We report on our ongoing project to develop a computational pipeline, AutoGraphForge, for an automated graph-theoretic conjecturing-refuting-formalizing-proving system. Conjecture generation is counterexample-guided and runs in rounds: a Graffiti3 generator proposes conjectures over a small, evolving snapshot table $T$ (initially a few hundred graphs with their computed invariants) that grows only by counterexamples to its own conjectures. A novelty filter of $559$ classical and folklore relations, closed under transitive composition and linear identity substitution, decides via a linear program whether a candidate is already implied by known results. Surviving candidates are tested against a dataset of about $348,000$ graphs, unioning the complete House of Graphs invariant export, the exhaustive census of all connected graphs on at most nine vertices, several extremal families (strongly regular, minimal Ramsey, Cayley, cages, barbells, lollipops, spiders), and random models. Counterexample-search algorithms then attack the remainder. Run for several rounds on an HPC cluster, the loop yields $6,522$ conjectures that survived the refutation dataset, the novelty filter and every active-search run -- among them nontrivial relations between the annihilation number and the edge-cover number for bipartite and regular graphs, which we prove by hand. A subsequent formalization and proving stage deterministically translates each surviving conjecture into a Lean 4 statement skeleton; every candidate proof is kernel-verified against a pinned mathlib4 and our custom invariant preamble. This stage integrates two neural provers -- DeepSeek-Prover-V2-671B (served with vLLM) and the Lean-specialised OProver-32B -- behind the independent kernel check. It is implemented end-to-end and passes initial sanity checks, with the full pipeline currently running on the cluster.
Ioannis Protogeros, Tibor Schneider, Laurent Vanbevercs.NI cs.AI
Symbolic network verifiers can reason about correctness across vast spaces of routing inputs and failures, but only for the protocols and features an expert has encoded by hand. Creating and maintaining a faithful model of the control plane is both difficult and never-ending, since no written source specifies perfectly what a network does: vendor implementations deviate from the RFCs, and behaviour shifts with releases. The burden of constant upkeep ultimately keeps verification out of many networks that need it. We argue that the model should instead evolve automatically to faithfully capture the actual network behaviour. To achieve that, we leverage the only source that specifies it unambiguously: the router software itself. In a counterexample-guided loop, a coding agent proposes extensions to the verifier's symbolic encoding, while a trusted oracle (e.g., emulated routers) supplies the ground-truth routing state. The agent iteratively refines the network model using each disagreement with the oracle. As early evidence, a prototype of this system taught a 3,000-line SMT-based verifier three features it did not support: OSPF areas, BGP route reflection, and L3VPN over EVPN, converging autonomously on models that match the oracle, even noticing vendor-specific behaviour. Automating model growth shifts the hard problem from writing verification systems to systematically testing them; we propose a research agenda for trusting and harnessing automatically evolved verifiers.