DeepCTL: Neural Branching-Time CTL Satisfiability Checking via Recursive Decision Trees

Computation Tree Logic (CTL) satisfiability checking is a cornerstone of formal verification, yet traditional model checkers like nuXmv struggle with scalability due to the exponential complexity of branching-time semantics. To address this, we propose DeepCTL, the first neural framework for CTL satisfiability checking that operates in polynomial time. Unlike prior works focused on linear-time logics (e.g., LTL), DeepCTL explicitly models CTL’s branching paths and recursive structure through three key modules: (1) feature embedding via hybrid encoding, (2) semantic learning using specialized architectures (Transformer, GNN, RvNN), and (3) a novel Recursive Neural Decision Tree Network (RvNDTN) that integrates path probabilities to handle universal (∀) and existential (∃) quantifiers. Experiments on synthetic and real-world datasets (e.g., NASA-Boeing) demonstrate DeepCTL’s efficiency: it achieves 99.21% accuracy on unbalanced-CTL formulas and processes large formulas (>1000 nodes) 10× faster than nuXmv. By preserving CTL’s recursivity, permutation-invariance, and sequentiality, DeepCTL generalizes across formula distributions and lengths, offering a scalable alternative to symbolic methods. While its reliance on learned approximations limits formal guarantees, DeepCTL is particularly valuable for rapid hypothesis testing in early-stage system design. This work bridges neural efficiency with temporal logic reasoning, opening new avenues for applying deep learning to formal verification.