Robert Erdmann, a senior scientist working for the Rijksmuseum, cannot help but smile when I ask him to explain -- in as much detail as possible -- how exactly he used artificial intelligence to recreate long-lost portions of Rembrandt van Rijn's most famous painting, The Night Watch (1642). "Most people just want the elevator pitch," he tells me over Zoom. The Night Watch is a mammoth of a painting, and it used to be even bigger. In 1715, it came into the possession of the bureaucrats in charge of Amsterdam's Town Hall. In order to fit it on their wall, they sliced off all four outer edges of Rembrandt's priceless masterpiece, inadvertently creating the compromised version we know today.

The cutdown painting is about 15 feet wide by 13 feet high. About two feet from the left of the canvas was shaved off, and another nine inches from the top. Lesser damage was done to the bottom, which lost about five inches, and the right side, which lost three. Temporarily restoring these parts will give visitors a glimpse of what had been lost: three figures on the left-hand side (two men and a boy) and, more important, a feel for Rembrandt's meticulous construction in the work's composition. With the missing pieces, the original dynamism of the masterpiece is stirred back to life.

One of Rembrandt's finest works, Militia Company of District II under the Command of Captain Frans Banninck Cocq (better known as The Night Watch) from 1642, is a prime representation of Dutch Golden Age painting. But the painting was greatly disfigured after the artist's death, when it was moved from its original location at the Arquebusiers Guild Hall to Amsterdam's City Hall in 1715. City officials wanted to place it in a gallery between two doors, but the painting was too big to fit. Instead of finding another location, they cut large panels from the sides as well as some sections from the top and bottom. The fragments were lost after removal.

In studying robots and planning problems, a basic question is what is the minimal information a robot must obtain to guarantee task completion. Erdmann's theory of action-based sensors is a classical approach to characterizing fundamental information requirements. That approach uses a plan to derive a type of virtual sensor which prescribes actions that make progress toward a goal. We show that the established theory is incomplete: the previous method for obtaining such sensors, using backchained plans, overlooks some sensors. Furthermore, there are plans, that are guaranteed to achieve goals, where the existing methods are unable to provide any action-based sensor. We identify the underlying feature common to all such plans. Then, we show how to produce action-based sensors even for plans where the existing treatment is inadequate, although for these cases they have no single canonical sensor. Consequently, the approach is generalized to produce sets of sensors. Finally, we show also that this is a complete characterization of action-based sensors for planning problems and discuss how an action-based sensor translates into the traditional conception of a sensor.