On time-space classes and their relation to the theory of real addition

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Abstract

A new lower bound on the computational complexity of the theory of real addition and several related theories is established: any decision procedure for these theories requires either space 2εn or nondeterministic time 2εn2 for some constant ε0 and infinitely many n.

The proof is based on the families of languages TISP(T(n), S(n)) which can be recognized simultaneously in time T(n) and S(n) and the conditions under which they form a hierarchy.

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This work was supported by NSF grant 77-19754MCS.