computational complexity – Quanta Magazine https://www.quantamagazine.org Illuminating science Fri, 21 Feb 2025 21:18:44 -0500 en-US hourly 1 https://wordpress.org/?v=6.6.2 Catalytic Computing Taps the Full Power of a Full Hard Drive https://www.quantamagazine.org/catalytic-computing-taps-the-full-power-of-a-full-hard-drive-20250218/ https://www.quantamagazine.org/catalytic-computing-taps-the-full-power-of-a-full-hard-drive-20250218/#respond Tue, 18 Feb 2025 15:15:12 +0000 https://www.quantamagazine.org/?p=146655 The post Catalytic Computing Taps the Full Power of a Full Hard Drive first appeared on Quanta Magazine

]]> “Obviously” is a dangerous word, even in scenarios that seem simple. Suppose, for instance, you need to do an important computation. You get to choose between two computers that are almost identical, except that one has an extra hard drive full of precious family photos. It’s natural to assume that the two options are equally good — that an extra drive with no space remaining won’t aid your…

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]]> https://www.quantamagazine.org/catalytic-computing-taps-the-full-power-of-a-full-hard-drive-20250218/feed/ 0 Chatbot Software Begins to Face Fundamental Limitations https://www.quantamagazine.org/chatbot-software-begins-to-face-fundamental-limitations-20250131/ https://www.quantamagazine.org/chatbot-software-begins-to-face-fundamental-limitations-20250131/#respond Fri, 31 Jan 2025 15:37:15 +0000 https://www.quantamagazine.org/?p=146131 The post Chatbot Software Begins to Face Fundamental Limitations first appeared on Quanta Magazine

]]> On December 17, 1962, Life International published a logic puzzle consisting of 15 sentences describing five houses on a street. Each sentence was a clue, such as “The Englishman lives in the red house” or “Milk is drunk in the middle house.” Each house was a different color, with inhabitants of different nationalities, who owned different pets, and so on. The story’s headline asked: “Who Owns…

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]]> https://www.quantamagazine.org/chatbot-software-begins-to-face-fundamental-limitations-20250131/feed/ 0 Why Computer Scientists Consult Oracles https://www.quantamagazine.org/why-computer-scientists-consult-oracles-20250103/ https://www.quantamagazine.org/why-computer-scientists-consult-oracles-20250103/#respond Fri, 03 Jan 2025 14:40:14 +0000 https://www.quantamagazine.org/?p=145383 The post Why Computer Scientists Consult Oracles first appeared on Quanta Magazine

]]> Pose a question to a Magic 8 Ball, and it’ll answer yes, no or something annoyingly indecisive. We think of it as a kid’s toy, but theoretical computer scientists employ a similar tool. They often imagine they can consult hypothetical devices called oracles that can instantly, and correctly, answer specific questions. These fanciful thought experiments have inspired new algorithms and helped…

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]]> https://www.quantamagazine.org/why-computer-scientists-consult-oracles-20250103/feed/ 0 Computer Scientists Combine Two ‘Beautiful’ Proof Methods https://www.quantamagazine.org/computer-scientists-combine-two-beautiful-proof-methods-20241004/ https://www.quantamagazine.org/computer-scientists-combine-two-beautiful-proof-methods-20241004/#respond Fri, 04 Oct 2024 13:33:16 +0000 https://www.quantamagazine.org/?p=142069 The post Computer Scientists Combine Two ‘Beautiful’ Proof Methods first appeared on Quanta Magazine

]]> How do you prove something is true? For mathematicians, the answer is simple: Start with some basic assumptions and proceed, step by step, to the conclusion. QED, proof complete. If there’s a mistake anywhere, an expert who reads the proof carefully should be able to spot it. Otherwise, the proof must be valid. Mathematicians have been following this basic approach for well over 2,000 years.

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]]> https://www.quantamagazine.org/computer-scientists-combine-two-beautiful-proof-methods-20241004/feed/ 0 How Does Math Keep Secrets? https://www.quantamagazine.org/how-does-math-keep-secrets-20240801/ https://www.quantamagazine.org/how-does-math-keep-secrets-20240801/#respond Thu, 01 Aug 2024 13:30:04 +0000 https://www.quantamagazine.org/?p=139467 The post How Does Math Keep Secrets? first appeared on Quanta Magazine

]]> Can you keep a secret? Modern techniques for maintaining the confidentiality of information are based on mathematical problems that are inherently too difficult for anyone to solve without the right hints. Yet what does that mean when quantum computers capable of solving many problems astronomically faster are on the horizon? In this episode, host Janna Levin talks with computer scientist Boaz…

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