Notation
Notation
a
foo
w, x, y, z
ε
k
n, m
L, S, A, B
∅
Σ
{w | foo}
ak
wk
Ak
A∗
A+
wrev
L
2A
|A|
|w|a
prefix (w)
pprefix (w)
prefix (L)
suffix (w)
psuffix (w)
suffix (L)
A∪B
A∩B
xy
A−B
A×B
#
N
Z
R
∴
Meaning
Example
The character ’a’
The string "foo"
Arbitrary string
The empty string
Numerical constant
Numerical variable
Language, set
The empty set
An alphabet
The set of all w such that foo holds
k repetitions of the character a
k repetitions of the string w
The set of all strings with k arbitrary elements from the set A
Kleene star operation on A
a,b,c
bar, thing
w ∈ Σ∗
Plus operator on the set A
Reverse of the string w
The complement language to L
The powerset of A
Number of elements in A (sometimes
denoted cardinality)
The number of a’s in the string w
The set of strings x such that w = xz
The set of proper prexes to w
The set of strings w such that w is a prex in some string in L
The set of strings x such that w = zx
The set of proper sufxes to w
The set of strings w such that w is a sufx in some string in L
The union of A and B
The intersection of A and B
The concatenation of the strings x and
y
The set of all elements which are in A
but not in B
The set of all combinations of an element in A concatenated with an element
in B.
The end of a string/stack
The set of natural numbers
The set of integers
The set of real numbers
Ergo, hence, therefore
End of proof
4
Other
notation
a, b, c
bar, foo
λ
k, −3, 1, 42
n = 2m
L = Σ∗
Σ = {a, b}
{w | wrev = w}
a4 = aaaa
w3 = www
{1, 2}2 = {11, 12, 21, 22}
{0, 1}∗ = {ε, 0, 1, 00, . . .},
a∗ = {ε, a, aa, . . .},
(foo)∗ = {ε, foo, foofoo, . . .}
{0, 1}+ = {0, 1, 00, 01, 10, . . .}
(foobar)rev = raboof
�
�
2{0,1} = ∅, {0}, {1}, {0, 1}
|{1, 2, 3}| = 3, |automation| = 7
|abracadabra|a = 5
prefix (abc) = {ε, a, ab, abc}
prefix (abc) = {a, ab}
prefix (Σ∗ ) = Σ∗
{}
ak , a4
wR
¬(L), LC
na (w), #a (w)
suffix (abc) = {ε, c, bc, abc}
psuffix (abc) = {c, bc}
suffix (Σ∗ ) = Σ∗
{1, 2, 3} ∪ {2, 3, 4} = {1, 2, 3, 4}
{1, 2, 3} ∩ {2, 3, 4} = {2, 3}
x = foo, y = bar, xy = foobar
A+B
{1, 2, 3} − {2, 3, 4} = {1}
A\B
{a, b} × {c, d} = {ac, ad, bc, bd}
N = {0, 1, 2, . . .}
Z = {. . . , −2, −1, 0, 1, 2, . . .}
47, 011 ∈ R