WEBVTT 1 00:00:00.200 --> 00:00:04.347 To help a system, we may need to change it, rather than only observe it. 2 00:00:04.347 --> 00:00:09.213 After an action, knowing where it is now may leave open where it began. 3 00:00:09.213 --> 00:00:14.320 Watch what an action changes, what a later reading teaches us, and why these are 4 00:00:14.320 --> 00:00:15.320 different steps. 5 00:00:16.640 --> 00:00:20.380 Earlier question trees held the unknown state fixed. 6 00:00:20.380 --> 00:00:23.280 Now allow a button press between readings. 7 00:00:23.280 --> 00:00:28.464 Ask two separate questions: where did the device begin, and where is it now? 8 00:00:28.464 --> 00:00:30.760 Call the beginning its origin. 9 00:00:30.760 --> 00:00:36.120 Use the same known rules: RESET sends every configuration to u. 10 00:00:36.120 --> 00:00:41.216 PULSE sends u to w and leaves v, w and z unchanged. 11 00:00:41.216 --> 00:00:45.840 READ gives the exact current lamp output without changing the state. 12 00:00:45.840 --> 00:00:49.360 This nondisturbing reader is an assumption of our example. 13 00:00:50.150 --> 00:00:54.710 Start a fresh run with either u or w as the origin. 14 00:00:54.710 --> 00:00:58.790 No reading has arrived yet, and no button has been pressed. 15 00:00:58.790 --> 00:01:03.398 The origin and current state are the same in each possible history. 16 00:01:03.398 --> 00:01:07.470 Take READ and suppose it returns zero. 17 00:01:07.470 --> 00:01:12.089 Only the u history fits that report, because w would give one. 18 00:01:12.089 --> 00:01:16.562 No action occurred, so origin and current state are both u. 19 00:01:16.562 --> 00:01:21.502 The observer has ruled out a possible history; the model still contains w. 20 00:01:22.742 --> 00:01:28.155 Begin a separate comparison run from u or w, with no prior reading. 21 00:01:28.155 --> 00:01:31.414 Do not carry over the conclusion of Run A. 22 00:01:31.414 --> 00:01:35.515 This time, press RESET before taking a reading. 23 00:01:35.515 --> 00:01:39.764 RESET is now the executed action in this run. 24 00:01:39.764 --> 00:01:43.018 Starting in u, RESET gives current u. 25 00:01:43.018 --> 00:01:47.266 Starting in w, RESET also gives current u. 26 00:01:47.266 --> 00:01:50.622 Preserve both origin labels. 27 00:01:50.622 --> 00:01:57.289 We know the current state from the supplied rule and the executed action, without knowing which origin was present. 28 00:01:58.159 --> 00:02:00.059 Now READ returns zero. 29 00:02:00.059 --> 00:02:05.459 The record, RESET followed by zero, is the same for both origins. 30 00:02:05.459 --> 00:02:11.699 The possible histories are origin u to current u, and origin w to current u. 31 00:02:11.699 --> 00:02:15.786 Exactly one happened, but the record does not choose which. 32 00:02:15.786 --> 00:02:20.351 After this RESET and reading, must the device have started in u? 33 00:02:20.351 --> 00:02:29.559 Keep the origin column separate from the current-state column while you decide. 34 00:02:29.559 --> 00:02:34.719 No. The current state is u; the origin could have been u or w. 35 00:02:34.719 --> 00:02:37.292 RESET made the current states converge. 36 00:02:37.292 --> 00:02:40.839 It did not supply a measurement distinguishing their origins. 37 00:02:42.079 --> 00:02:45.529 Start another run, this time from u or v. 38 00:02:45.529 --> 00:02:47.799 Execute PULSE. 39 00:02:47.799 --> 00:02:53.506 The u origin leads to current w; the v origin leads to current v. 40 00:02:53.506 --> 00:02:58.819 These are the possible histories of this run, not two actions on one device. 41 00:02:58.819 --> 00:03:05.959 With this declared u-or-v starting set, suppose the exact READ after PULSE reports one. 42 00:03:05.959 --> 00:03:13.919 What is the current state, and what was the origin? 43 00:03:13.919 --> 00:03:17.719 The current state is w and the origin was u. 44 00:03:17.719 --> 00:03:22.367 The other possible history, v to v, would have reported zero. 45 00:03:22.367 --> 00:03:26.692 This origin inference depends on starting with only u or v. 46 00:03:26.692 --> 00:03:32.399 If the new report were zero instead, the current state would be v and the origin v. 47 00:03:32.399 --> 00:03:38.079 A complete plan includes both possible answers, although an actual run receives one of them. 48 00:03:38.949 --> 00:03:44.569 For a time-stamped replay, first let READ give zero before PULSE. 49 00:03:44.569 --> 00:03:49.309 That earlier zero describes the lamp before the action. 50 00:03:49.309 --> 00:03:53.922 After PULSE, current possibilities are w or v. 51 00:03:53.922 --> 00:03:58.822 Do not reuse the old zero as if a new reading had just arrived. 52 00:03:58.822 --> 00:04:03.962 For a known action, move each current possibility through its transition rule. 53 00:04:03.962 --> 00:04:08.222 For a new report, keep the resulting possibilities that match it. 54 00:04:08.222 --> 00:04:12.162 Keep an origin tag when the question concerns the past. 55 00:04:12.162 --> 00:04:16.222 The current set of possibilities is sometimes called the support. 56 00:04:16.932 --> 00:04:21.446 Compare asking READ before RESET with asking it afterward. 57 00:04:21.446 --> 00:04:26.385 Before RESET, the lamp distinguishes the u and w origins. 58 00:04:26.385 --> 00:04:29.172 After RESET, both give zero. 59 00:04:29.172 --> 00:04:36.105 A plan that identifies the origin must therefore check the permitted timing of observations and actions. 60 00:04:36.105 --> 00:04:41.945 If the goal is only to know the current state after RESET, that same plan succeeds. 61 00:04:41.945 --> 00:04:45.860 If the goal is to reconstruct the origin, it fails. 62 00:04:45.860 --> 00:04:54.212 More constrained research models add other rules; this example establishes the timing distinction under its stated assumptions. 63 00:04:54.842 --> 00:04:59.702 After RESET from u or w, the current state is known to be u. 64 00:04:59.702 --> 00:05:02.568 The origin remains u or w. 65 00:05:02.568 --> 00:05:06.282 Saying only that we know the state would hide this difference. 66 00:05:06.282 --> 00:05:10.095 Some actions bring different current states to the same state. 67 00:05:10.095 --> 00:05:14.762 In our RESET run, later readings cannot distinguish the two origins. 68 00:05:14.762 --> 00:05:22.589 Our PULSE example showed how an action followed by a reading can instead distinguish the declared u-or-v origins. 69 00:05:22.589 --> 00:05:26.874 Every reading here was exact and every transition rule known. 70 00:05:26.874 --> 00:05:31.615 Next, keep the transitions fixed but declare a noisy reader. 71 00:05:31.615 --> 00:05:37.882 We will ask how a report changes an estimate when it cannot simply eliminate every disagreeing state.