Costs and Rewards in Priced Timed Automata

We consider Pareto analysis of reachable states of multi-priced timed automata (MPTA): timed automata equipped with multiple observers that keep track of costs (to be minimised) and rewards (to be maximised) along a computation. Each observer has a constant non-negative derivative which may depend on the location of the MPTA. We study the Pareto Domination Problem, which asks whether it is possible to reach a target location via a run in which the accumulated costs and rewards Pareto dominate a given objective vector. We show that this problem is undecidable in general, but decidable for MPTA with at most three observers. For MPTA whose observers are all costs or all rewards, we show that the Pareto Domination Problem is PSPACE-complete. We also consider an epsilon-approximate Pareto Domination Problem that is decidable without restricting the number and types of observers. We develop connections between MPTA and Diophantine equations. Undecidability of the Pareto Domination Problem is shown by reduction from Hilbert\u27s 10^{th} Problem, while decidability for three observers is shown by a translation to a fragment of arithmetic involving quadratic forms

Risk-Averse Model Predictive Control for Priced Timed Automata

In this paper, we propose a Risk-Averse Priced Timed Automata (PTA) Model Predictive Control (MPC) framework to increase flexibility of cyber-physical systems. To improve flexibility in these systems, our risk-averse framework solves a multi-objective optimization problem to minimize the cost and risk, simultaneously. While minimizing cost ensures the least effort to achieve a task, minimizing risk provides guarantees on the feasibility of the task even during uncertainty. Our framework explores the trade-off between these two qualities to obtain risk-averse control actions. The solution of risk-averse PTA MPC dynamic decision-making algorithm reacts relatively better to PTA changes compared to PTA MPC without risk-averse feature. An example from manufacturing systems is presented to show the application of the proposed control strategy.Comment: 7 page

Green computing: power optimisation of VFI-based real-time multiprocessor dataflow applications (extended version)

Execution time is no longer the only performance metric for computer systems. In fact, a trend is emerging to trade raw performance for energy savings. Techniques like Dynamic Power Management (DPM, switching to low power state) and Dynamic Voltage and Frequency Scaling (DVFS, throttling processor frequency) help modern systems to reduce their power consumption while adhering to performance requirements. To balance flexibility and design complexity, the concept of Voltage and Frequency Islands (VFIs) was recently introduced for power optimisation. It achieves fine-grained system-level power management, by operating all processors in the same VFI at a common frequency/voltage.This paper presents a novel approach to compute a power management strategy combining DPM and DVFS. In our approach, applications (modelled in full synchronous dataflow, SDF) are mapped on heterogeneous multiprocessor platforms (partitioned in voltage and frequency islands). We compute an energy-optimal schedule, meeting minimal throughput requirements. We demonstrate that the combination of DPM and DVFS provides an energy reduction beyond considering DVFS or DMP separately. Moreover, we show that by clustering processors in VFIs, DPM can be combined with any granularity of DVFS. Our approach uses model checking, by encoding the optimisation problem as a query over priced timed automata. The model-checker Uppaal Cora extracts a cost minimal trace, representing a power minimal schedule. We illustrate our approach with several case studies on commercially available hardware

Model-Based Verification, Optimization, Synthesis and Performance Evaluation of Real-Time Systems

International audienceThis article aims at providing a concise and precise Travellers Guide, Phrase Book or Reference Manual to the timed automata modeling formalism introduced by Alur and Dill [8, 9]. The paper gives comprehensive definitions of timed automata, priced (or weighted) timed automata, and timed games and highlights a number of results on associated decision problems related to model checking, equivalence checking, optimal scheduling, the existence of winning strategies, and then statistical model checking

On the complexity of resource-bounded logics

We revisit decidability results for resource-bounded logics and use decision problems on vector addition systems with states (VASS) in order to establish complexity characterisations of (decidable) model checking problems. We show that the model checking problem for the logic RB+-ATL is 2EXPTIME-complete by using recent results on alternating VASS (and in EXPTIME when the number of resources is bounded). Moreover, we establish that the model checking problem for RBTL is EXPSPACE-complete. The problem is decidable and of the same complexity for RBTL*, proving a new decidability result as a by-product of the approach. When the number of resources is bounded, the problem is in PSPACE. We also establish that the model checking problem for RB+-ATL*, the extension of RB+-ATL with arbitrary path formulae, is decidable by a reduction to parity games for single-sided VASS (a variant of alternating VASS). Furthermore, we are able to synthesise values for resource parameters. Hence, the paper establishes formal correspondences between model checking problems for resource bounded logics advocated in the AI literature and decision problems on alternating VASS, paving the way for more applications and cross-fertilizations