# Computer Science - Phase 2 Processes Backlog

## Overview

This document outlines the key processes for the Computer Science specialization, covering algorithm design, complexity analysis, programming language theory, systems research, and formal verification. These processes support both theoretical research and practical implementation workflows.

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## Category 1: Algorithm Design and Analysis

### 1. algorithm-complexity-analysis
**Purpose:** Systematically analyze time and space complexity of algorithms using asymptotic notation.

**Key Activities:**
- Identify computational model and input representation
- Apply Big-O, Big-Omega, and Big-Theta analysis
- Solve recurrence relations using master theorem or substitution
- Analyze best-case, worst-case, and average-case complexity
- Consider amortized analysis for sequences of operations
- Document complexity bounds with formal proofs

**Outputs:**
- Complexity analysis report with formal bounds
- Recurrence relation derivations
- Comparison with known lower bounds

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### 2. algorithm-correctness-proof
**Purpose:** Formally prove algorithm correctness using mathematical techniques.

**Key Activities:**
- Define preconditions, postconditions, and invariants
- Apply proof by induction for recursive algorithms
- Use loop invariants for iterative algorithms
- Verify termination guarantees
- Handle edge cases and boundary conditions
- Document proof steps in structured format

**Outputs:**
- Formal correctness proof document
- Loop invariant specifications
- Termination proof

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### 3. algorithm-design-paradigm-selection
**Purpose:** Select and apply appropriate algorithm design paradigms for computational problems.

**Key Activities:**
- Analyze problem structure (optimal substructure, overlapping subproblems)
- Evaluate divide-and-conquer applicability
- Assess dynamic programming feasibility
- Consider greedy algorithm potential with matroid analysis
- Explore randomization benefits
- Compare paradigm trade-offs

**Outputs:**
- Paradigm selection rationale
- High-level algorithm design
- Comparative analysis with alternative approaches

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### 4. approximation-algorithm-design
**Purpose:** Design polynomial-time approximation algorithms for NP-hard problems.

**Key Activities:**
- Establish problem NP-hardness via reduction
- Design approximation algorithm with guaranteed ratio
- Prove approximation bound correctness
- Apply LP relaxation and rounding techniques
- Consider PTAS/FPTAS feasibility
- Analyze inapproximability results (PCP-based)

**Outputs:**
- Approximation algorithm specification
- Approximation ratio proof
- Implementation guidelines

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### 5. randomized-algorithm-analysis
**Purpose:** Design and analyze algorithms using randomization for efficiency or simplicity.

**Key Activities:**
- Classify algorithm type (Las Vegas vs Monte Carlo)
- Analyze expected running time
- Bound error probability
- Apply Chernoff bounds and Markov inequality
- Design derandomization strategies if needed
- Implement random number generation requirements

**Outputs:**
- Randomized algorithm specification
- Probability analysis documentation
- Expected complexity bounds with confidence intervals

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## Category 2: Complexity Theory and Computability

### 6. computational-problem-classification
**Purpose:** Classify computational problems into appropriate complexity classes.

**Key Activities:**
- Define decision problem formally
- Identify membership in P, NP, co-NP, PSPACE, etc.
- Construct polynomial-time reduction for hardness proofs
- Verify reduction correctness (both directions)
- Place problem in complexity landscape
- Document implications and related problems

**Outputs:**
- Problem classification report
- Reduction proof documentation
- Complexity class placement diagram

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### 7. np-completeness-proof
**Purpose:** Establish NP-completeness of computational problems via reduction.

**Key Activities:**
- Verify problem is in NP (polynomial-time verifier)
- Select appropriate source problem for reduction
- Construct polynomial-time transformation
- Prove correctness (yes-instance to yes-instance mapping)
- Prove efficiency (polynomial construction time)
- Document gadget constructions

**Outputs:**
- NP-completeness proof document
- Reduction construction details
- Gadget library for future reductions

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### 8. decidability-analysis
**Purpose:** Analyze decidability and computability properties of problems.

**Key Activities:**
- Model problem in Turing machine framework
- Apply Rice's theorem for language properties
- Construct undecidability proofs via reduction from halting problem
- Identify semi-decidability (RE membership)
- Place in arithmetic hierarchy if applicable
- Document decidability boundaries

**Outputs:**
- Decidability classification report
- Undecidability proof documentation
- Computability landscape placement

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## Category 3: Programming Language Theory

### 9. type-system-design
**Purpose:** Design type systems with desired safety and expressiveness properties.

**Key Activities:**
- Define type syntax and semantics
- Establish typing rules (inference rules)
- Prove type soundness (progress and preservation)
- Design type inference algorithm
- Analyze decidability of type checking
- Handle polymorphism, subtyping, or dependent types as needed

**Outputs:**
- Type system specification document
- Typing rules in inference rule notation
- Soundness proof
- Type inference algorithm specification

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### 10. operational-semantics-specification
**Purpose:** Define precise operational semantics for programming languages.

