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.

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.