CTL$$^*$$ Model Checking for Data-Aware Dynamic Systems with Arithmetic

Abstract

The analysis of complex dynamic systems is a core research topic in formal methods and AI, and combined modelling of systems with data has gained increasing importance in applications such as business process management. In addition, process mining techniques are nowadays used to automatically mine process models from event data, often without correctness guarantees. Thus verification techniques for linear and branching time properties are needed to ensure desired behavior.Here we consider data-aware dynamic systems with arithmetic (DDSAs), which constitute a concise but expressive formalism of transition systems with linear arithmetic guards. We present a CTL$$^*$$ ∗ model checking procedure for DDSAs that addresses a generalization of the classical verification problem, namely to compute conditions on the initial state, called witness maps, under which the desired property holds. Linear-time verification was shown to be decidable for specific classes of DDSAs where the constraint language or the control flow are suitably confined. We investigate several of these restrictions for the case of CTL$$^*$$ ∗ , with both positive and negative results: witness maps can always be found for monotonicity and integer periodicity constraint systems, but verification of bounded lookback systems is undecidable. To demonstrate the feasibility of our approach, we implemented it in an SMT-based prototype, showing that many practical business process models can be effectively analyzed.

Decidable Fragments of LTLf Modulo Theories

“…Our results for the (MC) and (IPC) fragments strictly extend these decidability results, since we only restrict iteration conditions of formulas. The picture gets more diverse for branching-time temporal logics equipped with similar arithmetic theories; in this case, satisfiability and model checking do no longer coincide [11,10,23,21]. Damaggio et al [13] considered LTL model checking for transition systems that operate over databases and include arithmetic conditions, and proved decidability if the system together with the LTL formula satisfies the property of feedback freedom.…”