Table A.1
Table of notation symbols used in this article.
| Symbol | Description | 1st mention |
|---|---|---|
| M(n) | The complexity of Boolean n × n matrix multiplication | §1 |
| ω | Best well-known complexity for M(n), M(n) = O(nω) | §1 |
| [n] | Set of integers {1, … , n} | §2 |
| [n]0 | [n] ∪ {0} | §2 |
 | Nonterminals of the LCFRS | §2 |
 | Terminal symbols of the LCFRS | §2 |
 | Variables that denote spans in grammar | §2 |
 | Rules in the LCFRS | §2 |
| A,B,C | Nonterminals | §2 |
| f | Maximal fan-out of the LCFRS | Eq. (3) |
| φ(A) | Fan-out of nonterminal A | §2 |
| y | Denotes a variable in  (potentially subscripted) | §2 |
| T | Seed matrix | §3 |
| N, N(d) | Set of indices for addresses in the matrix | Eq. (4) |
| i, j | Indices for cells in T. i, j ∈ N | §4.1 |
| d | Grammar contact rank | §4.1 |
| M | Tij is a subset of M | §4.1 |
 | Copying/marking symbols for rows | §4.1 |
 | Copying/marking symbols for columns | §4.1 |
| n | Length of sentence to be parsed | §1 |
| < | Total order between the set of indices of T | §4.1 |
| m(i, j) | Merged sorted sequence of i ∪ j, divided into pairs | §4.1 |
| remove(v, x) | Removal of x from a sequence v | Figure 5 |
| insert(v, x) | Insertion of x in a sequence v | §4.5 |
| Π | Copying operator | §4.5 |
| Symbol | Description | 1st mention |
|---|---|---|
| M(n) | The complexity of Boolean n × n matrix multiplication | §1 |
| ω | Best well-known complexity for M(n), M(n) = O(nω) | §1 |
| [n] | Set of integers {1, … , n} | §2 |
| [n]0 | [n] ∪ {0} | §2 |
| | Nonterminals of the LCFRS | §2 |
| | Terminal symbols of the LCFRS | §2 |
| | Variables that denote spans in grammar | §2 |
| | Rules in the LCFRS | §2 |
| A,B,C | Nonterminals | §2 |
| f | Maximal fan-out of the LCFRS | Eq. (3) |
| φ(A) | Fan-out of nonterminal A | §2 |
| y | Denotes a variable in (potentially subscripted) | §2 |
| T | Seed matrix | §3 |
| N, N(d) | Set of indices for addresses in the matrix | Eq. (4) |
| i, j | Indices for cells in T. i, j ∈ N | §4.1 |
| d | Grammar contact rank | §4.1 |
| M | Tij is a subset of M | §4.1 |
| | Copying/marking symbols for rows | §4.1 |
| | Copying/marking symbols for columns | §4.1 |
| n | Length of sentence to be parsed | §1 |
| < | Total order between the set of indices of T | §4.1 |
| m(i, j) | Merged sorted sequence of i ∪ j, divided into pairs | §4.1 |
| remove(v, x) | Removal of x from a sequence v | Figure 5 |
| insert(v, x) | Insertion of x in a sequence v | §4.5 |
| Π | Copying operator | §4.5 |