Complex Problem Decomposition

From Lesson 5

In the previous lesson, we explored meta-prompting and recursive improvement. Now let’s build on that foundation. You’ve used meta-prompting to improve AI’s own processes. Now let’s apply architectural thinking to the hardest challenge: problems that seem too complex for AI. The secret isn’t making AI smarter–it’s making problems smaller.

The Impossible Problem

Here’s a problem that will stump any AI in a single prompt:

“Design a comprehensive go-to-market strategy for a new B2B SaaS product targeting mid-market healthcare companies, including market analysis, competitive positioning, pricing strategy, channel strategy, messaging framework, sales playbook, marketing plan, and 12-month execution timeline.”

Ask this in one prompt and you’ll get a superficial document that sounds good but lacks the depth to actually execute. Each section will be a paragraph or two of generic advice. No real strategic thinking. No specific tactical plans. No recognition of trade-offs.

But decompose this problem correctly, and AI can produce each component at expert-level quality.

By the end of this lesson, you’ll be able to:

• Identify the cognitive operations within any complex problem
• Design decomposition strategies that match problem structure
• Create interface contracts between steps that prevent information loss
• Handle cross-cutting concerns that span multiple components

The Cognitive Operations Framework

Every complex problem is made of simpler cognitive operations. Here are the most common:

The decomposition principle: Identify which cognitive operations your problem requires, then design one step per operation.

Decomposition Strategy 1: Vertical Slicing

Break the problem into independent “slices” that can each be solved fully before moving to the next.

Example: Go-to-Market Strategy

Instead of tackling everything at once, slice vertically:

Slice 1: Market Understanding

• Research: Healthcare SaaS market size, growth, trends
• Analysis: Customer segments, buying behavior, decision-making process
• Evaluation: Segment attractiveness scoring
• Output: Market opportunity map with priority segments

Slice 2: Competitive Positioning

• Research: Competitor product features, pricing, go-to-market approaches
• Analysis: Competitive gaps and white space
• Generation: Positioning options (3-4 alternatives)
• Evaluation: Position each option against criteria
• Output: Chosen positioning with rationale

Slice 3: Pricing and Packaging

• Research: Competitor pricing, customer willingness-to-pay signals
• Generation: Pricing model options
• Analysis: Revenue modeling for each option
• Critique: Stress-test each model
• Output: Recommended pricing with sensitivity analysis

Each slice is self-contained and can be worked through completely. The final integration step brings them together.

Quick check: Take a complex task you’ve struggled with. Can you identify 3-4 independent “slices” that could each be solved separately?

Decomposition Strategy 2: Horizontal Layering

When components aren’t independent but build on each other, layer them sequentially.

Example: Research Synthesis

Imagine you need AI to synthesize research on a complex topic.

Layer 1 – Evidence Collection

“Gather all relevant evidence related to [topic]. Organize by sub-topic. Do NOT draw any conclusions yet–just collect and categorize the evidence.”

Layer 2 – Pattern Identification

“Here is the evidence collected: [Layer 1 output]. Identify patterns, trends, and relationships across the evidence. What themes emerge? What contradictions exist? Note these as observations, not conclusions.”

Layer 3 – Hypothesis Formation

“Based on these patterns: [Layer 2 output]. Formulate 3-5 hypotheses that explain the observed patterns. For each hypothesis, identify what evidence supports it and what evidence contradicts it.”

Layer 4 – Hypothesis Evaluation

“Evaluate these hypotheses: [Layer 3 output]. For each, assess: strength of supporting evidence, strength of contradicting evidence, what additional evidence would confirm or refute it. Rank hypotheses by explanatory power.”

Layer 5 – Synthesis

“Based on the evaluated hypotheses: [Layer 4 output]. Write a synthesis that represents the best current understanding of [topic]. Include confidence levels, open questions, and areas where the evidence is insufficient.”

Each layer requires the previous layer’s output. That’s what makes this horizontal rather than vertical.

Interface Contracts

The most common failure in decomposed systems is information loss between steps. Interface contracts prevent this.

