It is important to automatically discover the underlying tree-structured formulae from large amounts of data. In this paper, we examine learning linear temporal logic on finite traces (LTLf) formulae, which is a tree structure syntactically and characterizes temporal properties semantically. Its core challenge is to bridge the gap between the concise tree-structured syntax and the complex LTLf semantics. Besides, the learning quality is endangered by explosion of the search space and wrong search bias guided by imperfect data. We tackle these challenges by proposing an LTLf encoding method to parameterize a neural network so that the neural computation is able to simulate the inference of LTLf formulae. We first identify faithful LTLf encoding, a subclass of LTLf encoding, which has a one-to-one correspondence to LTLf formulae. Faithful encoding guarantees that the learned parameter assignment of the neural network can directly be interpreted to an LTLf formula. With such an encoding method, we then propose an end-to-end approach, TLTLf, to learn LTLf formulae through neural networks parameterized by our LTLf encoding method. Experimental results demonstrate that our approach achieves state-of-the-art performance with up to 7% improvement in accuracy, highlighting the benefits of introducing the faithful LTLf encoding.

Linear temporal logic (LTL) satisfiability checking has a high complexity, i.e., PSPACE-complete. Recently, neural networks have been shown to be promising in approximately checking LTL satisfiability in polynomial time. However, there is still a lack of neural network-based approach to the problem of checking LTL satisfiability and generating traces as evidence, simply called SAT-and-GET, where a satisfiable trace is generated as evidence if the given LTL formula is detected to be satisfiable. In this paper, we tackle SAT-and-GET via bridging LTL trace checking to neural network inference. Our key theoretical contribution is to show that a well-designed neural inference process, named after neural trace checking, is able to simulate LTL trace checking. We present a neural network-based approach VSCNet. Relying on the differentiable neural trace checking, VSCNet is able to learn both to check satisfiability and to generate traces via gradient descent. Experimental results confirm the effectiveness of VSCNet, showing that it significantly outperforms the state-of-the-art (SOTA) neural network-based approaches for trace generation, on average achieving up to 41.68% improvement in semantic accuracy. Besides, compared with the SOTA logic-based approach nuXmv and Aalta, VSCNet achieves averagely 186X and 3541X speedups on large-scale datasets, respectively.

We study the problem of learning a single occurrence regular expression with interleaving (SOIRE) from a set of text strings possibly with noise. SOIRE fully supports interleaving and covers a large portion of regular expressions used in practice. Learning SOIREs is challenging because it requires heavy computation and text strings usually contain noise in practice. Most of the previous studies only learn restricted SOIREs and are not robust on noisy data. To tackle these issues, we propose a noise-tolerant differentiable learning approach SOIREDL for SOIRE. We design a neural network to simulate SOIRE matching and theoretically prove that certain assignments of the set of parameters learnt by the neural network, called faithful encodings, are one-to-one corresponding to SOIREs for a bounded size. Based on this correspondence, we interpret the target SOIRE from an assignment of the set of parameters of the neural network by exploring the nearest faithful encodings. Experimental results show that SOIREDL outperforms the state-of-the-art approaches, especially on noisy data.

With the superior learning ability of neural networks, it is promising to obtain highly confident results for linear temporal logic (LTL) satisfiability checking in polynomial time. However, existing neural approaches are limited in inductive ability and in supporting with an arbitrary number of atomic propositions. Besides, there is no mechanism to verify the results for satisfiability checking. In this paper, we propose an approach to checking the satisfiability of an LTL formula and meanwhile generating a satisfiable trace if the LTL formula is satisfiable, where the satisfiable trace verifies the satisfiability result. The core contribution is a new graph representation for LTL formulae - one-step unfolded graph (OSUG) to incorporate the syntax and semantic features of LTL. Preliminary results show that our approach is superior to the state-of-the-art neural approaches on synthetic datasets and confirms the effectiveness of OSUG.

Formal specifications are widely used in software testing approaches, while writing such specifications is a time-consuming job. Recently, a number of methods have been proposed to mine specifications from execution traces, typically in the form of linear temporal logic (LTL). However, existing works have the following disadvantages: (1) ignoring the negative impact of imperfect traces, which come from partial profiling, missing context information, or buggy programs; (2) relying on templates, resulting in limited expressiveness; (3) requesting negative traces, which are usually unavailable in practice. In this paper, we propose PURLTL, which is able to mine arbitrary LTL specifications from imperfect traces. To alleviate the search space explosion and the wrong search bias, we propose a neural-based method to search LTL formulae, which, intuitively, simulates LTL path checking through differentiable parameter operations. To solve the problem of lacking negative traces, we transform the problem into learning from positive and unlabeled samples, by means of data augmentation and applying positive and unlabeled learning to the training process. Experiments show that our approach surpasses the previous start-of-the-art (SOTA) approach by a large margin. Besides, the results suggest that our approach is not only robust with imperfect traces, but also does not rely on formula templates.

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.