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Abstract: We study the model checking problem, for fixed structures A, over positiveequality-free first-order logic - a natural generalisation of the non-uniformquantified constraint satisfaction problem QCSPA. We prove a completecomplexity classification for this problem when A ranges over 1. booleanstructures and 2. digraphs of size less than or equal to three. The formerclass displays dichotomy between Logspace and Pspace-complete, while the latterclass displays tetrachotomy between Logspace, NP-complete, co-NP-complete andPspace-complete.



Author: Barnaby Martin

Source: https://arxiv.org/







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