Testing properties of constraint-graphs

Shirley Halevy, Oded Lachish, Ilan Newman, Dekel Tsur

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study a model of graph related formulae that we call the Constraint-Graph model. A constraint-graph 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 associated 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 that consists 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 if and only if 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 of the edges in which every node is adjacent to at least one vertex of each color). Another implication is that every property of Boolean strings that can be represented by a Read-twice CNF formula is testable. We note that this is the best possible in terms of the number of occurrences of every variable in a formula.

Original languageEnglish
Title of host publicationProceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007
Number of pages14
StatePublished - 2007
Event22nd Annual IEEE Conference on Computational Complexity, CCC 2007 - San Diego, CA, United States
Duration: 13 Jun 200716 Jun 2007

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159


Conference22nd Annual IEEE Conference on Computational Complexity, CCC 2007
Country/TerritoryUnited States
CitySan Diego, CA

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics


Dive into the research topics of 'Testing properties of constraint-graphs'. Together they form a unique fingerprint.

Cite this