TERMS AND CONCEPTS (CPSC 241)

string
alphabet
power of an alphabet
empty string
word
equal words
length of a word
concatenation of strings
powers of a string
prefix
suffix
substring
concatenation of languages
positive closure of a language
Kleene closure of a language

finite state machine
state table
state diagram
sequence recognizers

relation from A to B
relation on A
reflexive relation
symmetric relation
transitive relation
antisymmetric relation
counting of relations
partial order
equivalence relation
Hasse diagram of a partial order
total order
poset
maximal element of a poset
minimal element of a poset
greatest element of a poset
least element of a poset
upper bound of B where B is a subset of A and (A,R) is a poset
lower bound of B where B is a subset of A and (A,R) is a poset
lub of B where B is a subset of A and (A,R) is a poset
glb of B where B is a subset of A and (A,R) is a poset
lattice
partition of a set
equivalence class

function
one-to-one function
onto function
one-to-one correspondence
A and B have the same cardinality
identity function
composite function
finite set
infinite set
countable set
uncountable set
finite sequence
infinite sequence
countable disjoint collection of sets

generating function of a sequence
binomial formula (finite and infinite)
geometric progression (finite and infinite)
partial fractions decomposition
first order linear recurrence relation (homogeneous
and non-homogeneous)
linear recurrence relation of order k (homogeneous
and non-homogeneous)
characteristic polynomial
initial conditions

Boolean operations
Boolean variable
Boolean functions (BF)
complement of a BF
sum of BFs
product of BFs
laws for BFs
dual of a theorem about equality of BFs
literal
fundamental conjunction
disjunctive normal form
minterms
fundamental disjunction
conjunctive normal form
maxterms

logic gates
inverter
AND gate
OR gate

directed graph
undirected graph
loop
loop-free graph
x-y walk
length of a walk
closed walk
open walk
trail
circuit
path
cycle
connected graph
components
multigraph
e is incident with a and b
a and b are adjacent
a is adjacent to b
b is adjacent from a
subgraph
spanning subgraph
induced subgraph
G-v
G-e
complement of a graph
complete graph
graph isomorphism
vertex degree
k-regular graph
Euler circuit
Eulerian graph
Fleury's algorithm
indegree of a vertex
outdegree of a vertex
bipartite graph
complete bipartite graph
Hamilton cycle
Hamilton path
cycle decomposition
tournament
distance between x and y
diameter of a graph
hypercube
properties of the hypercube
k-colouring
proper k-colouring
chromatic number of a graph
clique number of a graph
greedy colouring
examples of colouring problems
tree
forest
spanning tree
equivalent definitions of a tree
directed tree
rooted tree
leaf
internal vertex
child
parent
descendant
ancestor
siblings
subtree at v
universal address system
binary rooted tree
complete binary rooted tree
Polish notation
preorder
postorder
inorder