The paper presents a method for synthesizing and verifying Deterministic Register Automata (DRAs) over ordered data sequences such as time series and sensor streams. It introduces a local‑search synthesis procedure and an exact robustness checker that runs in polynomial time for a fixed number of registers, reducing robustness to a shortest‑path problem. The framework, implemented in RAExc, is applied to learn interpretable surrogate models for neural sequence classifiers, providing statistical guarantees of fidelity and local stability while verifying robustness on benchmark languages and sequentialized MNIST.
arXiv:2602.07599v2 Announce Type: replace Abstract: Standard Transformers excel at semantic modeling but struggle with rigid sequential logic and state tracking. Theoretical work establishes that...
The paper presents a polynomial‑time active learning procedure for deterministic register automata (DRAs) over ordered data domains, covering both dense domains like the rationals and non‑dense domains such as the integers. It unifies the learning framework for these domains using membership, equivalence, and memorability queries, and shows that minimization of DRAs over the integer domain is decidable. Additionally, the authors provide improved complexity bounds for several decision problems related to DRAs over ordered domains.
The paper evaluates how robust large language models are at generating SystemVerilog Assertions (SVA) when the underlying RTL code undergoes semantics‑preserving transformations such as operand reordering, identifier renaming, and redundant parenthesization. Using a curated dataset and two open‑source models (Qwen2.5‑Coder‑7B and DeepSeek‑Coder‑V2‑Lite), the authors find that 9.7%–27.0% of behaviors that were correct on the original RTL become incorrect after transformation, revealing significant instability that aggregate accuracy metrics can hide.
arXiv:2606. 29700v1 Announce Type: new Abstract: Planning often requires symbolic specifications that are both executable and verifiable.
The paper identifies a new failure mode in neurosymbolic systems called Verdict‑Preserving‑Unfaithfulness (VPU), where incorrect formal encodings can still pass solver checks. It introduces Generative Verification (GenV), a method that uses a language model to produce a continuous reference‑equivalence score without relying on explicit localization. Experiments show GenV+HN achieves high AUROC, generalizes to unseen translators, and improves downstream agent performance by 11.3 points.
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
arXiv:2607. 04631v1 Announce Type: new Abstract: The cost of producing code is rapidly diminishing with increasingly capable AI agents, while quality assurance of generated programs has not kept pace.
The paper presents a method for probabilistic model checking of autoregressive neural sequence models. It extracts a discrete-time Markov chain from the model’s token generation, verifies PCTL specifications with PRISM, and aggregates verdicts into a coverage curve over the input space. The approach includes a soundness theorem, a counterexample-guided refinement loop, and a maximum-likelihood algorithm to find the most probable falsifying trace, demonstrated on GPT‑2 and a SMILES molecular generator.
FormalEvolve is a neuro‑symbolic evolutionary search framework that treats autoformalization as a budgeted test‑time search problem. It builds a compilation‑feasible archive of formal statements and expands it using LLM‑driven mutation, crossover, bounded patch repair, and symbolic AST rewrites to generate diverse, semantically accepted formalizations. In experiments on CombiBench and ProofNet, FormalEvolve achieves higher SH@100 scores and improves theorem‑complete proving under fixed prover budgets compared to no‑archive baselines.
The paper introduces a neuro‑symbolic framework for scientific reasoning that separates symbolic validity and semantic groundedness. A deterministic symbolic verifier acts as a hard filter to guarantee syntactic and arithmetic correctness, while a Process Reward Model (PRM) is trained on verifier‑accepted steps to assess contextual grounding. The authors propose Counterfactual Symbolic Perturbation (CSP) to generate hard negative examples that pass the verifier but are logically flawed, enabling efficient PRM training and a verifier‑first constrained search at inference.
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
arXiv:2606. 09930v1 Announce Type: cross Abstract: The boundary between program execution and gradient-based optimization has long limited the use of code itself as a learnable scientific model.