The boundary conditions (BCs) have shown great potential in requirements engineering because a BC captures the particular combination of circumstances, i.e., divergence, in which the goals of the requirement cannot be satisfied as a whole. Existing researches have attempted to automatically identify lots of BCs. Unfortunately, a large number of identified BCs make assessing and resolving divergences expensive. Existing methods adopt a coarse-grained metric, generality, to filter out less general BCs. However, the results still retain a large number of redundant BCs since a general BC potentially captures redundant circumstances that do not lead to a divergence. Furthermore, the likelihood of BC can be misled by redundant BCs resulting in costly repeatedly assessing and resolving divergences.In this paper, we present a fine-grained metric to filter out the redundant BCs. We first introduce the concept of contrasty of BC. Intuitively, if two BCs are contrastive, they capture different divergences. We argue that a set of contrastive BCs should be recommended to engineers, rather than a set of general BCs that potentially only indicates the same divergence. Then we design a post-processing framework (P P F c ) to produce a set of contrastive BCs after identifying BCs. Experimental results show that the contrasty metric dramatically reduces the number of BCs recommended to engineers. Results also demonstrate that lots of BCs identified by the state-of-the-art method are redundant in most cases. Besides, to improve efficiency, we propose a joint framework (J F c ) to interleave assessing based on the contrasty metric with identifying BCs. The primary intuition behind J F c is that it considers the search bias toward contrastive BCs during

Learning linear temporal logic on finite traces (LTLf) formulae aims to learn a target formula that characterizes the high-level behavior of a system from observation traces in planning. Existing approaches to learning LTLf formulae, however, can hardly learn accurate LTLf formulae from noisy data. It is challenging to design an efficient search mechanism in the large search space in form of arbitrary LTLf formulae while alleviating the wrong search bias resulting from noisy data. In this paper, we tackle this problem by bridging LTLf inference to GNN inference. Our key theoretical contribution is showing that GNN inference can simulate LTLf inference to distinguish traces. Based on our theoretical result, we design a GNN-based approach, GLTLf, which combines GNN inference and parameter interpretation to seek the target formula in the large search space. Thanks to the non-deterministic learning process of GNNs, GLTLf is able to cope with noise. We evaluate GLTLf on various datasets with noise. Our experimental results confirm the effectiveness of GNN inference in learning LTLf formulae and show that GLTLf is superior to the state-of-the-art approaches.

Linear temporal logic over finite traces (LTLf) satisfiability checking is a fundamental and hard (PSPACE-complete) problem in the artificial intelligence community. We explore teaching end-to-end neural networks to check satisfiability in polynomial time. It is a challenge to characterize the syntactic and semantic features of LTLf via neural networks. To tackle this challenge, we propose LTLfNet, a recursive neural network that captures syntactic features of LTLf by recursively combining the embeddings of sub-formulae. LTLfNet models permutation invariance and sequentiality in the semantics of LTLf through different aggregation mechanisms of sub-formulae. Experimental results demonstrate that LTLfNet achieves good performance in synthetic datasets and generalizes across large-scale datasets. They also show that LTLfNet is competitive with state-of-the-art symbolic approaches such as nuXmv and CDLSC.

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