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ICALP
2007
Springer

Affine Systems of Equations and Counting Infinitary Logic

11 years 10 months ago
Affine Systems of Equations and Counting Infinitary Logic
We study the definability of constraint satisfaction problems (CSP) in various fixed-point and infinitary logics. We show that testing the solvability of systems of equations over a finite Abelian group, a tractable CSP that was previously known not to be definable in Datalog, is not definable in the infinitary logic with finitely many variables and counting. This implies that it is not definable in least fixed point logic or its extension with counting. We relate definability of CSPs to their classification obtained from tame congruence theory of the varieties generated by the algebra of polymorphisms of the template structure. In particular, we show that if this variety admits either the unary or affine type, the corresponding CSP is not definable in the infinitary logic with counting.
Albert Atserias, Andrei A. Bulatov, Anuj Dawar
Added 16 Aug 2010
Updated 16 Aug 2010
Type Conference
Year 2007
Where ICALP
Authors Albert Atserias, Andrei A. Bulatov, Anuj Dawar
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