Abstract
We investigate second order (SO) logic with partial fixed point (PFP) operators for finite models. It is known that PFP-logic corresponds to PSPACE, and SO-logic for finite structures corresponds to the union of polynomial hierarchy. We propose an explicit algorithm for translation first order (FO) logic with PFP-operators to FO-logic with only one PFP-operator for finite models with linear order. Next we generalize this result to SO-logic.
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(Submitted by M. M. Arslanov)
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Sekorin, V.S. Partial Fixed Point for Finite Models in Second Order Logic. Lobachevskii J Math 41, 1672–1679 (2020). https://doi.org/10.1134/S1995080220090231
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DOI: https://doi.org/10.1134/S1995080220090231