Table A.1

SymbolDescription1st mention
M(nThe complexity of Boolean n × n matrix multiplication §1
ω Best well-known complexity for M(n), M(n) = O(nω§1
[nSet 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(AFan-out of nonterminal A §2
y Denotes a variable in (potentially subscripted) §2
T Seed matrix §3
N, N(dSet of indices for addresses in the matrix Eq. (4)
i, j Indices for cells in T. i, jN §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, jMerged sorted sequence of ij, divided into pairs §4.1
remove(v, xRemoval of x from a sequence v Figure 5
insert(v, xInsertion of x in a sequence v §4.5
Π Copying operator §4.5
SymbolDescription1st mention
M(nThe complexity of Boolean n × n matrix multiplication §1
ω Best well-known complexity for M(n), M(n) = O(nω§1
[nSet 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(AFan-out of nonterminal A §2
y Denotes a variable in (potentially subscripted) §2
T Seed matrix §3
N, N(dSet of indices for addresses in the matrix Eq. (4)
i, j Indices for cells in T. i, jN §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, jMerged sorted sequence of ij, divided into pairs §4.1
remove(v, xRemoval of x from a sequence v Figure 5
insert(v, xInsertion of x in a sequence v §4.5
Π Copying operator §4.5
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