Any-Horizon Uniform Random Sampling and Enumeration of Constrained Scenarios for Simulation-Based Formal Verification

Abstract

Model-based approaches to the verification of non-terminating Cyber-Physical Systems (CPSs) usually rely on numerical simulation of the System Under Verification (SUV) model under input scenarios of possibly varying duration, chosen among those satisfying given constraints. Such constraints typically stem from requirements (or assumptions) on the SUV inputs and its operational environment as well as from the enforcement of additional conditions aiming at, e.g., prioritising the (often extremely long) verification activity, by, e.g., focusing on scenarios explicitly exercising selected requirements, or avoiding vacuity in their satisfaction. In this setting, the possibility to efficiently sample at random (with a known distribution, e.g., uniformly) within, or to efficiently enumerate (possibly in a uniformly random order) scenarios among those satisfying all the given constraints is a key enabler for the practical viability of the verification process, e.g., via simulation-based statistical model checking. Unfortunately, in case of non-trivial combinations of constraints, iterative approaches like Markovian random walks in the space of sequences of inputsin general fail in extracting scenarios according to a given distribution (e.g., uniformly), and can be very inefficient to produce at all scenarios that are both legal (with respect to SUV assumptions) and of interest (with respect to the additional constraints). For example, in our case studies, up to 91% of the scenarios generated using such iterative approaches would need to be neglected. In this article, we show how, given a set of constraints on the input scenarios succinctly defined by multiple finite memory monitors, a data structure (scenario generator ) can be synthesised, from which any-horizon scenarios satisfying the input constraints can be efficiently extracted by (possibly uniform) random sampling or (randomised) enumeration. Our approach enables seamless support to virtually all simulation-based approaches to CPS verification, ranging from simple random testing to statistical model checking and formal (i.e., exhaustive) verification, when a suitable bound on the horizon or an iterative horizon enlargement strategy is defined, as in the spirit of bounded model checking.

Optimizing Highly-Parallel Simulation-Based Verification of Cyber-Physical Systems

“…As argued in [38], our assumptions are in line with an engineering (rather than purely mathematical) point of view, where man-made CPSs need to satisfy the properties under verification with some degree of robustness with respect to the actual input time functions (see, e.g., [1], [16] and references thereof). Our case studies in Section 6 contain uses of several of such features, and show that our setting can be easily met in practice.…”

“…To overcome this obstruction, previous work [28], [38] proposed to lift the hand-crafted definition of operational scenarios into the definition of a declarative constraint-based specification of the system operational environment via an automaton encoded in a high-level language. The set of possible scenarios against which to verify the CPS model is then defined as the set of time series of inputs and other uncontrollable events encoded by accepting computation paths on such an automaton.…”

“…The set of possible scenarios against which to verify the CPS model is then defined as the set of time series of inputs and other uncontrollable events encoded by accepting computation paths on such an automaton. Also, one such form of automaton, named scenario generator in [38], allows the efficient extraction of any of its entailed scenarios from their unique indices. The definition of the CPS operational environment by such high-level models greatly eases the task of the verification engineers to capture all scenarios deemed plausible, also allowing them to dynamically focus on those scenarios satisfying additional constraints (see [38] for examples), thus enabling prioritisation of the (typically very long) verification activity.…”

“…Input traces are given either explicitly in the form of a database in mass memory, or symbolically, by means of a scenario generator, as designed in [38]. In particular, a scenario generator G is a symbolic data structure built from a set of requirements (or constraints), in turn defined by means of multiple automata (monitors).…”

XGB-Hybrid Fingerprint Classification Model for Virtual Screening of Meningitis Drug Compounds Candidate

“…However, not all data decoys are used to form the dataset. This study randomly selected decoy data to balance and enrich the data used [32]. The election results leave as many as 6608 decoy data which means about 5% of the total previous data.…”