The complexity of positive first-order logic without equality
F Madelaine, B Martin - ACM Transactions on Computational Logic …, 2012 - dl.acm.org
We study the complexity of evaluating positive equality-free sentences of first-order (FO)
logic over a fixed, finite structure B. This may be seen as a natural generalisation of the
nonuniform quantified constraint satisfaction problem QCSP (B). We introduce surjective
hyper-endomorphisms and use them in proving a Galois connection that characterizes
definability in positive equality-free FO. Through an algebraic method, we derive a complete
complexity classification for our problems as B ranges over structures of size at most three …
logic over a fixed, finite structure B. This may be seen as a natural generalisation of the
nonuniform quantified constraint satisfaction problem QCSP (B). We introduce surjective
hyper-endomorphisms and use them in proving a Galois connection that characterizes
definability in positive equality-free FO. Through an algebraic method, we derive a complete
complexity classification for our problems as B ranges over structures of size at most three …
The complexity of positive first-order logic without equality II: The four-element case
B Martin, J Martin - International Workshop on Computer Science Logic, 2010 - Springer
We study the complexity of evaluating positive equality-free sentences of first-order logic
over fixed, finite structures B. This may be seen as a natural generalisation of the non-
uniform quantified constraint satisfaction problem QCSP (B). Extending the algebraic
methods of a previous paper, we derive a complete complexity classification for these
problems as B ranges over structures of domain size 4. Specifically, each problem is either
in L, is NP-complete, is co-NP-complete or is Pspace-complete.
over fixed, finite structures B. This may be seen as a natural generalisation of the non-
uniform quantified constraint satisfaction problem QCSP (B). Extending the algebraic
methods of a previous paper, we derive a complete complexity classification for these
problems as B ranges over structures of domain size 4. Specifically, each problem is either
in L, is NP-complete, is co-NP-complete or is Pspace-complete.
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