Complexity Theory for Computer Science

Complexity theory studies the intrinsic resource requirements of computational problems.

Why This Section Matters

  • Distinguishes feasible from infeasible exact computation
  • Provides reduction-based hardness reasoning
  • Guides use of approximation/randomization/heuristics
  • Clarifies time-space tradeoffs in practical systems

Topic Roadmap

flowchart LR
  A[Decision Problems] --> B[Complexity Classes]
  B --> C[Polynomial Reductions]
  C --> D[NP-Completeness]
  B --> E[Randomized Complexity]
  B --> F[Space Complexity]
  D --> G[Approximation/Heuristics]

Learning Goals

  1. classify problems by formal resource bounds,
  2. prove hardness via reductions,
  3. reason about randomized/approximate alternatives,
  4. understand memory-bounded computation classes.

Exercises

  1. Define decision vs optimization problem with one example each.
  2. Explain why polynomial-time reductions preserve tractability implications.