Massively Decomposed Agentic Processes (MDAPs)

• MDAPs are formal frameworks that decompose high-level intents into fine-grained microtasks executed by independent agents, ensuring modularity and error isolation.
• They employ rigorous orchestration mechanisms, including localized error correction and voting schemes, to control context drift and achieve high reliability.
• MDAPs have practical applications in industrial automation and scalable symbolic reasoning, as demonstrated by predictive maintenance and Towers of Hanoi case studies.

Massively Decomposed Agentic Processes (MDAPs) are formal frameworks and architectures for scaling agentic systems to complex or long-horizon tasks by decomposing high-level objectives into large numbers of fine-grained, minimally scoped microtasks. Each microtask—or "micro-subtask"—is executed by an independent autonomous agent (microagent), typically leveraging LLMs for planning, action selection, and tool invocation. MDAP approaches are explicitly designed to address reliability, scalability, transparency, and compositionality in domains ranging from industrial automation to symbolic reasoning and beyond (Romero et al., 5 Jun 2025, Meyerson et al., 12 Nov 2025).

1. Formal Models and Definitions

The core of MDAP is a rigorous decomposition procedure, transforming a high-level intent or multi-step task into a set of independent, atomic subproblems, each solved by a dedicated agentic call.

Industrial Automation Paradigm

In agentic industrial automation, an MDAP is formally captured as the tuple

$$\text{MDAP} = (I, A_0, \{A_j\}_{j=1..M}, \text{Tools})$$

• $I$: High-level intent (natural language).
• $A_0$: Root agent, responsible for parsing and decomposing $I$.
• $\{A_j\}$: Specialized sub-agents (domain skills, tool access).
• $\text{Tools}$: Library of permitted callable APIs/functions.

The intent $I$ is parsed into components:

$I = \{E, C, T, X, D\}$

• $E=\{e_1,\dots,e_p\}$: Expectations.
• $C=\{c_1,\dots,c_q\}$: Conditions (over states, KPIs).
• $T=\{t_1,\dots,t_r\}$: Targets (entities/resources).
• $X$: Contextual parameters.
• $D$: Data/Information.

Microagent Decomposition for Sequential Tasks

In the context of complex sequential tasks (e.g., Towers of Hanoi), MDAP is defined for an $s$-step task using $s$ microagents:

• State $x_0$; action sequence $A=(a_1,\dots,a_s)$.
• Each microagent solves a single task step $m=1$.
• Three key functions:
  • $\phi(x_i)$: Prompt templating for state/subtask.
  • $\psi_a(r)$: Parsing action from model output.
  • $\psi_x(r)$: Extracting next state.

The process is:

$$r_{i+1} \sim M(\phi(x_i)),\,\, a_{i+1} = \psi_a(r_{i+1}),\,\, x_{i+1} = \psi_x(r_{i+1}),\,\, i=0,...,s-1$$

This design controls context bloat and isolates errors to single steps.

2. System Architectures and Orchestration Mechanisms

Industrial MDAP Orchestration

The orchestration pipeline is:

• Human expresses $I$
• $A_0$ parses $\rightarrow (E,C,T,X,D)$
• Generation of $M$ sub-intents $I_j$
• Agent mapping: $I_j \rightarrow A_j$
• Tool scheduling per sub-agent
• Execution and aggregation of results $R_j$
• Iterative feedback based on satisfaction of $C$, dynamic replanning if needed

High-Level Orchestration Pseudocode:

\begin{algorithmic}[1] \Function{MDAP\_Orchestrate}{I} \State %%%%30%%%% \State %%%%31%%%% \For{%%%%32%%%%} \State %%%%33%%%% \State %%%%34%%%% \State %%%%35%%%% \State %%%%36%%%% \If{%%%%37%%%%} \textbf{break} \EndIf \EndFor \State \Return %%%%38%%%% \EndFunction \end{algorithmic}

Tool selection within each sub-agent is modeled as a pathfinding routine in a tool–dependency DAG, typically executed via topological sorting.

Sequential Task MDAP Orchestration

Tasks are split into $s$ microjobs, each processed by independently sampled LLM calls. A per-step consensus mechanism—“first-to-ahead-by-$k$” voting—ensures action correctness at each microstep. Inputs and outputs are strictly formatted, with “red flag” filtering to discard ill-formed responses prior to voting.

Parallelization of microagents is used for efficiency, with state and vote aggregation enabling full or partial synchronization.

3. Error Correction, Reliability, and Scalability

Traditionally, monolithic chain-of-thought LLM pipelines have prohibitive error rates over long chains due to compounded stepwise failure probabilities: $p_{\text{mono}} \approx p^s$. MDAP isolates errors and applies localized error correction.

The first-to-ahead-by-$k$ voting scheme is theoretically characterized as follows:

$p_{\text{sub}} = \frac{1}{1+((1-p)/p)^k}$

• $p$: single-call correctness probability ($p>0.5$).
• $k$: voting margin.

