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Text of the page (random words):
_count total number of input variables result_vector integer representing the output bits of the truth table returns true if the input is irrelevant false otherwise considered_to_resultbits 0 1 for in_count in range 2 input_count considered_bit in_count considered 1 resultbit result_vector in_count 1 considered_to_resultbits considered_bit append resultbit return considered_to_resultbits 0 considered_to_resultbits 1 def find_irrelevant_ttable_inputs input_count int result_vector int list int identify which input variables are irrelevant in a standardized truth table args input_count number of input variables result_vector integer representing the output bits of the truth table returns list of input indices that are irrelevant irrelevant i for i in range input_count if is_irrelevant i input_count result_vector return irrelevant relevant and irrelevant result vectors for stt s i am interested in the truthtables boolean expressions of an increasing number of inputs previously i was taking all the zero input stt then all the 1 input all the 2 input that had repetitions and irrelevancies i can now take just the relevant result vectors for each case or take the maximum inputs i can handle and sort the result vectors so that those with the most irrelevancies for that maximum number of inputs come first here s the code i used to investigate these properties of irrelevances def print_stt_results_sensitive_to_inputs max_input_count int none print a summary of irrelevance patterns across all standardized truth tables stts for input counts from 0 up to max_input_count 1 for each input count i the function computes all possible result vectors 2 2 i identifies which inputs are irrelevant for each result summarizes how many result vectors have at least one irrelevant input prints spacing patterns diffs between result indices with irrelevance checks whether irrelevance indices for input count i begin with those from i 1 args max_input_count the exclusive upper bound on input counts to analyze imax2irrelevances for imax in range max_input_count print f n inputs imax n result_count 2 2 imax print f total_possible_tt_results result_count result2irrelevances r i for i in range imax if is_irrelevant i imax r for r in range result_count txt pprint pformat result2irrelevances compact true indent 2 replace n n txt txt replace n print result2irrelevances txt irrelevances k for k v in result2irrelevances items if v imax2irrelevances imax irrelevances relevances result_count len irrelevances print f irrelevances print f len irrelevances relevances table chop_line format_irrelevance_table_full result2irrelevances imax 0 220 print n stt result irrelevance vs input table f n table first order differences between irrelevance indices diff0 irrelevances j irrelevances j 1 for j in range 1 len irrelevances print f diff0 second order differences between irrelevance indices diff1 diff0 j diff0 j 1 for j in range 1 len diff0 print f diff1 print n n irrelevance indices reflected about the center of the r count f n is_irrelevance_reflected imax2irrelevances true so far print irrelevances for i inputs begin with those from i 1 previous_prefixed all i0 imax2irrelevances i 1 imax2irrelevances i len i0 for i in range 1 max_input_count print f previous_prefixed true so far def is_irrelevance_reflected ins2irrel dict int list int bool check whether irrelevance indices are symmetric about the center of the result vector space for each input count i the result vector space has size 2 2 i this function checks whether for every irrelevance index r half_range its mirror index full_range 1 r is also marked as irrelevant args ins2irrel mapping from input count to list of result indices with irrelevance returns true if all irrelevance sets are symmetric about the center false otherwise for imax irrelevances in ins2irrel items irrel_set set irrelevances full_range 2 2 imax half_range full_range 2 if not all full_range 1 i in irrel_set for i in irrel_set if i half_range return false return true def format_irrelevance_table result2irrelevances dict int list int input_count int tuple str str create a compact table showing which inputs are irrelevant for each result vector r each column is sized to match the width of its corresponding r value only includes columns for r values that have at least one irrelevant input each row corresponds to an input index with if that input is irrelevant for that r else blank returns a tuple of plain text table string markdown table string if input_count 0 msg no inputs to analyze input_count 0 md input none n n none return msg md filtered_r r for r irrels in result2irrelevances items if irrels if not filtered_r msg no irrelevant inputs found for any result vector md input none n n n join f i i for i in range input_count return msg md determine individual column widths based on r string length r_labels str r for r in filtered_r col_widths len label for label in r_labels header row header_plain 8 join label rjust w for label w in zip r_labels col_widths header_md input join label rjust w for label w in zip r_labels col_widths markdown separator row separator_md join w 2 for w in col_widths rows rows_plain rows_md for i in range input_count label f i i ljust 8 row_plain label join rjust w if i in result2irrelevances r else w for r w in zip filtered_r col_widths row_md f i i ljust 5 join rjust w if i in result2irrelevances r else w for r w in zip filtered_r col_widths rows_plain append row_plain rows_md append row_md plain_table n join header_plain rows_plain markdown_table n join header_md separator_md rows_md return plain_table markdown_table def format_irrelevance_table_full result2irrelevances dict int list int input_count int tuple str str create a full table showing which inputs are irrelevant for each result vector r includes columns for all result vector indices 0 to