🛰️
Tool Space Exploration
Collect real MCP & web agent trajectories, then mine adjacent calls with deterministic rules — shared arguments become data edges, state preconditions become state edges, repeated-after-failure calls become retry edges. Cluster the weighted graph into environments; synthesize a database only for operation clusters, restore snapshots for state-query tools, replay cached returns for stateless ones.
𝒢TS = (𝒱, ℰ, w) · 69 / 25 / 6 edge mix
🎲
State-Aware Random Walks + Rollback
From a tool bound to \((𝒟_k, s_0)\), repeatedly sample a state-compatible successor proportionally to edge weight and execute it. Every argument must trace to the task, \(s_0\), or an earlier return. A failed or relation-violating step restores \(s_{t-1}\) and resamples — chains that cannot proceed are discarded.
P(vt+1=v ∣ vt) = w(vt,v) / Σu w(vt,u)
✅
Decompile, Verify, Replay
Each successful walk \(\omega\) is decompiled into a natural-language task \(q\) (no tool names, no call order) plus assertions over final state, intermediate snapshots, and required output fields. The sample enters \(\mathcal{X}_{TS}\) only if re-executing \(\omega\) from \(s_0\) passes every check.
V = Vstate ∪ Vtrace ∪ Vout · replay or discard