Abstract
The logics LFP (least fixed point logic), SO (second order logic), and PFP (partial fixed point logic), are known to capture the complexity classes PTIME, PH, and PSPACE respectively. We investigate hierarchies within these logics which emerge from imposing boundaries on the arities of second order variables. The computational relevance of this genuinely logical concept is under study. As for PFP, arity levels can be closely related to degree levels of PSPACE. In the case of LFP, or SO, the arity hierarchies do not seem to have natural computational counterparts. However, both strictness as well as collapse of those hierarchies would solve long open problems of complexity theory.
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© 1997 Springer-Verlag Berlin Heidelberg
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Imhof, H. (1997). Computational aspects of arity hierarchies. In: van Dalen, D., Bezem, M. (eds) Computer Science Logic. CSL 1996. Lecture Notes in Computer Science, vol 1258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63172-0_41
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DOI: https://doi.org/10.1007/3-540-63172-0_41
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