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This has been called the microstructure complement when the edges represent the forbidden partial assignments. I personally prefer the term clause structure. The clause structure of a constraint sat …

Much of the attention paid to optimization variants of the constraint satisfaction problem (CSP) has focused on satisfying some number of constraints (MAX-CSP), or in the Boolean case on picking the solution … MAXIMUM PARTIAL CSP: Input: CSP instance Output: prop $f$ Criterion: maximize $|f|$ In an instance with $n$ variables, clearly a prop of cardinality $n$ will be a solution. …

I'm not altogether convinced by the previous work on open and interactive constraints. An attempt to study the tractability questions was: Martin J. Green and Christopher Jefferson, Structural Trac …

This includes CSPs as a special case of more general quantified formulas (since a CSP instance is just an existentially quantified conjunctive formula). …

CSP(C$_0$,_) is in NP, but neither in P nor NP-complete (unless P = NP). Moreover, the set C$_0$ can be decided in deterministic polynomial time. … doi:10.1007/978-3-540-70575-8_48 (PDF) Finally, any class of CSP instances can be transformed into a representation with worst-case fractional hypertree width. …

CSP($\Gamma$) is a special kind of constraint satisfaction problem. … Schaefer's Theorem says that when $\Gamma$ contains only relations over $\{0,1\}$, then CSP($\Gamma$) is either NP-complete or in P, but says nothing at all about other collections of CSP instances. …