Correct predictions are in blue. If we detect only a subset of a labelled sentence, we highlight the caught part as blue, the missing part light blue. False positives are in green and false negatives are in red.

Problem 028 (Balanced incomplete block design) — Constraint detection

Balanced Incomplete Block Design -LRB- BIBD -RRB- generation is a standard combinatorial problem from design theory , originally used in the design of statistical experiments but since finding other applications such as cryptography . It is a special case of Block Design , which also includes Latin Square problems . BIBD generation is described in most standard textbooks on combinatorics . A BIBD is defined as an arrangement of $ v $ distinct objects into $ b $ blocks such that each block contains exactly $ k $ distinct objects , each object occurs in exactly $ r $ different blocks , and every two distinct objects occur together in exactly $ \ lambda $ blocks . Another way of defining a BIBD is in terms of its incidence matrix , which is a $ v $ by $ b $ binary matrix with exactly $ r $ ones per row , $ k $ ones per column , and with a scalar product of $ \ lambda $ between any pair of distinct rows . A BIBD is therefore specified by its parameters $ -LRB- v , b , r , k , \ lambda -RRB- $ .

Problem 028 (Balanced incomplete block design) — Detection of the decisions and objects to be modeled

Balanced Incomplete Block Design -LRB- BIBD -RRB- generation is a standard combinatorial problem from design theory , originally used in the design of statistical experiments but since finding other applications such as cryptography . It is a special case of Block Design , which also includes Latin Square problems . BIBD generation is described in most standard textbooks on combinatorics . A BIBD is defined as an arrangement of $ v $ distinct objects into $ b $ blocks such that each block contains exactly $ k $ distinct objects , each object occurs in exactly $ r $ different blocks , and every two distinct objects occur together in exactly $ \ lambda $ blocks . Another way of defining a BIBD is in terms of its incidence matrix , which is a $ v $ by $ b $ binary matrix with exactly $ r $ ones per row , $ k $ ones per column , and with a scalar product of $ \ lambda $ between any pair of distinct rows . A BIBD is therefore specified by its parameters $ -LRB- v , b , r , k , \ lambda -RRB- $ .

Back to list