xii ~ Notations
Symbol
Meaning
Section in which the
symbol appears first
and is explained
n
UA;
i:::::!
*, 0
xRy
xR'y
i =j modulo n
C n
R+
R*
R] 0 R z
f: X -7 Y
f(x)
rxl
L*
Ixl
(Q, L, 0, qo, F)
q:
$
(Q, L, 0. Qo, F)
(Q, L, fl, 0, )" qo)
Irk
(~v, L, P, S)
a=?f3
G
*
a=?f3
G
a~f3
G
L(G)
,io
The union of the sets AI> A z , ..., An
Binary operations
x is related to y under the relation
x is not related to y under the relation R
i is congruent to j modulo n
The equivalence class containing a
The transitive closure of R
The reflexive-transitive closure of R
The composite of the relations R 1 and R z
Map/function from a set X to a set Y
The image of x under f
The smallest integer;::; x
The set of all strings over the alphabet set L
The empty string
The set of all nonempty strings over L
The lertgthof the string x
A finite automaton
Left endmarker in input tape
Right endmarker in input tape
A transition system
A MealyIMoore machine
Partition corresponding to equivalence of states
Partition corresponding to k-equivalence of states
A grammar
a directly derives f3 in grammar G
a derives f3 in grammar G
a derives f3 in n steps in grammar G
The language generated by G
The family of type 0 languages
The family of context-sensitive languages
2.1.2
2.1.2, 2.1.3
2.1.4
2.1.4
2.1.4
2.1.4
2.1.5
2.1.5
2.1.5
2.1.6
2.1.6
2.2.2
2.3
2.3
2.3
2.3
3.2
3.2
3.2
3.3
3.8
3.9
3.9
4.1.1
4.1.2
4.1.2
4.1.2
4.1.2
4.3
4.3
The family of context-free languages
4.3
The family of regular languages
4.3
The union of regular expressions R] and R z
5.1
The concatenation of regular expressions R] and R z 5.1
The iteration (closure) of R
5.1
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