Simulation-based verification of hybrid automata stochastic logic formulas for stochastic symmetric nets

Abstract

The Hybrid Automata Stochastic Logic (HASL) has been recently defined as a flexible way to express classical performance measures as well as more complex, path-based ones (generically called "HASL formulas"). The considered paths are executions of Generalized Stochastic Petri Nets (GSPN), which are an extension of the basic Petri net formalism to define discrete event stochastic processes. The computation of the HASL formulas for a GSPN model is demanded to the COSMOS tool, that applies simulation techniques to the formula computation. Stochastic Symmetric Nets (SSN) are a high level Petri net formalism, of the colored type, in which tokens can have an identity, and it is well known that colored Petri nets allow one to describe systems in a more compact and parametric form than basic (uncolored) Petri nets. In this paper we propose to extend HASL and COSMOS to support colors, so that performance formulas for SSN can be easily defined and evaluated. This requires a new definition of the logic, to ensure that colors are taken into account in a correct and useful manner, and a significant extension of the COSMOS tool.

Modelling and Evaluation of a Control Room Application

“…Stochastic logics for CTMCs define formulas of the type Prob α (ϕ) that are satisfied by a CTMC if the probability of the set of executions of the CTMC that satisfy the constraints ϕ is α. The most well-known of the stochastic logics is CSL [7], that, in the desire to limit the cost of the model-checking, trades simplicity of ϕ for efficiency, resulting in a logic that is not adequate for passage time computation [4].…”

“…The relationship between passage time and stochastic logics has been investigated in [4], in the context of HASL (Hybrid Automata Stochastic Logic) [10]. HASL allows very complicated properties to be expressed as Prob α (H), where H is an Hybrid Automata.…”

“…Cosmos [9] is a simulation-based model-checker for HASL that operates on systems specified as Petri nets. Following the approach in [4] we use a stochastic logic to compute the passage times. We have used CSL TA : the reason why CSL TA has been preferred over HASL is that CSL TA is part of the GreatSPN suite and allows an exact numerical solution, while HASL properties can only be checked through simulation.…”

“…Following the ideas in [4] the DTA of Figure 6 accepts, at the beginning (while in location l 3 ) all the GSPN behaviours (Act stays for "any transition firing", there is no constraint on the value of the clock x, and the atomic proposition associated to l 3 is Fig. 8.…”

HASL: A new approach for performance evaluation and model checking from concepts to experimentation

“…Accuracy comparison. To assess the accuracy of COSMOS we compared its output with the one produced by PRISM via both its numerical engine (PRISM-n) and its statistical engine (PRISM-s) 5 : results indicate that COSMOS and PRISM-s are comparably accurate with the estimated intervals always containing the (actual) value obtained with the numerical engine of PRISM. Using the value computed by the numerical engine of PRISM, we perform a coverage test of COSMOS: we compute the ratio of simulations that return a confidence interval which contains the real value.…”