Data and Event Sequences
Information is often represented as a sequence of symbols. A binary file
of length N is a sequence b1,
b2, ..., bN, where each bi
is a binary symbol, 0 or 1. The file is a function
File: {1, 2,
... , N} ® Binary
An English text with N words is
a sequence w1, w2, ..., wN
.
The text is a function
EnglishText: {1, 2, ...
, N} ® EnglishWords
A data sequence is a signal
Data: {1, 2, ...
, N} ® SymbolSet
where SymbolSet is an appropriate set of symbols eg. Binary,
EnglishWords. Data signals arise in computer storage, computer communication
networks.
An event stream is a record of the significant events
that occur in a system of interest. The trace of events in a phone call
might be
LiftHandset, HearDialTone, DialDigits, HearTelephoneRing,
...
or, if the other phone is busy, the trace might be
LiftHandset, HearDialTone, DialDigits, HearBusyTone,
...
An event stream is a function
EventStream: {1, 2, ...
, N} ® EventSet
The behavior of state machines is described by event streams.
In general a data sequence is a function
Data: Indices ®
SymbolSet
and an event stream is a function
EventStream: Indices ®
EventSet
where Indices is an ordered set of indices eg. {1, 2, 3,
... }