Zhenya Zhang

Formal verification of transformers has become increasingly important due to their widespread deployment in safety-critical applications. Compared to classic neural networks, the inferences of transformers involve highly complex computations, such as dot products in self-attention layers, rendering their verification extremely difficult. Existing approaches explored over-approximation methods by constructing convex constraints to bound the output ranges of transformers, which can achieve high efficiency. However, they may sacrifice verification precision, and consequently introduce significant approximation error that leads to frequent occurrences of false alarms. In this paper, we propose a transformer verification approach that can achieve improved precision. At the core of our approach is a novel usage of ReLU, by which we represent a precise but non-linear bound for dot products such that we can further exploit the rich body of literature for convex relaxation of ReLU to derive precise bounds. We extend two classic approaches to the context of transformers, a rule-based one and an optimization-based one, resulting in two new frameworks for efficient and precise verification. We evaluate our approaches on different model architectures and robustness properties derived from two datasets about sentiment analysis, and compare with the state-of-the-art baseline approach. Compared to the baseline, our approach can achieve significant precision improvement for most of the verification tasks with acceptable compromise of efficiency, which demonstrates the effectiveness of our approach.

Modern cyber-physical systems are complex, and requirements are often written in Signal Temporal Logic (STL). Writing the right STL is difficult in practice; engineers benefit from concrete executions that illustrate what a specification actually admits. Trace synthesis addresses this need, but a single witness rarely suffices to understand intent or explore edge cases—diverse satisfying behaviors are far more informative. We introduce diversified trace synthesis: the automatic generation of sets of behaviorally diverse traces that satisfy a given STL formula. Building on a MILP encoding of STL and system model, we formalize three complementary diversification objectives—Boolean distance, random Boolean distance, and value distance—all captured by an objective function and solved iteratively. We implement these ideas in STLts-Div, a lightweight Python tool that integrates with Gurobi.

In real-time and safety-critical cyber-physical systems (CPSs), control synthesis must guarantee that generated policies meet stringent timing and correctness requirements under uncertain and dynamic conditions. Signal temporal logic (STL) has emerged as a powerful formalism of expressing real-time constraints, with its semantics enabling quantitative assessment of system behavior. Meanwhile, reinforcement learning (RL) has become an important method for solving control synthesis problems in unknown environments. Recent studies incorporate STL-based reward functions into RL to automatically synthesize control policies. However, the automatically inferred rewards obtained by these methods represent the global assessment of a whole or partial path but do not accumulate the rewards of local changes accurately, so the sparse global rewards may lead to non-convergence and unstable training performances. In this paper, we propose an online reward generation method guided by the online causation monitoring of STL. Our approach continuously monitors system behavior against an STL specification at each control step, computing the quantitative distance toward satisfaction or violation and thereby producing rewards that reflect instantaneous state dynamics. Additionally, we provide a smooth approximation of the causation semantics to overcome the discontinuity of the causation semantics and make it differentiable for using deep-RL methods. We have implemented a prototype tool and evaluated it in the Gym environment on a variety of continuously controlled benchmarks. Experimental results show that our proposed STL-guided RL method with online causation semantics outperforms existing relevant STL-guided RL methods, providing a more robust and efficient reward generation framework for deep-RL.

Timed regular expressions serve as a formalism for specifying real-time behaviors of Cyber-Physical Systems. In this paper, we consider the synthesis of timed regular expressions, focusing on generating a timed regular expression consistent with a given set of system behaviors including positive and negative examples, i.e., accepting all positive examples and rejecting all negative examples. We first prove the decidability of the synthesis problem through an exploration of simple timed regular expressions. Subsequently, we propose our method of generating a consistent timed regular expression with minimal length, which unfolds in two steps. The first step is to enumerate and prune candidate parametric timed regular expressions. In the second step, we encode the requirement that a candidate generated by the first step is consistent with the given set into a Satisfiability Modulo Theories (SMT) formula, which is consequently solved to determine a solution to parametric time constraints. Finally, we evaluate our approach on benchmarks, including randomly generated behaviors from target timed models and a case study.