From 4f60714def210a8954391cc9830428977a02f1d3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tristan=20St=C3=A9rin?= Date: Sat, 16 Jul 2022 20:02:51 +0100 Subject: [PATCH 1/3] Decider closed states --- .gitignore | 2 + decider-closed-states/README.md | 8 + decider-closed-states/bbchallenge_utils.py | 75 + decider-closed-states/main.py | 115 + decider-closed-states/main_test.py | 19 + .../output/machines-closed-states.csv | 5650 +++++++++++++++++ decider-closed-states/requirements.txt | 9 + 7 files changed, 5878 insertions(+) create mode 100644 decider-closed-states/README.md create mode 100644 decider-closed-states/bbchallenge_utils.py create mode 100644 decider-closed-states/main.py create mode 100644 decider-closed-states/main_test.py create mode 100644 decider-closed-states/output/machines-closed-states.csv create mode 100644 decider-closed-states/requirements.txt diff --git a/.gitignore b/.gitignore index 9a46a8e..b8ebd8b 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,5 @@ +__pycache__ +venv decider-cyclers/decider-cyclers rsync_indexes.sh unsorted_indexes diff --git a/decider-closed-states/README.md b/decider-closed-states/README.md new file mode 100644 index 0000000..9e56042 --- /dev/null +++ b/decider-closed-states/README.md @@ -0,0 +1,8 @@ +# Decider closed states + +```python +python3.9 -m venv venv +pip install -r requirements.txt +python -m unittest main_test.py +python main.py +``` diff --git a/decider-closed-states/bbchallenge_utils.py b/decider-closed-states/bbchallenge_utils.py new file mode 100644 index 0000000..b741cd0 --- /dev/null +++ b/decider-closed-states/bbchallenge_utils.py @@ -0,0 +1,75 @@ +import os +from tabulate import tabulate + + +def get_machine_i(machine_db_path, i, db_has_header=True): + with open(machine_db_path, "rb") as f: + c = 1 if db_has_header else 0 + f.seek(30 * (i + c)) + return f.read(30) + + +def get_indices_from_index_file(index_file_path): + index_file_size = os.path.getsize(index_file_path) + + machines_indices = [] + with open(index_file_path, "rb") as f: + for i in range(index_file_size // 4): + chunk = f.read(4) + machines_indices.append(int.from_bytes(chunk, byteorder="big")) + + return machines_indices + + +R, L = 0, 1 + + +def ithl(i): + return chr(ord("A") + i) + + +def g(move): + if move == R: + return "R" + return "L" + + +def pptm(machine, return_repr=False): + headers = ["s", "0", "1"] + table = [] + + for i in range(5): + row = [ithl(i)] + for j in range(2): + write = machine[6 * i + 3 * j] + move = machine[6 * i + 3 * j + 1] + goto = machine[6 * i + 3 * j + 2] - 1 + + if goto == -1: + row.append("???") + continue + + row.append(f"{write}{g(move)}{ithl(goto)}") + table.append(row) + + if