Due to the high complexity of linear temporal logic (LTL) satisfiability checking (PSPACE-complete), its applications in downstream testing tasks are limited. Neural networks are promising to approximately check LTL satisfiability in polynomial time. However, there is a lack of effective neural-network-based approaches to SAT-verifiably check LTL satisfiability, where if a formula is satisfiable, approaches generate its satisfiable trace as evidence.

In this paper, we tackle SAT-verifiable LTL satisfiability checking via bridging LTL trace checking to neural network inference. Our key theoretical contribution is to show that a well-designed neural network inference, called neural trace checking, can simulate LTL trace checking. We design a neural-network-based approach, VSCNet, which benefits from differentiable neural trace checking such that it is able to effectively jointly learn to check satisfiability and generate traces via gradient descent. Experimental results confirm the effectiveness of our theoretical contribution and show that VSCNet significantly improves the state-of-the-art performance on trace generation (at least up to $35.79%$ accuracy improvements on in-distribution datasets). Besides, in the best case, VSCNet can achieve $186$X speedup than the state-of-the-art logic-based approach nuXmv on large-scale datasets.