🧮 TCS Orbit

⊢ Logic

🔢 Complexity

📐 Automata

🧮 Computation

🧮 Theoretical Computer Science

Automata • Computability • Complexity • Logic • Algorithms • Information Theory • Cryptography

Master the mathematical foundations of computing — from finite automata and Turing machines to complexity classes, formal languages, and the limits of computation.

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Theoretical CS Concepts & Formalisms

TCS Basics

What is TCS, formal models, proofs.

Mathematical Foundations

Sets, relations, functions, logic.

Finite Automata

DFA, NFA, ε-NFA, regular languages.

Regular Expressions

Operators, pumping lemma, equivalence.

Context-Free Grammars

CFG, CYK parsing, ambiguity.

Pushdown Automata

PDA, stack, context-free languages.

Turing Machines

TM, variants, decidability.

Chomsky Hierarchy

Type 0-3, grammars, automata.

Computability Theory

Recursive functions, decidability.

Halting Problem

Undecidability, reduction.

Reducibility

Many-one, Turing reductions.

Recursion Theorem

Fixed point, Kleene's theorem.

Complexity Classes

P, NP, PSPACE, EXP, NEXP.

P vs NP

The problem, implications, consequences.

NP-Completeness

SAT, 3-SAT, reductions, Cook-Levin.

Approximation Algorithms

PTAS, FPTAS, APX.

Randomized Complexity

RP, BPP, ZPP, derandomization.

Quantum Complexity

BQP, QMA, quantum supremacy.

Descriptive Complexity

Logic and complexity, Fagin's theorem.

Formal Languages

Alphabets, strings, languages, operations.

Language Hierarchy

Regular, context-free, context-sensitive.

Context-Sensitive Languages

LBA, CSG, membership.

Propositional Logic

Formulas, truth tables, SAT.

Predicate Logic

First-order, quantifiers, inference.

Gödel's Incompleteness Theorems

Completeness, incompleteness.

Modal Logic

Kripke semantics, modalities.

Algorithms Analysis

Asymptotic, recurrences, master theorem.

Sorting Theory

Comparison lower bound, sorting networks.

Lower Bounds

Decision trees, adversary arguments.

Randomized Algorithms

Las Vegas, Monte Carlo, Chernoff.

Information Theory

Entropy, mutual information, coding.

Coding Theory

Error-correcting codes, Hamming.

Compression Theory

Huffman, LZ, Kolmogorov complexity.

Cryptography Theory

One-way functions, PRG, pseudorandomness.

Zero-Knowledge Proofs

Interactive proofs, ZK-SNARKs.

Lambda Calculus

Church encodings, combinators, reduction.

Type Theory

Simple types, System F, dependent types.

Category Theory

Functors, natural transformations, adjunctions.

Graph Theory

Graphs, colorings, paths, cycles.

Graph Algorithms

Flow, matching, connectivity.

Quantum Computing Theory

Qubits, gates, circuits, algorithms.

Quantum Information Theory

Entanglement, channels, capacity.

🧮 Theoretical CS Mastery Roadmap

🔰 Foundation

Math foundations, logic basics, automata intro

📶 Core

Regular/CFL, Turing machines, P vs NP, algorithms

🔥 Deep Dive

NP-completeness, complexity classes, computability

🏆 Frontier

Quantum complexity, zero-knowledge, descriptive complexity

🧮 Prove, Compute, Explore — Master Theoretical CS

From automata to complexity, explore the fundamental nature of computation.

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