Testing Properties of Constraint-Graphs

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We study a model of graph related formulae that we call the Constraint-Graph model. A constraintgraph is a labeled multi-graph (a graph where loops and parallel edges are allowed), where each edge e is labeled by a distinct Boolean variable and every vertex is associate with a Boolean function over the variables that label its adjacent edges. A Boolean assignment to the variables satisﬁes the constraint graph if it satisﬁes every vertex function. We associate with a constraint-graph G the property of all assignments satisfying G, denoted SAT(G). We show that the above model is quite general. That is, for every property of strings P there exists a property of constraint-graphs PG such that P is testable using q queries iﬀ PG is thus testable. In addition, we present a large family of constraint-graphs for which SAT(G) is testable with constant number of queries. As an implication of this, we infer the testability of some edge coloring problems (e.g. the property of two coloring o...

Shirley Halevy, Oded Lachish, Ilan Newman, Dekel T

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