Chomsky Hierarchy
There is more consensus on the "characterization" of the notion of "simple algorithm".
All algorithms need to be specified in a formal language, and the "simplicity notion" arises from the simplicity of the language. The Chomsky (1956) hierarchy is a containment hierarchy of classes of formal grammars that generate formal languages. It is used for classifying of programming languages and abstract machines.
From the Chomsky hierarchy perspective, if the algorithm can be specified on a simpler language (than unrestricted), it can be characterized by this kind of language, else it is a typical "unrestricted algorithm".
Examples: a "general purpose" macro language, like M4 is unrestricted (Turing complete), but the C preprocessor macro language is not, so any algorithm expressed in C preprocessor is a "simple algorithm".
See also Relationships between complexity classes.
Read more about this topic: Algorithm Characterizations
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