The system-wide reliability over $s$ steps:

$p_{\text{full}} = (p_{\text{sub}})^s$

To achieve target $p_{\text{full}} \geq t$, the minimal voting threshold is

$$k_{\min} = \left\lceil \frac{\ln(t^{-1/s}-1)}{\ln((1-p)/p)} \right\rceil = \Theta(\ln s)$$

Thus, even for $s \approx 10^6$ steps, only a logarithmic increase in votes ($k$) is needed, rendering million-step zero-error runs attainable for suitable $p$.

Red-flagging (format validation) further reduces correlated or systematic step errors. Context management is explicit: each microagent’s context is scoped strictly to its microtask, preventing error propagation due to compounding context drift.

4. Empirical Results and Case Studies

Industrial Automation, CMAPSS Case (Romero et al., 5 Jun 2025)

A proof-of-concept was executed on a predictive maintenance scenario:

• Targets: 20 engines
• Sub-agents: $M=2$ (data_agent, maintenance_agent)
• Root-agent response: $\sim$2 s/intent (Gemini 2.0 Flash, cloud GPUs)
• Data retrieval: 21 sensor reads + 3 operational settings/engine
• Termination: $RUL_i \geq RUL_{\text{threshold}}$ per engine; actions were MONITOR, REPAIR, or STOP.
• Doubling fleet to 40 engines increased orchestration time nearly linearly: $O(|T|)$ sequential scaling witnessed

Symbolic Reasoning, Towers of Hanoi Case (Meyerson et al., 12 Nov 2025)

• Task: 20-disk Towers of Hanoi ($s \approx 1.05\times 10^6$ steps)
• Model: gpt-4.1-mini ($1-p = 0.22\%$ per step)
• With $k = 3$ and red-flag filtering, all steps were correct; majority finalized in $\leq 3$ votes.
• Projected cost for $1\,000\,000$-step, $95\%$-solved run (with $p = 0.9978$): under \$5\,000 using moderate-size models.
• Observed empirical error rates remained stable across problem sizes (up to 20 disks).

Model	Per-Step Error (1-p)	Output Tokens
gpt-4.1-mini	0.22%	538
o3-mini	0.18%	535
gpt-oss-20B	3.58%	1104

5. Comparative Analysis: MDAPs vs Monolithic Pipelines

MDAPs strongly differ from single–chain-of-thought approaches:

• Error Scaling: Monolithic’s $p^s$ scales poorly; MDAP’s local voting yields $p_{\text{full}} \approx 1$ for large $s$ with manageable computation.
• Context Drift: Monolithic context grows and compounds errors; MDAP enforces step-local context.
• System Modularity: Microagents and sub-agents are sandboxed, permitting auditing, updating, and heterogeneity in tools/roles.
• Efficiency: MDAP’s computational cost is $\Theta(s\ln s)$; parallel sampling and local decision rules enable practical runtime at extreme scale.
• Task Suitability: MDAP requires tasks to admit micro-subtask decomposition and decorrelated model outputs. Highly heterogeneous or unstructured processes may demand advanced prompt engineering or explicit role partitioning.

6. Limitations and Future Directions

MDAP frameworks, while effective and theoretically justified, have limitations:

• Prompt Sensitivity: Decomposition and orchestration routines may be sensitive to phrasing; structured prompts or few-shot calibration is needed.
• Explainability: Opaque LLM sub-agent decisions; post-hoc rationalization or chain-of-thought logging integration is recommended.
• Data Quality: Requires high-fidelity datasets; real-world deployments necessitate anomaly and validation layers.
• Scalability in $M$: Large $M$ (number of parallel sub-agents) implies the need for batched/hierarchical orchestration (agent trees).
• Security and Governance: Agentic access to process data must be tightly controlled to prevent leakage or unauthorized actions.
• Area for Innovation: Future paths include dynamic decomposition depth control, hybrid on-prem/in-cloud LLM inference, RAG for fresh knowledge injection, and standardized benchmarking suites for agentic workflows (latency, throughput, SLA-compliance).

A plausible implication is that MDAPs constitute a principled alternative to monolithic AI pipelines for complex automation and organizational-scale reasoning, particularly in domains where near-zero error rates and compositional transparency are critical.

7. Application Domains and Theoretical Significance

MDAPs have demonstrated utility in two primary classes of problems:

1. Intent-Based Industrial Automation: Translating natural language business goals into machine-executable plans for predictive maintenance and resource management, as instantiated via an LLM–root-agent orchestrating specialized sub-agents and toolchains (Romero et al., 5 Jun 2025).
2. Scalable Symbolic Reasoning: Executing million-step logical tasks (e.g., solving 20-disk Towers of Hanoi) with formal proof of zero errors via microagent voting and aggressive task decomposition (Meyerson et al., 12 Nov 2025).

These results suggest MDAPs are robust candidates for future large-scale, safety-critical, and mission-critical AI process control, encompassing supply chains, regulatory compliance, medical protocols, and other high-reliability multi-agent settings.