SNP (complexity)

Article summary

In computational complexity theory, SNP (from Strict NP) is a complexity class containing a limited subset of NP based on its logical characterization in terms of graph-theoretical properties. It forms the basis for the definition of the class MaxSNP of optimization problems. It is defined as the class of problems that are properties of relational structures (such as graphs) expressible by a second-order logic formula of the following form: : \exists S_1 \dots \exists S_\ell \, \forall v_1 \dots \forall v_m \,\phi(R_1,\dots,R_k,S_1,\dots,S_\ell,v_1,\dots,v_m) where R_1,\dots,R_k are relations of the structure (such as the adjacency relation, for a graph), S_1,\dots,S_\ell are unknown relations (sets of tuples of vertices), and \phi is a quantifier-free formula: any boolean combination of the relations. That is, only existential second-order quantification (over relations) is allowed and only universal first-order quantification (over vertices) is allowed. If existential quantification over vertices were also allowed, the resulting complexity class would be equal to NP (more precisely, the class of those properties of relational structures that are in NP), a fact known as Fagin's theorem.…

Key claims

No claims recorded.

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.