Harnessing LLMs as Agents: What Does It Cost?

Language-model agents increasingly rely on harnesses that manage bounded context, persistent memory, tools, verification, and repeated execution, yet existing notions of model capability do not capture the computational resources these mechanisms consume. We study these costs through the *Language Model Agent Machine* (LAM), a resource-bounded model that fixes the underlying semantic model while explicitly accounting for harness-level resources. Our theory yields four main results: **Communication:** LAM execution is instancewise equivalent to red–blue pebbling under joint call–transfer budgets, characterizing the discrete resource frontier and transferring classical I/O lower bounds to context–memory traffic. **Access:** memory interfaces can change asymptotic cost, including a $\Theta (n)$ separation between random and non-speculative sequential access for pointer chasing and an exact frontier for single-stack FIFO access. **Recomputation:** bit-reversal DAGs require $\Theta (n^2/(C+S)+n)$ model calls with context capacity $C$ and persistent-memory capacity $S$, quantifying when stored intermediate state avoids repeated semantic computation. **Reliability:** we derive tight stage-local sampling bounds, exact imperfect-verification costs, and a Young–Daly-type checkpoint law with a closed-form optimal verification interval. Controlled and held-out experiments on GPT-6 Astra compare these predictions with observed measurements, including checkpoint optima and a held-out policy-selection tournament conditioned on a programmatic segment check. Held-out chained MATH further illustrates the tradeoff between whole-task call granularity, logical input traffic, and reliability, while prescribed-schedule runs are reported separately as implementation checks. Together, these results provide a resource theory for the computational cost of language-model agent harnesses. Project page: https://anonymous1776research.github.io/LAM-ICLR2027/.