**Key Activities:**
- Choose semantics style (small-step vs big-step)
- Define abstract syntax
- Specify evaluation rules
- Handle binding and substitution
- Define evaluation contexts if needed
- Prove semantic properties (determinism, confluence)

**Outputs:**
- Operational semantics specification
- Evaluation rules in standard notation
- Semantic property proofs

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### 11. compiler-optimization-design
**Purpose:** Design and verify compiler optimization passes.

**Key Activities:**
- Define optimization transformation
- Specify correctness criteria (semantic preservation)
- Design data-flow analysis if needed
- Implement SSA-based transformations
- Prove optimization correctness
- Measure performance impact

**Outputs:**
- Optimization specification document
- Correctness proof
- Performance benchmarks
- Integration with compiler pipeline

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### 12. dsl-design-implementation
**Purpose:** Design and implement domain-specific languages for specialized problem domains.

**Key Activities:**
- Analyze domain requirements and idioms
- Design syntax for domain expressiveness
- Define semantics (embedded or standalone)
- Implement parser and type checker
- Create compilation/interpretation backend
- Develop standard library for domain

**Outputs:**
- DSL specification document
- Language implementation
- Domain-specific standard library
- User documentation and examples

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## Category 4: Systems Research and Design

### 13. distributed-consensus-protocol-design
**Purpose:** Design and verify distributed consensus protocols.

**Key Activities:**
- Define system model (synchrony, failure assumptions)
- Specify safety and liveness properties
- Design protocol message flow
- Prove safety properties (agreement, validity)
- Analyze liveness under failure scenarios
- Optimize for common case performance

**Outputs:**
- Protocol specification document
- TLA+ or similar formal specification
- Safety and liveness proofs
- Performance analysis

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### 14. cache-optimization-analysis
**Purpose:** Analyze and optimize algorithms and data structures for cache efficiency.

**Key Activities:**
- Analyze memory access patterns
- Model cache behavior (external memory model)
- Optimize data layout for spatial locality
- Design cache-oblivious algorithms
- Measure cache performance (cache misses)
- Compare theoretical and empirical performance

**Outputs:**
- Cache analysis report
- Optimized data structure design
- Performance benchmarks
- Memory access pattern documentation

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### 15. concurrent-data-structure-design
**Purpose:** Design lock-free or wait-free concurrent data structures.

**Key Activities:**
- Define sequential specification
- Choose synchronization strategy (lock-free, wait-free)
- Design atomic operations and memory ordering
- Prove linearizability
- Analyze progress guarantees
- Benchmark concurrent performance

**Outputs:**
- Concurrent data structure specification
- Linearizability proof
- Progress guarantee analysis
- Performance benchmarks under contention

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### 16. system-performance-modeling
**Purpose:** Build analytical models to predict and analyze system performance.

**Key Activities:**
- Define system components and interactions
- Model workload characteristics
- Apply queuing theory or Markov models
- Identify bottlenecks via analysis
- Validate model against empirical data
- Predict performance under varying conditions

**Outputs:**
- Performance model documentation
- Bottleneck analysis report
- Capacity planning recommendations
- Model validation results

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## Category 5: Formal Methods and Verification

### 17. model-checking-verification
**Purpose:** Apply model checking to verify system properties automatically.

**Key Activities:**
- Define system model in checker input language
- Specify properties in temporal logic (LTL, CTL)
- Handle state space explosion (abstraction, symmetry)
- Analyze counterexamples for violations
- Refine model based on spurious counterexamples
- Document verification results

**Outputs:**
- Model specification files
- Property specifications
- Verification results report
- Counterexample analysis (if any)

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### 18. theorem-prover-verification
**Purpose:** Use interactive theorem provers to verify system or algorithm correctness.

**Key Activities:**
- Formalize system in proof assistant (Coq, Isabelle, Lean)
- Define specifications and invariants
- Develop proof strategy
- Construct machine-checked proofs
- Extract verified implementation if applicable
- Maintain proof artifacts

**Outputs:**
- Formalized specification in proof assistant
- Machine-checked proofs
- Extracted implementation (if applicable)
- Proof documentation and maintenance guide

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### 19. abstract-interpretation-analysis
**Purpose:** Design abstract interpretation frameworks for static program analysis.

