Looking for languages that are not Turing complete

Question

I know a little about what is a turing-machine and a turing-complete language, but to understand better, could someone give examples of languages that are not Turing complete? (

Answer 1

Regular languages - those that can be described as regular expressions - are not Turing complete.

Markup languages (used for describing data, not computation) like XML and JSON are not Turing complete.

Answer 2

Regular expressions, in the formal definition, consisting only of:

• concatenation ( ab )
• unbounded repetition ( a* )
• alternation ( a|b )
• grouping ( (ab)|(cd) )

can only recognise regular languages. A Turing-complete programming language can recognise recursively-enumerable languages.

An example is that regular expressions cannot tell you if a string consists of matched pairs of parentheses: eg ()(()) is accepted while ()((())() is rejected, while Turing-complete programming languages can.

(Note that regexes in modern programming languages are more powerful than the formal academic definition of regular expressions. Some may even be Turing complete.)