not return_repr: + print(tabulate(table, headers=headers)) + else: + return tabulate(table, headers=headers) + + +def format_machine(machine): + to_return = [] + for i in range(5): + for j in range(2): + write = machine[6 * i + 3 * j] + move = machine[6 * i + 3 * j + 1] + goto = machine[6 * i + 3 * j + 2] - 1 + + if goto == -1: + to_return.append("---") + continue + + to_return.append(f"{write}{g(move)}{ithl(goto)}") + + return "_".join(to_return) diff --git a/decider-closed-states/main.py b/decider-closed-states/main.py new file mode 100644 index 0000000..7348e6b --- /dev/null +++ b/decider-closed-states/main.py @@ -0,0 +1,115 @@ +import tqdm +from bbchallenge_utils import * + +DB_PATH = "../all_5_states_undecided_machines_with_global_header" +UNDECIDED_INDEX_PATH = "../bb5_undecided_index" + + +def get_states_with_undefined_transition(machine: bytes): + to_return = [] + nb_states = len(machine) // 6 # 3 bytes per transition, 6 per state + for i_state in range(nb_states): + if machine[6 * i_state + 2] == 0 or machine[6 * i_state + 5] == 0: + to_return.append(i_state) + + return to_return + + +def get_states_reachable_from( + machine: bytes, i_state: int, debug: bool = False +): + # BFS logic + visited = set({}) + to_visit = [i_state] + if debug: + print() + + while len(to_visit) != 0: + curr_state = to_visit[0] + to_visit = to_visit[1:] + + if curr_state in visited: + continue + + visited.add(curr_state) + + goto_0 = machine[6 * curr_state + 2] + if goto_0 != 0: + to_visit.append(goto_0 - 1) + + goto_1 = machine[6 * curr_state + 5] + if goto_1 != 0: + to_visit.append(goto_1 - 1) + + if debug: + print(curr_state, goto_0, goto_1, to_visit) + return visited + + +def decider_closed_states( + machine: bytes, debug: bool = False, reachables_to_return: set = {} +): + """If the machine ever enters a closed set of states where + all transitions are defined, then it never halts. + + Note that by: + + 1. By construction, any state of a machine of bbchallenge that + contains at least one defined transition has been reach at some point in the + execution of the machine. + + 2. Furthermore, there are no machines in the db with a state that has 2 undefined transitions, + since this is solved by BB(4) = 107 during enumeration. This means that with point 1. we know + that all the states of the machine are reached at some point by the machine when started from + blank tape. + + Hence we don't need to run the machine at all, but we just need to check its code to see if there + exists such a closed set of states where all transitions are defined. We know that it'll be reached + and that the machine does not halt. + """ + + states_with_one_undefined_transition = get_states_with_undefined_transition( + machine + ) + + if debug: + pptm(machine) + print(states_with_one_undefined_transition) + + nb_states = len(machine) // 6 + + for i_state in range(nb_states): + reachables = get_states_reachable_from(machine, i_state, debug) + if debug: + print(i_state, reachables) + closed_states = True + for reachable_state in reachables: + if reachable_state in states_with_one_undefined_transition: + closed_states = False + break + + if closed_states: + reachables_to_return.update(reachables) + return True + + return False + + +if __name__ == "__main__": + undecided_machines_indices = get_indices_from_index_file( + UNDECIDED_INDEX_PATH + ) + + print("machine_id; machine; closed states") + + decided_ids = [] + for machine_id in tqdm.tqdm(undecided_machines_indices): + machine = get_machine_i(DB_PATH, machine_id) + closed_states = set({}) + if decider_closed_states(machine, reachables_to_return=closed_states): + print(machine_id, end="; ") + print(format_machine(machine), end="; ") + print(set(map(lambda x: chr(ord("A") + x), closed_states))) + + print(decided_ids[:20]) + print(len(decided_ids)) diff --git a/decider-closed-states/main_test.py b/decider-closed-states/main_test.py new file mode 100644 index 0000000..c503182 --- /dev/null +++ b/decider-closed-states/main_test.py @@ -0,0 +1,19 @@ +import unittest +from main import decider_closed_states, DB_PATH +from bbchallenge_utils import get_machine_i + + +class TestDeciderClosedStates(unittest.TestCase): + def test_examples(self): + ids_to_test = [4, 9] + + for machine_id in ids_to_test: + machine = get_machine_i(DB_PATH, machine_id) + self.assertTrue(decider_closed_states(machine)) + + def test_counterexamples(self): + ids_to_test = [5, 207] + + for machine_id in ids_to_test: + machine = get_machine_i(DB_PATH, machine_id) + self.assertFalse(decider_closed_states(machine, debug=False)) diff --git a/decider-closed-states/output/machines-closed-states.csv b/decider-closed-states/output/machines-closed-states.csv new file mode 100644 index 0000000..2fbee02 --- /dev/null +++ b/decider-closed-states/output/machines-closed-states.csv @@ -0,0 +1,5650 @@ +machine_id; 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1RB_1LD_1LC_---_0RA_0LB_1LE_0RE_1RD_0LD; {'E', 'D'} +84272141; 1RB_1LD_1LC_---_0RA_1LB_1RE_0LE_1LD_0RD; {'E', 'D'} +84272461; 1RB_1LD_1LC_---_0RA_1LB_1LE_0RE_1RD_0LD; {'E', 'D'} +84361495; 1RB_1LD_1LC_---_1RA_0LB_1RE_0LE_1LD_0RD; {'E', 'D'} +84362144; 1RB_1LD_1LC_---_1RA_0LB_1LE_0RE_1RD_0LD; {'E', 'D'} +84371692; 1RB_1LD_1LC_---_1RA_1LB_1RE_0LE_1LD_0RD; {'E', 'D'} +84372236; 1RB_1LD_1LC_---_1RA_1LB_1LE_0RE_1RD_0LD; {'E', 