# What is theoretical computer science (TCS)?

by Stephen M. Walker II, Co-Founder / CEO

## What is theoretical computer science (TCS)?

Theoretical Computer Science (TCS) is a subset of general computer science and mathematics that focuses on the mathematical and abstract aspects of computing. It is concerned with the theory of computation, formal language theory, the lambda calculus, and type theory.

TCS covers a wide variety of topics including algorithms, data structures, computational complexity, parallel and distributed computation, probabilistic computation, and quantum computation. It also dives into program semantics and quantification theory.

Theoretical computer science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. It looks at the notion of information and how information can be processed.

Common divisions of theoretical computer sciences include:

- Automata theory: This is an abstraction of a machine, which changes its internal state according to some rules. Automata theory also looks at the kinds of problems that can be solved by such automata.
- Computability theory and Computational complexity theory: These look at the question if a problem can be solved by a given automaton, and how well a given solution is, compared to others.
- Formal languages: These are the way to communicate with a given automaton. Most of the time, the question is whether the automaton will accept a word of a formal language, that is, when the word is fed into the automaton, the automaton will end up in an exit state.

It was in 1931 that the mathematician Kurt Godel developed what is known as the incompleteness theory, which is the framework for the study of logic and of computability, leading ultimately to the overarching field of computer science.

## How is theoretical computer science different from applied computer science?

Theoretical Computer Science (TCS) focuses on the foundational mathematical concepts and theories of computation, such as algorithms, data structures, computational complexity, and quantum computation. It is ideal for those with a penchant for abstract reasoning and conceptual synthesis.

Applied Computer Science (ACS), in contrast, is oriented towards the practical application of these principles to address real-world challenges across various industries. It involves a hands-on approach to technology implementation, without delving deeply into the underlying theoretical framework.

While TCS is concerned with developing and proving the efficacy of new algorithms and their computational complexity, ACS professionals might adapt these algorithms for specific applications or optimize them for performance on particular hardware.

Career opportunities in TCS typically include academia, research, and industry roles that demand a deep understanding of theoretical concepts. ACS, on the other hand, offers paths in software development, IT consulting, and systems analysis, among others, where the focus is on applying computing technology to practical problems.

Despite these differences, TCS and ACS are not mutually exclusive, with significant overlap and many professionals contributing to both fields, bridging the gap between theory and application.

## What is the relationship between TCS and AI?

TCS underpins AI by providing essential theoretical frameworks and algorithms for AI system development. Computational models and algorithms, central to machine learning, natural language processing, and computer vision, are rooted in TCS. TCS contributes to AI by analyzing learning algorithm complexity, crafting efficient problem-solving search algorithms, and delineating computational limits. Innovations in AI, including reinforcement learning and deep learning, draw on TCS principles and have proven successful in addressing complex challenges. Thus, TCS is integral to advancing AI systems capable of tackling real-world problems with high efficiency and effectiveness.

## What are the goals of TCS?

The goals of TCS are to provide a theoretical foundation for computer science that can guide the development of practical applications and technologies. Specifically, TCS aims to understand the fundamental limitations and capabilities of computers, design efficient algorithms for solving problems, and develop rigorous mathematical models for analyzing computational systems.

## What are the main methods used in TCS?

The main methods used in TCS include formal proofs, abstract models of computation, and mathematical analysis. Formal proofs are used to establish the correctness and completeness of algorithms and systems, while abstract models of computation provide a framework for studying the behavior of computers and their capabilities. Mathematical analysis is used to quantify the complexity of algorithms and prove their worst-case performance bounds.

## What are the main challenges in TCS?

The main challenges in TCS include understanding the limits of computation, designing efficient algorithms for solving hard problems, and developing rigorous mathematical models that can capture the behavior of complex systems. Moreover, TCS faces the challenge of keeping up with the rapid pace of technological advancements, such as the development of quantum computers, which may require new theoretical frameworks and methods.

## What are the future directions of TCS?

The future directions of TCS include exploring the potential of quantum computing, developing more efficient algorithms for solving hard problems, and expanding the scope of computational models to capture the behavior of complex systems, such as biological networks or social networks. Additionally, TCS is likely to continue playing a key role in the development of AI systems by providing theoretical foundations and algorithms that can guide their design and analysis.