Abstract
We characterize complexity classes by function algebras that neither contain bounds nor any kind of variable segregation. The class of languages decidable in logarithmic space is characterized by the closure of a neat class of initial functions (projections and constants) under composition and simultaneous recursion on notation. We give a similar characterization of the class of number-theoretic 0--1 valued functions computable in linear space using simultaneous recursion on natural numbers in place of simultaneous recursion on notation.
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