Abstract
A simple problem concerning evaluation of programs is shown to be nonelementary recursive. The problem is the following: Given an input-free programP (i.e. all variables are initially 0) without nested loops using only instructions of the formx ← 1, x ← x + y,\(x \leftarrow x\dot - y\),do x... end, doesP output 0? This problem has time complexity\(2^{2^{ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} ^2 } } \)}cn-levels for some constantc. Other results are presented which show how the complexity of the 0-evaluation problem changes when the nonlooping instructions are varied. For example, it is shown that 0-evaluation is PSPACE-complete even for the case when the nonlooping instructions are onlyx ← x + 1,if x = 0then y ←y \(y \leftarrow y\dot - 1\).
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This research was supported in part by NSF Grant MCS78-01736 and MCS81-02853.
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Ibarra, O.H., Leininger, B.S. & Rosier, L.E. A note on the complexity of program evaluation. Math. Systems Theory 17, 85–96 (1984). https://doi.org/10.1007/BF01744435
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DOI: https://doi.org/10.1007/BF01744435