iterative problem solving and verification using LLM - chunhualiao/public-docs GitHub Wiki

IMO25

Yes, this rigorous iterative verification strategy can be adapted to solve many other types of complex problems that require systematic reasoning and validation. Here are the key problem types where this approach would be effective:

1. Formal Logic and Proof Systems

Why it works: The core emphasis on rigor, step-by-step justification, and gap identification directly translates to formal logic proofs, theorem proving, and logical argument validation.

Applications:

  • Philosophical argument analysis
  • Computer science proof verification
  • Legal reasoning and case analysis
  • Formal verification of software/hardware systems

2. Scientific Research and Hypothesis Validation

Why it works: The verification loop mirrors the scientific method - hypothesis, testing, peer review, and refinement.

Applications:

  • Research paper methodology review
  • Experimental design validation
  • Statistical analysis verification
  • Clinical trial protocol development

3. Engineering Design and Safety Analysis

Why it works: Engineering requires rigorous justification of each design decision and systematic identification of failure modes.

Applications:

  • Structural engineering calculations
  • Safety-critical system design
  • Risk assessment and mitigation
  • Quality assurance protocols

4. Financial and Economic Analysis

Why it works: Financial models require rigorous assumptions, step-by-step calculations, and risk validation.

Applications:

  • Investment analysis and due diligence
  • Risk modeling and stress testing
  • Economic policy impact analysis
  • Actuarial calculations

5. Legal Case Analysis and Contract Review

Why it works: Legal reasoning requires systematic argument construction, precedent analysis, and identification of logical gaps.

Applications:

  • Contract review and risk identification
  • Legal brief preparation
  • Regulatory compliance analysis
  • Intellectual property analysis

6. Complex Problem-Solving in Operations Research

Why it works: OR problems require systematic optimization, constraint validation, and solution verification.

Applications:

  • Supply chain optimization
  • Resource allocation problems
  • Scheduling and logistics
  • Game theory applications

7. Medical Diagnosis and Treatment Planning

Why it works: Medical reasoning requires systematic elimination of possibilities, evidence-based conclusions, and risk assessment.

Applications:

  • Differential diagnosis
  • Treatment protocol development
  • Drug interaction analysis
  • Clinical decision support

8. Cybersecurity Threat Analysis

Why it works: Security analysis requires systematic threat modeling, vulnerability assessment, and defense validation.

Applications:

  • Penetration testing methodologies
  • Security architecture review
  • Incident response planning
  • Risk assessment frameworks

9. Academic Research Across Disciplines

Why it works: Academic rigor requires systematic literature review, methodology validation, and peer review.

Applications:

  • Literature review and meta-analysis
  • Research methodology design
  • Peer review processes
  • Grant proposal evaluation

10. Strategic Business Planning

Why it works: Strategic planning requires systematic analysis of assumptions, market conditions, and competitive factors.

Applications:

  • Market entry strategies
  • Competitive analysis
  • Business model validation
  • Strategic risk assessment

Key Adaptations Required:

Domain-Specific Modifications:

  1. Verification Criteria: Replace mathematical rigor with domain-appropriate standards (legal precedent, scientific method, engineering codes, etc.)

  2. Expert Personas: Adapt the "IMO mathematician" verifier to domain experts (senior engineer, medical specialist, legal scholar, etc.)

  3. Evidence Standards: Modify what constitutes "rigorous justification" for each field (peer-reviewed sources, regulatory compliance, industry standards, etc.)

  4. Output Formats: Adapt the structured response format to domain conventions (legal briefs, engineering reports, medical assessments, etc.)

Process Enhancements:

  1. Multi-Expert Verification: Use different specialist verifiers for complex interdisciplinary problems
  2. Stakeholder Validation: Include relevant stakeholder perspectives in the verification loop
  3. Real-World Testing: Incorporate practical validation steps where applicable
  4. Compliance Checking: Add regulatory and ethical compliance verification layers

Limitations and Considerations:

Not suitable for:

  • Creative or artistic endeavors (where subjectivity is valued)
  • Problems requiring real-time decision making
  • Simple routine tasks that don't benefit from rigorous analysis
  • Problems where "good enough" solutions are preferred over perfect ones

Requires careful adaptation for:

  • Problems with incomplete information
  • Ethical dilemmas with multiple valid perspectives
  • Rapidly changing environments
  • Problems where iteration costs outweigh benefits

The key insight is that this strategy works best for high-stakes problems where the cost of error is significant and where systematic reasoning can lead to better outcomes than intuitive or heuristic approaches.