'D'} +[] +0 diff --git a/decider-closed-states/requirements.txt b/decider-closed-states/requirements.txt new file mode 100644 index 0000000..a7a210d --- /dev/null +++ b/decider-closed-states/requirements.txt @@ -0,0 +1,9 @@ +black==22.6.0 +click==8.1.3 +mypy-extensions==0.4.3 +pathspec==0.9.0 +platformdirs==2.5.2 +tabulate==0.8.10 +tomli==2.0.1 +tqdm==4.64.0 +typing-extensions==4.3.0 From 7ab54a233f59ffca2d3c0a3623fc24e490e3d346 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tristan=20St=C3=A9rin?= Date: Sat, 16 Jul 2022 20:12:15 +0100 Subject: [PATCH 2/3] Decider closed states --- decider-closed-states/main.py | 4 ---- decider-closed-states/output/machines-closed-states.csv | 4 +--- 2 files changed, 1 insertion(+), 7 deletions(-) diff --git a/decider-closed-states/main.py b/decider-closed-states/main.py index 7348e6b..0de7888 100644 --- a/decider-closed-states/main.py +++ b/decider-closed-states/main.py @@ -102,7 +102,6 @@ def decider_closed_states( print("machine_id; machine; closed states") - decided_ids = [] for machine_id in tqdm.tqdm(undecided_machines_indices): machine = get_machine_i(DB_PATH, machine_id) closed_states = set({}) @@ -110,6 +109,3 @@ def decider_closed_states( print(machine_id, end="; ") print(format_machine(machine), end="; ") print(set(map(lambda x: chr(ord("A") + x), closed_states))) - - print(decided_ids[:20]) - print(len(decided_ids)) diff --git a/decider-closed-states/output/machines-closed-states.csv b/decider-closed-states/output/machines-closed-states.csv index 2fbee02..2cfb563 100644 --- a/decider-closed-states/output/machines-closed-states.csv +++ b/decider-closed-states/output/machines-closed-states.csv @@ -5645,6 +5645,4 @@ machine_id; machine; closed states 84361495; 1RB_1LD_1LC_---_1RA_0LB_1RE_0LE_1LD_0RD; {'E', 'D'} 84362144; 1RB_1LD_1LC_---_1RA_0LB_1LE_0RE_1RD_0LD; {'E', 'D'} 84371692; 1RB_1LD_1LC_---_1RA_1LB_1RE_0LE_1LD_0RD; {'E', 'D'} -84372236; 1RB_1LD_1LC_---_1RA_1LB_1LE_0RE_1RD_0LD; {'E', 'D'} -[] -0 +84372236; 1RB_1LD_1LC_---_1RA_1LB_1LE_0RE_1RD_0LD; {'E', 'D'} \ No newline at end of file From 9f4cbd20cce920f9bad423723e9fc15c16d94335 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Tristan=20St=C3=A9rin?= Date: Sat, 16 Jul 2022 20:16:39 +0100 Subject: [PATCH 3/3] Decider closed states --- decider-closed-states/bbchallenge_utils.py | 6 +- decider-closed-states/main.py | 2 +- .../output/machines-closed-states.csv | 11296 ++++++++-------- 3 files changed, 5653 insertions(+), 5651 deletions(-) diff --git a/decider-closed-states/bbchallenge_utils.py b/decider-closed-states/bbchallenge_utils.py index b741cd0..5b24078 100644 --- a/decider-closed-states/bbchallenge_utils.py +++ b/decider-closed-states/bbchallenge_utils.py @@ -61,15 +61,17 @@ def pptm(machine, return_repr=False): def format_machine(machine): to_return = [] for i in range(5): + state_rep = "" for j in range(2): write = machine[6 * i + 3 * j] move = machine[6 * i + 3 * j + 1] goto = machine[6 * i + 3 * j + 2] - 1 if goto == -1: - to_return.append("---") + state_rep += "---" continue - to_return.append(f"{write}{g(move)}{ithl(goto)}") + state_rep += f"{write}{g(move)}{ithl(goto)}" + to_return.append(state_rep) return "_".join(to_return) diff --git a/decider-closed-states/main.py b/decider-closed-states/main.py index 0de7888..71e5b5f 100644 --- a/decider-closed-states/main.py +++ b/decider-closed-states/main.py @@ -100,7 +100,7 @@ def decider_closed_states( UNDECIDED_INDEX_PATH ) - print("machine_id; machine; closed states") + print("machine_id; machine; closed_states") for machine_id in tqdm.tqdm(undecided_machines_indices): machine = get_machine_i(DB_PATH, machine_id) diff --git a/decider-closed-states/output/machines-closed-states.csv b/decider-closed-states/output/machines-closed-states.csv index 2cfb563..4be577e 100644 --- a/decider-closed-states/output/machines-closed-states.csv +++ b/decider-closed-states/output/machines-closed-states.csv @@ -1,5648 +1,5648 @@ -machine_id; machine; closed states -66559; 1RB_---_0RC_0RD_0LC_1LA_0RE_0RD_1LE_1RD; {'E', 'D'} -66562; 1RB_---_0RC_0RD_0LC_1LA_0RE_0LD_1LD_1RE; {'E', 'D'} -66567; 1RB_---_0RC_0RD_0LC_1LA_0RE_1LD_1LD_1RE; {'E', 'D'} -66580; 1RB_---_0RC_0RD_0LC_1LA_0LD_1RE_1LD_0RE; {'E', 'D'} -66607; 1RB_---_0RC_0RD_0LC_1LA_0LE_0RD_1RD_1LE; {'E', 'D'} -66633; 1RB_---_0RC_0RD_0LC_1LA_0LE_1RD_1RD_1LE; {'E', 'D'} -66688; 1RB_---_0RC_0RD_0LC_1LA_1RE_1LD_0LD_0RE; {'E', 'D'} -66690; 1RB_---_0RC_0RD_0LC_1LA_1RE_1LD_0LD_1RE; {'E', 'D'} -66694; 1RB_---_0RC_0RD_0LC_1LA_1RE_1LD_1LD_1RE; {'E', 'D'} -66715; 1RB_---_0RC_0RD_0LC_1LA_1LD_1RE_0RD_0RE; {'E', 'D'} -66727; 1RB_---_0RC_0RD_0LC_1LA_1LD_1RE_1LD_0RE; {'E', 'D'} -66748; 1RB_---_0RC_0RD_0LC_1LA_1LE_0RD_0LE_1RD; {'E', 'D'} -66752; 1RB_---_0RC_0RD_0LC_1LA_1LE_0RD_1LE_1RD; {'E', 'D'} -66775; 1RB_---_0RC_0RD_0LC_1LA_1LE_1RD_0RD_0LE; {'E', 'D'} -66776; 1RB_---_0RC_0RD_0LC_1LA_1LE_1RD_0RD_1LE; {'E', 'D'} -66777; 1RB_---_0RC_0RD_0LC_1LA_1LE_1RD_1RD_1LE; {'E', 'D'} -92590; 1RB_---_0RC_0RD_1LC_1LA_0RD_1LE_1RD_0LE; {'E', 'D'} -92632; 1RB_---_0RC_0RD_1LC_1LA_0RE_0RD_1LE_1RD; {'E', 'D'} -92670; 1RB_---_0RC_0RD_1LC_1LA_0RE_0LD_1LD_1RE; {'E', 'D'} -92747; 1RB_---_0RC_0RD_1LC_1LA_0RE_1LD_1LD_1RE; {'E', 'D'} -92838; 1RB_---_0RC_0RD_1LC_1LA_0LD_1RE_1LD_0RE; {'E', 'D'} -92884; 1RB_---_0RC_0RD_1LC_1LA_0LE_0RD_1RD_1LE; {'E', 'D'} -92936; 1RB_---_0RC_0RD_1LC_1LA_0LE_0LD_1RE_1LD; {'E', 