concatenate

In computer programming, string concatenation is the operation of joining two character strings end-to-end. For example, the strings "snow" and "ball" may be concatenated to give "snowball". In many programming languages, string concatenation is a binary infix operator.

For example, the following expression uses the "+" symbol as the concatenation operator to join 2 strings: "Hello, " + "World";, and has the value "Hello, World".

Concatenation of sets of strings

In computer science, in particular in the theory of computation, the concatenation operation on strings is generalized to an operation on sets of strings as follows:

For two sets of strings S₁ and S₂, the concatenation S₁S₂ consists of all strings of the form vw where v is a string from S₁ and w is a string from S₂.

In this definition, the string vw is the ordinary concatenation of strings v and w as defined in the introductory section. In this context, sets of strings are often referred to as formal languages. Notice that we do not use an explicit operator symbol for representing the concatenation.

Applications

Audio/telephony

In programming for telephony, concatenation is used to provide dynamic audio feedback to a user. For example in a "time of day" speaking clock, concatenation is used to give the correct time by playing the appropriate recordings concatenated together. For example:

• "At the tone the time will be"
• "Eight"
• "Thirty"
• "Five"
• "and"
• "Twenty"
• "Two"
• "seconds"

The recordings themselves exist separately, but playing them one after the other provides a grammatically correct sentence to the listener.

This technique is also used in number change announcements, voice mail systems, or most telephony applications that provide dynamic feedback to the caller (e.g. moviefone, tellme, and others).

Programming for any kind of computerized public address system can also employ concatenation for dynamic public announcements (for example, flights in an airport). The system would archive recorded speech of numbers, routes or airlines, destinations, times, etc. and play them back in a specific sequence to produce a grammatically correct sentence that is announced throughout the facility.

Database Theory

One of the principles of relational database design is that the fields of data tables should reflect a single characteristic of the table's subject, which means that they should not contain concatenated strings. When concatenation is desired in a report, it should be provided at the time of running the report. For example, to display the physical address of a certain customer, the data might include building number, street name, building subunit number, city name, state/province name, postal code, and country name, e.g., "123 Fake St Apt 4, Boulder, CO 80302, USA", which combines 7 fields. However, the customers data table should not use one field to store that concatenated string; rather, the concatenation of the 7 fields should happen upon running the report. The reason for such principles is that without them, the entry and updating of large volumes of data becomes error-prone and labor-intensive. Separately entering the city, state, ZIP code, and nation allows data-entry validation (such as detecting an invalid state abbreviation). Then those separate items can be used for sorting or indexing the records, such as all with "Boulder" as the city name.

References

• John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley Publishing, Reading Massachusetts, 1979. ISBN 0-201-029880-X.