Abstract
A Boolean constraint satisfaction instance is a set of constraint applications where the allowed constraints are drawn from a fixed set C of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent and prove a dichotomy theorem by showing that for all finite sets C of constraints, this problem is either polynomial-time solvable or coNP-complete, and we give a simple criterion to determine which case holds. A more general problem addressed in this paper is the isomorphism problem, the problem of determining whether there exists a renaming of the variables that makes two given constraint satisfaction instances equivalent in the above sense. We prove that this problem is coNP-hard if the corresponding equivalence problem is coNP-hard, and polynomial-time many-one reducible to the graph isomorphism problem in all other cases.
Supported in part by grant NSF-INT-9815095/DAAD-315-PPP-gü-ab.
Supported in part by an RIT FEAD grant. Work done in part while visiting Julius-Maximilians-Universität Würzburg.
Work done in part while employed at Julius-Maximilians-Universität Würzburg.
Work done in part while employed at Julius-Maximilians-Universität Würzburg.
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Böhler, E., Hemaspaandra, E., Reith, S., Vollmer, H. (2002). Equivalence and Isomorphism for Boolean Constraint Satisfaction. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_28
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DOI: https://doi.org/10.1007/3-540-45793-3_28
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