Defining an Interface Contract

For each step transition, specify:

1. Output format: Exactly what format the current step produces
2. Required fields: What information must be included
3. Quality criteria: Minimum quality bar for the output
4. Handoff instruction: How to present the output to the next step

Example Contract

Step 2 (Competitive Analysis) to Step 3 (Positioning):

Output from Step 2 must include:
- Competitor comparison matrix (at least 5 competitors, at least 8 dimensions)
- Identified market gaps (minimum 3, with supporting evidence)
- Competitor weakness assessment (for each major competitor)
- Customer pain points not addressed by current market

Format: Structured markdown with tables
Quality gate: All claims must reference specific evidence from the analysis
Handoff: Present as "competitive intelligence brief" to Step 3

Without this contract, Step 2 might produce a vague summary that Step 3 can’t work with. The contract ensures the handoff is clean.

Handling Cross-Cutting Concerns

Some elements don’t fit neatly into one step–they span the entire problem. Budget constraints, regulatory requirements, and brand guidelines are examples.

Strategy: The Context Layer

Create a “context document” that gets loaded into every step:

“Context for all steps in this analysis:

Budget constraint: $500K total marketing budget for 12 months Regulatory: HIPAA compliance required for all customer-facing materials Brand: Enterprise-grade, trustworthy, not flashy. No consumer-style marketing. Timeline constraint: Must show traction within 6 months for Series B narrative Non-negotiable: No cold outreach to C-suite–our industry frowns on it

Every recommendation must respect these constraints. Flag any conflict between optimal strategy and these constraints.”

Load this context into every step, and cross-cutting concerns are consistently addressed.

Real-World Decomposition: A Full Example

Let’s decompose a genuinely difficult problem: designing an employee onboarding program.

Step 1: Stakeholder Needs Analysis

“Identify every stakeholder affected by employee onboarding (new hire, manager, HR, team, leadership). For each, list their needs, pain points, and success criteria. Do not design solutions yet.”

Step 2: Current State Assessment

“Based on these stakeholder needs: [Step 1 output]. What does a typical onboarding program do well and poorly? Identify the top 5 gaps between stakeholder needs and typical onboarding approaches.”

Step 3: Best Practices Research

“Research onboarding best practices from high-performing organizations. Focus on evidence-based approaches. Organize findings by the gap areas identified in [Step 2 output].”

Step 4: Program Design

“Using the gaps from Step 2 and best practices from Step 3, design an onboarding program. For each component: describe the activity, timing, responsible person, expected outcome, and how it addresses a specific stakeholder need.”

Step 5: Critique and Refinement

“As an onboarding expert, review the program design from Step 4. What’s missing? What’s unrealistic? Where would this program fail? Suggest improvements.”

Step 6: Implementation Plan

“Create a phased implementation plan for the refined onboarding program. Include: quick wins (Week 1), core rollout (Month 1-2), full implementation (Month 3-6). Add resource requirements, training needs, and success metrics.”

Each step is focused, builds on the previous step’s validated output, and produces a clear deliverable.

Decomposition Anti-Patterns

Watch out for these common mistakes:

Over-decomposition: Breaking simple problems into too many steps. If a step produces trivial output, merge it with an adjacent step.

Under-decomposition: The most common error. If a step requires more than one cognitive operation, it probably needs splitting.

Missing dependencies: Designing steps that need information from a step that hasn’t happened yet. Map dependencies before building the chain.

Ignored integration: Perfectly decomposed components that never get properly synthesized into a coherent whole. Always plan the integration step explicitly.

Key Takeaways

• Every complex problem is made of simpler cognitive operations–identify them first
• Vertical slicing works for independent components; horizontal layering works for dependent ones
• Interface contracts prevent information loss between steps
• Cross-cutting concerns need a shared context document loaded into every step
• Watch for anti-patterns: over-decomposition, under-decomposition, missing dependencies, and ignored integration

Up Next

In Lesson 7, you’ll learn to evaluate and benchmark AI performance systematically. Because if you can’t measure it, you can’t improve it. We’ll cover evaluation frameworks, benchmark design, and quality assurance for AI systems.