Abstract
In the 1960’s, before the boom in complexity theory, several subrecursive classes of functions and languages were investigated extensively. One such hierarchy of functions (contained in the primitive recursive functions) considers the depth of nesting of (FOR) loops. It turns out that there is a decided difference in the complexity of the equivalence problems for LOOP(l)- and LOOP(2)-programs: the former is coNP-complete, but the latter is undecidable.
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References
V. Claus: The equivalence problem of loop-2-programs, Report No. 40/77, Abteilung fur Informatik, Universität Dortmund.
A.R. Meyer, D.M.Ritchie: Computation complexity and program structure, IBM Research Report RC 1817, 1967.
D. Tsichritzis: The equivalence of simple programs, Journal of the ACM 17 (1970), 729–738.
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© 1998 Springer-Verlag Berlin Heidelberg
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Schöning, U., Pruim, R. (1998). The Equivalence Problem for LOOP(1)- and LOOP(2)-Programs. In: Gems of Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60322-8_4
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DOI: https://doi.org/10.1007/978-3-642-60322-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64352-1
Online ISBN: 978-3-642-60322-8
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