What is the theory of computation?

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

What is the theory of computation?

The theory of computation, a core branch of computer science and mathematics, explores the boundaries of computation and the solvability of problems via algorithms. It employs various computational models, including Turing machines, recursive functions, and finite-state automata, to understand these limits and possibilities.

  • Automata Theory — This branch focuses on the logic of computation with respect to simple machines called automata. Automata theory helps scientists understand how machines compute functions and solve problems.

  • Computability Theory — This area studies the limits of computation by identifying solvable problems and those that are inherently unsolvable. It finds applications in various computer science domains and beyond, such as cryptography and artificial intelligence.

  • Complexity Theory — This theoretical computer science branch is concerned with studying the cost of solving problems while considering the running time of an algorithm and its growth with the size of the input. Measuring complexity involves analyzing algorithms to determine how much time they take while evaluating their relative rates of growth as the size of the input grows.

The theory of computation is instrumental in various fields. It underpins cryptographic algorithms, ensuring secure data transmission and storage. Additionally, it plays a pivotal role in the development of AI systems by providing insights into the capabilities and limitations of computational systems. Thus, the theory of computation forms a solid foundation for understanding advanced concepts and techniques in computer science.

What is the relationship between AI and computation?

The relationship between AI and computation is essential for understanding the power and capabilities of AI systems. AI algorithms, especially deep learning algorithms, require significant computational power to function effectively. By using cloud-based AI, companies can increase their computational power without substantial investments in hardware. This symbiotic relationship between AI and computation has several benefits:

  • Scalability — Cloud computing allows AI systems to access various information sources, which can improve the quality and accuracy of AI decision-making.
  • Data Accessibility — The cloud provides access to diverse data sources, enabling AI systems to learn and generate more accurate outputs.
  • Parallel Processing — Training, testing, and deploying AI algorithms require a high degree of computational power. Cloud computing enables parallel processing, which can speed up these processes.

The success of modern AI techniques relies on computation on a scale unimaginable even a few years ago. For example, training a leading AI algorithm can require a month of computing time and cost $100 million. This enormous computational power is delivered by computer chips that not only pack the maximum computational capacity but also have AI-optimized design features, such as GPUs and AI chips.

AI and cloud computing are also interconnected in terms of automation. The implementation of AI streamlines simple processes, increasing efficiency and allowing IT talent to focus on more innovative development. This symbiotic relationship between AI and computation is a powerful catalyst for change, as it combines the computational power of quantum computing with the intelligence of AI to solve complex problems and make more accurate predictions.

What are the major branches of computational theory?

The major branches of the theory of computation include Automata Theory and Languages, Computability Theory, and Computational Complexity Theory.

Automata Theory and Languages study abstract machines, known as automata, and the computational problems they can solve. These machines range from finite automata to pushdown automata and Turing machines. Formal languages, sets of strings over an alphabet, specify computational problems and describe the capabilities of automata.

Computability Theory, also known as recursion theory, investigates which problems are solvable using algorithms. The central concept revolves around the computable function, which an algorithm can calculate. The Church-Turing thesis, a significant result in this area, suggests that any function computable by an algorithm can also be computed by a Turing machine.

Computational Complexity Theory addresses the efficiency of problem-solving, including the time and memory space a machine requires to solve a problem. It provides insights into the limitations of computational models and the efficiency of algorithms.

What are recent breakthroughs in computational theory?

Recent breakthroughs in computational theory include:

  1. NLTS Conjecture — In theoretical computer science, researchers posted a proof of the NLTS conjecture, which has implications for our understanding of the physical world and the nature of quantum computing.

  2. Deep Neural Networks — Researchers found a way to idealize deep neural networks using kernel machines, an important step in the field of artificial intelligence.

  3. Quantum Gravity — A mathematician managed to model quantum gravity, a long-standing problem in the field of physics.

  4. Biological Reinforcement Learning — Scientists built a computational model of the biological reinforcement learning system, which has implications for how humans learn and make decisions.

  5. Optical Tweezers — A new method has been advanced using Stampede2 supercomputer simulations that makes optical tweezers more efficient at manipulating small particles.

  6. Sparse Tensors — New computational techniques, 'HighLight' and 'Tailors and Swiftiles,' could dramatically boost the speed and performance of high-dimensional AI models.

  7. Quantum Computing — Quantum physicists simulated super diffusion on a quantum computer, demonstrating the potential for new computing systems.

These breakthroughs showcase the rapid advancements in computational theory and the growing influence of AI and large language models in various fields, from physics to chemistry and computer science.

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