# Data and Event Sequences

Information is often represented as a sequence of symbols. A binary file
of length *N* is a sequence** ***b*_{1},
*b*_{2}, ..., *b _{N}*, where each

*b*is a binary symbol, 0 or 1. The file is a function

_{i }*File*

**:**{1, 2, ... ,

*N*} →

*Binary*

*N*words is a sequence

*w*

_{1},

*w*

_{2}, ...,

*w*. The text is a function

_{N }*EnglishText*

**:**{1, 2, ... ,

*N*} →

*EnglishWords*

**data sequence**is a signal

*Data*

**:**{1, 2, ... ,

*N*} →

*SymbolSet*

*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*,

**...**

*LiftHandset*,

*HearDialTone*,

*DialDigits*,

*HearBusyTone*,

**...**

*EventStream*

**:**{1, 2, ... ,

*N*} →

*EventSet*

In general a **data sequence** is a function

*Data*

**:**

*Indices*→

*SymbolSet*

**event stream**is a function

*EventStream*

**:**

*Indices*→

*EventSet*

*Indices*is an

**ordered set**of indices eg. {1, 2, 3, ... }