An Efficient Algorithm for Computing Causal Trace Sets in Causality Checking

Abstract

Causality Checking [LL13a] has been proposed as a finite state space exploration technique which computes ordered sequences of events that are considered to cause the violation of a reachability property. A crucial point in the implementation of Causality Checking is the computation and storage of all minimal counterexamples found during state space exploration. We refer to the set of all minimal counterexamples as a causal trace set. However, the Duplicate State Prefix Matching (DSPM) Algorithm that is currently used in Causality Checking only under-approximates the causal trace set. As we argue, without the approximation the DSPM algorithm is inefficient. We propose the, to the best of our knowledge, first efficient algorithm that precisely computes a causal trace set, avoiding approximation, called Causal Trace Backward Search (CTBS). We compare the DSPM and CTBS a lgorithms with respect to their worst case complexities, and by applying them to several case studies.

From Verification to Causality-Based Explications (Invited Talk)

“…There, causes for reachability properties are formulas of a temporal logic called event order logic, used to describe temporal relations between events. Algorithms to compute causes in this sense were also studied in [15,77], and the approach was extended to handle general LTL formulas as effects rather than just reachability in [20].…”

An Algorithm to Compute a Strict Partial Ordering of Actions in Action Traces

“…Currently, QuantUM depicts the set of actions in a causality class by a fault tree without indicating the order of the contained actions. In previous work, amongst others we applied Causality Checking to the architecture of a self-driving car [KL19], and showed that Causality Checking supports the safety assessment in the development of a safety-critical system.…”

“…Afterwards, QuantUM pools the causal action traces with the same set of actions to a causality class. The disjunction of the different causality classes constitutes the cause of the property violation and will be displayed as a fault tree [KL19]. Currently, QuantUM depicts the set of actions in a causality class by a fault tree without indicating the order of the contained actions.…”

“…1(c). In [KL19], we analyzed a slightly different model of the railroad crossing example which includes the functionality of a gate. Without the use of the algorithms proposed in the current paper, QuantUM computes the fault tree in Fig.…”

“…Without the use of the algorithms proposed in the current paper, QuantUM computes the fault tree in Fig. 2 in [KL19] that does not depict the order of the actions. When using the proposed algorithms, QuantUM computes the fault tree in Fig.…”