Table A.1

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(n^{ω}) | §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 | ^{T}_{ij} 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(n^{ω}) | §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 | ^{T}_{ij} 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 |

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