**Key Activities:**
- Define concrete semantics
- Design abstract domain
- Establish Galois connection
- Define abstract transfer functions
- Prove soundness of abstraction
- Implement fixpoint computation

**Outputs:**
- Abstract interpretation framework specification
- Abstract domain definition
- Soundness proof
- Analysis implementation

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### 20. program-synthesis-specification
**Purpose:** Specify and implement program synthesis from high-level specifications.

**Key Activities:**
- Define specification language (examples, logical, sketch)
- Design search space representation
- Implement synthesis algorithm (enumerative, constraint-based, neural)
- Verify synthesized programs against specification
- Optimize for synthesis speed and output quality
- Handle ambiguous specifications

**Outputs:**
- Synthesis system specification
- Specification language definition
- Synthesized program correctness guarantees
- Performance benchmarks

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## Category 6: Research Methodology

### 21. theoretical-cs-paper-development
**Purpose:** Structure and develop theoretical computer science research papers.

**Key Activities:**
- Formalize problem statement precisely
- Conduct comprehensive literature review
- Develop and prove main results
- Construct clear proof presentation
- Position contribution relative to prior work
- Prepare technical appendices

**Outputs:**
- Research paper draft
- Proof appendices
- Related work comparison table
- Conference/journal submission materials

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### 22. algorithm-engineering-evaluation
**Purpose:** Conduct rigorous experimental evaluation of algorithm implementations.

**Key Activities:**
- Design benchmark suite covering problem instances
- Implement algorithms with engineering best practices
- Control experimental variables
- Collect and analyze performance data
- Compare against state-of-the-art baselines
- Report results with statistical rigor

**Outputs:**
- Benchmark suite and test instances
- Experimental methodology documentation
- Performance data and analysis
- Publication-ready figures and tables

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### 23. complexity-lower-bound-proof
**Purpose:** Establish lower bounds on computational complexity of problems.

**Key Activities:**
- Identify appropriate lower bound technique
- Apply communication complexity, cell probe, or information-theoretic methods
- Construct adversary arguments
- Prove conditional lower bounds (SETH, 3SUM)
- Document assumptions and implications
- Compare with known upper bounds

**Outputs:**
- Lower bound proof document
- Technique selection rationale
- Conditional assumption documentation
- Gap analysis (upper vs lower bounds)

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### 24. formal-specification-development
**Purpose:** Develop formal specifications for systems and algorithms.

**Key Activities:**
- Choose specification language (TLA+, Z, Alloy)
- Model system state and transitions
- Specify safety and liveness properties
- Validate specification against requirements
- Iteratively refine with stakeholders
- Prepare specification for verification

**Outputs:**
- Formal specification document
- Property catalog
- Specification validation report
- Verification-ready artifacts

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### 25. cross-area-cs-integration
**Purpose:** Integrate techniques across computer science subfields for research problems.

**Key Activities:**
- Identify relevant subfield connections
- Survey cross-cutting techniques
- Adapt methods to target problem
- Combine theoretical and systems approaches
- Validate integrated approach
- Document interdisciplinary contributions

**Outputs:**
- Integration strategy document
- Cross-area technique catalog
- Unified solution approach
- Interdisciplinary contribution summary

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## Summary Statistics

| Category | Process Count |
|----------|---------------|
| Algorithm Design and Analysis | 5 |
| Complexity Theory and Computability | 3 |
| Programming Language Theory | 4 |
| Systems Research and Design | 4 |
| Formal Methods and Verification | 4 |
| Research Methodology | 5 |
| **Total** | **25** |

## Implementation Priority

### High Priority (Core CS Research)
1. algorithm-complexity-analysis
2. algorithm-correctness-proof
3. computational-problem-classification
4. type-system-design
5. model-checking-verification

### Medium Priority (Advanced Topics)
6. approximation-algorithm-design
7. np-completeness-proof
8. operational-semantics-specification
9. distributed-consensus-protocol-design
10. theorem-prover-verification

### Standard Priority (Specialized Research)
11. randomized-algorithm-analysis
12. decidability-analysis
13. compiler-optimization-design
14. dsl-design-implementation
15. cache-optimization-analysis
16. concurrent-data-structure-design
17. system-performance-modeling
18. abstract-interpretation-analysis
19. program-synthesis-specification
20. theoretical-cs-paper-development
21. algorithm-engineering-evaluation
22. complexity-lower-bound-proof
23. formal-specification-development
24. algorithm-design-paradigm-selection
25. cross-area-cs-integration

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## References

See `references.md` for comprehensive citations including:
- Algorithm textbooks (CLRS, Kleinberg/Tardos, Skiena)
- Complexity theory (Arora/Barak, Sipser, Papadimitriou)
- Programming language theory (Pierce TAPL, Dragon Book)
- Systems (Tanenbaum, Hennessy/Patterson)
- Formal methods (Baier/Katoen, Software Foundations)
