Introduction to Circuit Complexity and Parallel Computation

How do we measure the power of parallel computers mathematically? Circuit complexity provides the foundational framework for understanding what can be computed efficiently in parallel. This text-based course offers a clear, step-by-step introduction to Boolean circuits, uniform circuit families, and parallel computation theory. You will learn to analyze computational problems through the lens of circuit depth and size, bridging the gap between abstract math and practical parallel limits. What you'll learn: Learn the foundational definitions of Boolean circuits, size, and depth; Understand the polynomial hierarchy and circuit complexity bounds, including Kannan's theorem; Explore uniform circuits and parallel complexity classes such as NC and its hierarchy; Analyze P-complete problems and their significance in parallelization limits; Study the relationships between NC1, Logspace, and NC2 complexity classes; Examine efficient parallel circuits for fundamental arithmetic operations. Starting with basic definitions and circuit structures, the course guides you through complexity classes, reductions, and concrete parallel algorithms. This course is designed for beginners in theoretical computer science, programmers, and math enthusiasts looking for an accessible entry point into complexity theory. Begin your journey into the mathematical limits of parallel computing today.