Transcript 5 S Formalisms More formally: Definitions • Definition: A stream is a sequence whose codomain is a non empty set. • Definition: A.

5 S Formalisms
More formally: Definitions
• Definition: A stream is a sequence
whose codomain is a non empty set.
• Definition: A structure is a tuple (G, L, F)
where G = (V,E) is a directed graph with
vertex set V and edge set E, L is a set
of label values, and F is a labeling
function. F : (V ∪ E ) → L.
See http://www.mathsisfun.com/sets/domain-range-codomain.html
for a nice description of domain, range, codomain if you need it.
Structure illustration
Collection
includes
What are the G, L,F,
V, E parts of this
example?
Books
Audio
files
Images
A very simple structure. How might it be enhanced? How would
an index be included? What substructures might be added?
Definitions, cont’d
• Definition: A space is a measurable space,
measure space, probability space, vector
space, topological space, or metric space
– A vector space is a representation for the set of
elements in a collection. The vector representing
each element is a set of characteristics held by
that element and both connecting that element to
others that are similar and distinguishing it from
those that are different.
– We will do an exercise to illustrate
Vector space illustration
• Consider a car. What are the
characteristics that you associate with a
car? If you want to compare one car to
another, what characteristics would you
choose?
• Make a vector of those characteristics.
• Then, fill in the vector for several
specific cars.
Definitions - 3
• Definition: A scenario is a sequence of
related transition events (e1, e2, …, en) on
state set S such that ek = (sk, sk+1,) for 1 <= k
<= n.
– More easily visualized, a scenario is a path in a
directed graph, G = (S, ∑e), where vertices
correspond to states in the state set S and
directed edges are equivalent to events in a set of
events, ∑e, and correspond to transitions between
states.
– Scenarios must be implemented to make a
working system.
Definitions - 4
• Definition: A society is a tuple (C,R) where
– C = (c1, c2, …, cn) is a set of conceptual
communities, each community referring to a set of
individuals of the same class or type (e.g. actors,
activities, components, hardware, software, data);
– R = (r1, r2, …, rm) is a set of relationships, each
relationship being a tuple rj = (ej, ij) where ej is a
Cartesian product ck1 x ck2 x … x cknj. 1<= k1 < k2 < …
< knj<= n, which specifies the communities involved in the
relationship and ij is an activity.