max r each row corresponds to an input index with if that input is irrelevant for that r else blank returns a tuple of plain text table string markdown table string if input_count 0 msg no inputs to analyze input_count 0 md input none n n none return msg md all_r sorted result2irrelevances keys r_labels str r for r in all_r col_widths len label for label in r_labels header row header_plain 8 join label rjust w for label w in zip r_labels col_widths header_md input join label rjust w for label w in zip r_labels col_widths markdown separator row separator_md join w 2 for w in col_widths rows rows_plain rows_md for i in range input_count label f i i ljust 8 row_plain label join rjust w if i in result2irrelevances get r else w for r w in zip all_r col_widths row_md f i i ljust 5 join rjust w if i in result2irrelevances get r else w for r w in zip all_r col_widths rows_plain append row_plain rows_md append row_md plain_table n join header_plain rows_plain markdown_table n join header_md separator_md rows_md return plain_table markdown_table def chop_line table_text str max_length int str chop each line in a multi line string to a maximum length if a line exceeds max_length it is truncated to max_length 3 and is appended args table_text the full multi line string to process max_length the maximum allowed line length returns a new multi line string with long lines chopped and marked with chopped_lines for line in table_text splitlines if len line max_length chopped_lines append line max_length 3 else chopped_lines append line return n join chopped_lines print_stt_results_sensitive_to_inputs 5 irrelevances output inputs 0 total_possible_tt_results 2 irrelevances len irrelevances 0 relevances 2 stt result irrelevance vs input table no inputs to analyze input_count 0 inputs 1 total_possible_tt_results 4 irrelevances 0 3 len irrelevances 2 relevances 2 stt result irrelevance vs input table 0 1 2 3 i 0 inputs 2 total_possible_tt_results 16 irrelevances 0 3 5 10 12 15 len irrelevances 6 relevances 10 stt result irrelevance vs input table 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 i 0 i 1 inputs 3 total_possible_tt_results 256 irrelevances 0 3 5 10 12 15 17 34 48 51 60 63 68 80 85 90 95 102 119 136 153 160 165 170 175 187 192 195 204 207 221 238 240 243 245 250 252 255 len irrelevances 38 relevances 218 stt result irrelevance vs input table 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 i 0 i 1 i 2 inputs 4 total_possible_tt_results 65536 irrelevances 0 3 5 10 12 15 17 34 48 51 60 63 68 80 85 90 95 102 119 136 153 160 165 170 175 187 192 195 204 207 221 238 240 243 245 250 252 255 257 514 768 771 780 783 816 819 828 831 960 963 972 975 1008 1011 1020 1023 1028 1280 1285 1290 1295 1360 1365 1370 1375 1440 1445 1450 1455 1520 1525 1530 1535 1542 1799 2056 2313 2560 2565 2570 2575 2640 2645 2650 2655 2720 2725 2730 2735 2800 2805 2810 2815 2827 3072 3075 3084 3087 3120 3123 3132 3135 3264 3267 3276 3279 3312 3315 3324 3327 3341 3598 3840 3843 3845 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46517 46774 47031 47288 47545 47802 47872 47889 47906 47923 47940 47957 47974 47991 48008 48025 48042 48059 48076 48093 48110 48127 48316 48573 48830 49087 49152 49155 49164 49167 49200 49203 49212 49215 49344 49347 49356 49359 49392 49395 49404 49407 49601 49858 49920 49923 49932 49935 49968 49971 49980 49983 50112 50115 50124 50127 50160 50163 50172 50175 50372 50629 50886 51143 51400 51657 51914 52171 52224 52227 52236 52239 52241 52258 52272 52275 52284 52287 52292 52309 52326 52343 52360 52377 52394 52411 52416 52419 52428 52431 52445 52462 52464 52467 52476 52479 52685 52942 52992 52995 53004 53007 53040 53043 53052 53055 53184 53187 53196 53199 53232 53235 53244 53247 53456 53713 53970 54227 54484 54741 54998 55255 55512 55769 56026 56283 56540 56576 56593 56610 56627 56644 56661 56678 56695 56712 56729 56746 56763 56780 56797 56814 56831 57054 57311 57568 57825 58082 58339 58596 58853 59110 59367 59624 59881 60138 60395 60652 60909 60928 60945 60962 60979 60996 61013 61030 61047 61064 61081 61098 61115 61132 61149 61166 61183 61423 61440 61443 61445 61450 61452 61455 61488 61491 61500 61503 61520 61525 61530 61535 61600 61605 61610 61615 61632 61635 61644 61647 61680 61683 61685 61690 61692 61695 61937 62194 62208 62211 62220 62223 62256 62259 62268 62271 62400 62403 62412 62415 62448 62451 62460 62463 62708 62720 62725 62730 62735 62800 62805 62810 62815 62880 62885 62890 62895 62960 62965 62970 62975 63222 63479 63736 63993 64000 64005 64010 64015 64080 64085 64090 64095 64160 64165 64170 64175 64240 64245 64250 64255 64507 64512 64515 64524 64527 64560 64563 64572 64575 64704 64707 64716 64719 64752 64755 64764 64767 65021 65278 65280 65283 65285 65290 65292 65295 65297 65314 65328 65331 65340 65343 65348 65360 65365 65370 65375 65382 65399 65416 65433 65440 65445 65450 65455 65467 65472 65475 65484 65487 65501 65518 65520 65523 65525 65530 65532 65535 len irrelevances 942 relevances 64594 stt result irrelevance vs input table 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 i 0 i 1 i 2 i 3 irrelevance indices reflected about the center of the r count true irrelevances for i inputs begin with those from i 1 true oeis the sequence of relevances 2 2 10 218 64594 is already present as a000371 on oeis the sequences of irelevances 0 2 6 38 942 had no exact match although a005530 came close end posted by paddy3118 at 12 51 pm 0 comments email this blogthis share to x share to facebook share to pinterest older posts home subscribe to posts atom about me paddy3118 view my complete profile followers subscribe now google go deh too whos amung us blog archive 2025 6 september 1 from all truths to ir relevancies august 1 july 1 march 2 january 1 2024 5 november 1 may 2 april 1 march 1 2023 10 december 1 november 1 august 5 may 1 march 1 february 1 2022 10 october 3 september 1 july 1 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