Abstract
Let Sp(d∨) denote the class of spectra of first-order sentences with d universal quantifiers. Let NRAM(T(n)) denote the class of sets (of positive integers) accepted by Nondeterministic Random Access Machines (with successor as the only arithmetical operation), in time O(T(n)) where n is the input integer. We prove Sp(d∨) = NRAM(nd) for d≥2.
A similar result holds for generalized spectra.
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Grandjean, E. (1984). Universal quantifiers and time complexity of random access machines. In: Börger, E., Hasenjaeger, G., Rödding, D. (eds) Logic and Machines: Decision Problems and Complexity. LaM 1983. Lecture Notes in Computer Science, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13331-3_52
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DOI: https://doi.org/10.1007/3-540-13331-3_52
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