| --- Log opened Tue Nov 08 00:00:12 2022 |
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| 01:41 | <&McMartin> | Were there other limitations on the game that made this not literally the halting problem? |
| 01:42 | <&McMartin> | (I forget if, for instance, the paper tape was of limited length) |
| 01:59 | <&ToxicFrog> | I do not recall! I last played this in university. |
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| 03:21 | <@mac> | McMartin: Only half the puzzles were halting problems. The other half required you to output the given robot with the symbol tape manipulated in some specified manner instead. |
| 03:21 | <@mac> | E.g. 'move all reds to the end'. |
| 03:23 | <@mac> | Though obviously it isn't a /true/ Turing machine since the number of states and transitions are limited. |
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| 03:53 | <~Vornicus> | the capstones in the original were iirc "add two binary numbers" and some similar stuff where a correct answer took up basically the entire grid |
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| 04:28 | <&McMartin> | mac: No, I mean, "does this Turing Machine decide this property" and the obvious generalizations of it all reduce to the halting problem and thus are themselves undecidable |
| 04:28 | <&McMartin> | Zachtronics games address this by giving you a Stop key, basically |
| 04:29 | <&McMartin> | The trailer shows an infinite loop detector, which given the general nature of the problems will be feasible for "sane" infinite loops and comprehensive if there's a maximum tape length. |
| 04:29 | <@mac> | Pretty sure there's just a maximum runtime permittefd per robot. |
| 04:30 | <&McMartin> | (The conveyors are all fixed in place so if the robot hits a cell twice with the same tape, you can immediately flag that as a loop) |
| 04:30 | <@mac> | In the original, that is. |
| 04:30 | <&McMartin> | Capping the number of steps will also accomplish this, yes. |
| 04:30 | <&McMartin> | ... though it occurs to me that the proof for doing so is that a machine that runs for a finite number of steps only has a finite-sized tape and finite-sized tape is known to be solvable. |
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| 07:07 | <~Vornicus> | this thing, in the zachtronics tradition, includes leaderboards, but also goal values for the things it counts |
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| --- Log closed Wed Nov 09 00:00:14 2022 |