Equivalence and Isomorphism for Boolean Constraint Satisfaction

Title: Equivalence and Isomorphism for Boolean Constraint Satisfaction

Research Question: How can we determine if two constraint satisfaction problems are equivalent or isomorphic?

Methodology: The researchers used the concept of constraint satisfaction problems, which involve finding assignments that satisfy a set of constraints. They focused on Boolean constraint satisfaction problems, where the constraints are drawn from a fixed set of Boolean functions. They proposed a dichotomy theorem, which states that for any set of allowed constraints, the problem of determining equivalence or isomorphism between two constraint satisfaction problems is either polynomial-time solvable or coNP-complete. They also provided a simple criterion to determine which case holds.

Results: The researchers proved that the problem of determining equivalence between two constraint satisfaction problems is coNP-hard if the corresponding equivalence problem is coNP-hard. They also showed that the problem of determining isomorphism is coNP-hard if the corresponding equivalence problem is coNP-hard.

Implications: These results have significant implications for the field of constraint satisfaction problems and their applications in areas such as artificial intelligence and database theory. They provide insights into the complexity of these problems and may help in the design of more efficient algorithms and systems.

Link to Article: https://arxiv.org/abs/0202036v1 Authors: arXiv ID: 0202036v1