.Comment: Submitted to SAMOS 2014; International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation (SAMOS XIV