Abstract: In this paper we discuss the observability of hybrid systems and turing machines. We give an elementary example to show that observability is undecidable for turing machines with output.

BLUF: This repo demonstrates the reduction pattern in runnable form under explicit bounds. It does not solve the Halting Problem, and it is not a safety certification tool for real autonomous systems.

Japanese autonomous driving start-up Turing has closed the first tranche of its Series A, raising a total of Y15.27bn ($98.6m) through a mix of equity and debt. The company said it raised Y9.77bn in ...

Using a new computer model, scientists simulated the stripes, spots and hexagons on a species of boxfish, imperfections and all. A male ornate boxfish with distinctive, complex patterns of stripes and ...

The Alan Turing Institute (ATI) has begun a significant organisational transformation, which will see it pivot towards major challenges in defence and national security. In July, Peter Kyle, during ...

A mixture of two types of pigment-producing cells undergoes diffusiophoretic transport to self-assemble into a hexagonal pattern. Credit: Siamak Mirfendereski and Ankur Gupta/CU Boulder A zebra’s ...

If a machine or an AI program matches or surpasses human intelligence, does that mean it can simulate humans perfectly? If yes, then what about reasoning—our ability to apply logic and think ...

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🛍️ Amazon Big Spring Sale: 100+ editor-approved deals worth buying right now 🛍️ By Andrew Paul Published Jun 18, 2025 12:54 PM EDT Add Popular Science (opens in a new tab) Adding us as a Preferred ...

Add Yahoo as a preferred source to see more of our stories on Google. When you buy through links on our articles, Future and its syndication partners may earn a commission. Several Alan Turing papers, ...

Artificial intelligence chatbots like ChatGPT are getting a whole lot smarter, a whole lot more natural, and a whole lot more…human-like. It makes sense — humans are the ones creating the large ...

Today mathematician Alan Turing is world-famous because he helped the Allies achieve victory against the Axis powers by deciphering an encryption that was considered unbreakable. That story inspired ...