'D'} -92972; 1RB_---_0RC_0RD_1LC_1LA_0LE_1RD_1RD_1LE; {'E', 'D'} -93081; 1RB_---_0RC_0RD_1LC_1LA_1RD_1LE_0LD_0LE; {'E', 'D'} -93085; 1RB_---_0RC_0RD_1LC_1LA_1RD_1LE_1RD_0LE; {'E', 'D'} -93118; 1RB_---_0RC_0RD_1LC_1LA_1RE_0LD_0RE_1LD; {'E', 'D'} -93122; 1RB_---_0RC_0RD_1LC_1LA_1RE_0LD_1RE_1LD; {'E', 'D'} -93146; 1RB_---_0RC_0RD_1LC_1LA_1RE_1LD_0LD_0RE; {'E', 'D'} -93148; 1RB_---_0RC_0RD_1LC_1LA_1RE_1LD_0LD_1RE; {'E', 'D'} -93151; 1RB_---_0RC_0RD_1LC_1LA_1RE_1LD_1LD_1RE; {'E', 'D'} -93197; 1RB_---_0RC_0RD_1LC_1LA_1LD_1RE_0RD_0RE; {'E', 'D'} -93201; 1RB_---_0RC_0RD_1LC_1LA_1LD_1RE_1LD_0RE; {'E', 'D'} -93232; 1RB_---_0RC_0RD_1LC_1LA_1LE_0RD_0LE_1RD; {'E', 'D'} -93239; 1RB_---_0RC_0RD_1LC_1LA_1LE_0RD_1LE_1RD; {'E', 'D'} -93278; 1RB_---_0RC_0RD_1LC_1LA_1LE_1RD_0RD_0LE; {'E', 'D'} -93279; 1RB_---_0RC_0RD_1LC_1LA_1LE_1RD_0RD_1LE; {'E', 'D'} -93286; 1RB_---_0RC_0RD_1LC_1LA_1LE_1RD_1RD_1LE; {'E', 'D'} -197717; 1RB_---_0RC_0LD_0LC_1LA_0RD_1LE_1RD_0LE; {'E', 'D'} -197735; 1RB_---_0RC_0LD_0LC_1LA_0RE_0LD_1LD_1RE; {'E', 'D'} -197774; 1RB_---_0RC_0LD_0LC_1LA_0RE_1LD_1LD_1RE; {'E', 'D'} -197797; 1RB_---_0RC_0LD_0LC_1LA_0LD_1RE_1LD_0RE; {'E', 'D'} -197805; 1RB_---_0RC_0LD_0LC_1LA_0LE_0RD_1RD_1LE; {'E', 'D'} -197836; 1RB_---_0RC_0LD_0LC_1LA_0LE_1RD_1RD_1LE; {'E', 'D'} -197875; 1RB_---_0RC_0LD_0LC_1LA_1RD_1LE_0LD_0LE; {'E', 'D'} -197878; 1RB_---_0RC_0LD_0LC_1LA_1RD_1LE_1RD_0LE; {'E', 'D'} -197914; 1RB_---_0RC_0LD_0LC_1LA_1RE_1LD_0LD_0RE; {'E', 'D'} -197915; 1RB_---_0RC_0LD_0LC_1LA_1RE_1LD_0LD_1RE; {'E', 'D'} -197921; 1RB_---_0RC_0LD_0LC_1LA_1RE_1LD_1LD_1RE; {'E', 'D'} -197931; 1RB_---_0RC_0LD_0LC_1LA_1LD_1RE_0RD_0RE; {'E', 'D'} -197936; 1RB_---_0RC_0LD_0LC_1LA_1LD_1RE_1LD_0RE; {'E', 'D'} -197956; 1RB_---_0RC_0LD_0LC_1LA_1LE_1RD_0RD_0LE; {'E', 'D'} -197957; 1RB_---_0RC_0LD_0LC_1LA_1LE_1RD_0RD_1LE; {'E', 'D'} -197962; 1RB_---_0RC_0LD_0LC_1LA_1LE_1RD_1RD_1LE; {'E', 'D'} -227816; 1RB_---_0RC_0LD_1LC_1LA_0RD_1LE_1RD_0LE; {'E', 'D'} -227841; 1RB_---_0RC_0LD_1LC_1LA_0RE_0RD_1LE_1RD; {'E', 'D'} -227860; 1RB_---_0RC_0LD_1LC_1LA_0RE_0LD_1LD_1RE; {'E', 'D'} -227917; 1RB_---_0RC_0LD_1LC_1LA_0RE_1LD_1LD_1RE; {'E', 'D'} -227976; 1RB_---_0RC_0LD_1LC_1LA_0LD_1RE_1LD_0RE; {'E', 'D'} -227984; 1RB_---_0RC_0LD_1LC_1LA_0LE_0RD_1RD_1LE; {'E', 'D'} -228010; 1RB_---_0RC_0LD_1LC_1LA_0LE_0LD_1RE_1LD; {'E', 'D'} -228032; 1RB_---_0RC_0LD_1LC_1LA_0LE_1RD_1RD_1LE; {'E', 'D'} -228085; 1RB_---_0RC_0LD_1LC_1LA_1RD_1LE_0LD_0LE; {'E', 'D'} -228088; 1RB_---_0RC_0LD_1LC_1LA_1RD_1LE_1RD_0LE; {'E', 'D'} -228126; 1RB_---_0RC_0LD_1LC_1LA_1RE_0LD_0RE_1LD; {'E', 'D'} -228130; 1RB_---_0RC_0LD_1LC_1LA_1RE_0LD_1RE_1LD; {'E', 'D'} -228158; 1RB_---_0RC_0LD_1LC_1LA_1RE_1LD_0LD_0RE; {'E', 