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Table A.1 

Table of notation symbols used in this article.

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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