Super-exponential Complexity of Presburger Arithmetic
Name
MIT-LCS-TM-043.pdf
Size
730.61 KB
Format
Adobe PDF
Checksum (MD5)
3b9f2ef79d1d4dcdf0c314605805a228
Author(s)
Fischer, Michael J.
Rabin, Michael O.
Date Issued
February 1974
Series/Report no.
MIT-LCS-TM-043
MAC-TM-043
Abstract
Lower bounds are established on the computational complexity of the decision problem and on the inherent lengths of proofs for two classical decidable theories of logic: the first order theory of the real numbers under addition, and Presburger arithmetic -- the first order theory of addition on the natural numbers. There is a fixed constant c > 0 such that for every (non-deterministic) decision procedure for determining the truth of sentences of real addition and for all sufficiently large n, there is a sentence of length n for which the decision procedure runs for more than 2 cn steps.
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