'D'} -228159; 1RB_---_0RC_0LD_1LC_1LA_1RE_1LD_0LD_1RE; {'E', 'D'} -228163; 1RB_---_0RC_0LD_1LC_1LA_1RE_1LD_1LD_1RE; {'E', 'D'} -228187; 1RB_---_0RC_0LD_1LC_1LA_1LD_1RE_0RD_0RE; {'E', 'D'} -228190; 1RB_---_0RC_0LD_1LC_1LA_1LD_1RE_1LD_0RE; {'E', 'D'} -228213; 1RB_---_0RC_0LD_1LC_1LA_1LE_1RD_0RD_0LE; {'E', 'D'} -228214; 1RB_---_0RC_0LD_1LC_1LA_1LE_1RD_0RD_1LE; {'E', 'D'} -228218; 1RB_---_0RC_0LD_1LC_1LA_1LE_1RD_1RD_1LE; {'E', 'D'} -343350; 1RB_---_0RC_1RD_0LC_1LA_0RE_0RD_1LE_1RD; {'E', 'D'} -343355; 1RB_---_0RC_1RD_0LC_1LA_0RE_0LD_1LD_1RE; {'E', 'D'} -343377; 1RB_---_0RC_1RD_0LC_1LA_0RE_1LD_1LD_1RE; {'E', 'D'} -343400; 1RB_---_0RC_1RD_0LC_1LA_0LD_1RE_1LD_0RE; {'E', 'D'} -343459; 1RB_---_0RC_1RD_0LC_1LA_0LE_0RD_1RD_1LE; {'E', 'D'} -343492; 1RB_---_0RC_1RD_0LC_1LA_0LE_0LD_1RE_1LD; {'E', 'D'} -343516; 1RB_---_0RC_1RD_0LC_1LA_0LE_1RD_1RD_1LE; {'E', 'D'} -343598; 1RB_---_0RC_1RD_0LC_1LA_1RE_1LD_0LD_0RE; {'E', 'D'} -343600; 1RB_---_0RC_1RD_0LC_1LA_1RE_1LD_0LD_1RE; {'E', 'D'} -343604; 1RB_---_0RC_1RD_0LC_1LA_1RE_1LD_1LD_1RE; {'E', 'D'} -343657; 1RB_---_0RC_1RD_0LC_1LA_1LD_1RE_0RD_0RE; {'E', 'D'} -343668; 1RB_---_0RC_1RD_0LC_1LA_1LD_1RE_1LD_0RE; {'E', 'D'} -343687; 1RB_---_0RC_1RD_0LC_1LA_1LE_0RD_0LE_1RD; {'E', 'D'} -343690; 1RB_---_0RC_1RD_0LC_1LA_1LE_0RD_1LE_1RD; {'E', 'D'} -343722; 1RB_---_0RC_1RD_0LC_1LA_1LE_1RD_0RD_0LE; {'E', 'D'} -343723; 1RB_---_0RC_1RD_0LC_1LA_1LE_1RD_0RD_1LE; {'E', 'D'} -343726; 1RB_---_0RC_1RD_0LC_1LA_1LE_1RD_1RD_1LE; {'E', 'D'} -376963; 1RB_---_0RC_1RD_1LC_1LA_0RD_1LE_1RD_0LE; {'E', 'D'} -376985; 1RB_---_0RC_1RD_1LC_1LA_0RE_0RD_1LE_1RD; {'E', 'D'} -377024; 1RB_---_0RC_1RD_1LC_1LA_0RE_0LD_1LD_1RE; {'E', 'D'} -377090; 1RB_---_0RC_1RD_1LC_1LA_0RE_1LD_1LD_1RE; {'E', 'D'} -377239; 1RB_---_0RC_1RD_1LC_1LA_0LD_1RE_1LD_0RE; {'E', 'D'} -377297; 1RB_---_0RC_1RD_1LC_1LA_0LE_0RD_1RD_1LE; {'E', 'D'} -377350; 1RB_---_0RC_1RD_1LC_1LA_0LE_0LD_1RE_1LD; {'E', 'D'} -377398; 1RB_---_0RC_1RD_1LC_1LA_0LE_1RD_1RD_1LE; {'E', 'D'} -377440; 1RB_---_0RC_1RD_1LC_1LA_1RD_1LE_0LD_0LE; {'E', 'D'} -377441; 1RB_---_0RC_1RD_1LC_1LA_1RD_1LE_1RD_0LE; {'E', 'D'} -377474; 1RB_---_0RC_1RD_1LC_1LA_1RE_0LD_0RE_1LD; {'E', 'D'} -377479; 1RB_---_0RC_1RD_1LC_1LA_1RE_0LD_1RE_1LD; {'E', 'D'} -377507; 1RB_---_0RC_1RD_1LC_1LA_1RE_1LD_0LD_0RE; {'E', 'D'} -377509; 1RB_---_0RC_1RD_1LC_1LA_1RE_1LD_0LD_1RE; {'E', 'D'} -377518; 1RB_---_0RC_1RD_1LC_1LA_1RE_1LD_1LD_1RE; {'E', 'D'} -377561; 1RB_---_0RC_1RD_1LC_1LA_1LD_1RE_0RD_0RE; {'E', 'D'} -377565; 1RB_---_0RC_1RD_1LC_1LA_1LD_1RE_1LD_0RE; {'E', 'D'} -377578; 1RB_---_0RC_1RD_1LC_1LA_1LE_0RD_0LE_1RD; {'E', 'D'} -377582; 1RB_---_0RC_1RD_1LC_1LA_1LE_0RD_1LE_1RD; 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