35 terms

Automata Theory

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automation
a construct that possesses all the indispensable features of a digital computer
formal language
an abstraction of the characteristics of programming languages
set
a collection of elements without any structure other than membership
set union
the set of all elements in the collection; one of the fundamental operations through which sets can be combined and related to each other
set intersection
the set that contains all elements of a set that also belong to another set
set difference
a generalization of the idea of the complement of a set and as such is sometimes called the relative complement of T with respect to S
set complementation
the items which are not in a set
empty set
a set that contains nothing
singleton set
a set containing only one item
De Morgans law
the compliment of the union of two sets is the intersection of their compliments and the complement of the intersection of two sets is the union of their complements
subset
a set which is contained in a larger set ⊆ (note: two sets can be exactly the same and be subsets of each other)
proper subset
a subset which is not equal to its superset ⊂
disjoint set
two sets that do not have any common elements
finite set
a set that contains a finite number of elements
infinite set
a set that contains an infinite number of elements
power set
the set of all subsets of a set including the empty set and the set itself
Cartesian product
a mathematical operation that returns ordered sequences of elements from other sets
set partition
a grouping of a set's elements into non-empty subsets in such a way that every element is included in one and only one of the subsets
function
a rule that assigns to elements of one set a unique element of another set
domain
the complete set of possible values of the independent variable
range
the set of all output values of a function
total function
a function which is defined for all possible input values
partial function
a function which is not defined for all possible input values
order at most
the maximum number of operations that could be carried out for a function's best case
order at least
the minimum number of operations that could be carried out for a function's best case
same order of magnitude
two functions' orders who are this magnitude which is identical
relation
a relationship between sets of information when the qualifications of being a function are not satisfied
equivalence
relations that satisfy the reflexivity rule, the symmetry rule, and the transitivity rule
equivalent classes
the class of all members of a set that are in a given equivalence relation
vertex or node
the fundamental unit of which graphs are formed
edge
the connection between nodes in graph theory
path
a walk in which no edge is repeated
walk
in graph theory, the traversal among edges and vertices in a graph
simple path
a path in which no vertices are repeated
cycle
a walk from one vertex to another
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