Testing Formula Satisfaction
We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in ε and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasipolynomial in ε. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size.
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- 2.Ben-Sasson, E., Harsha, P., Lachish, O., Matsliah, A.: Sound 3-query pcpps are long. ACM Trans. Comput. Theory 1, 7:1–7:49 (2009)Google Scholar
- 6.Fischer, E.: The art of uninformed decisions: A primer to property testing. Current Trends in Theoretical Computer Science: The Challenge of the New Century I, 229–264 (2004)Google Scholar
- 7.Fischer, E., Goldhirsh, Y., Lachish, O.: Testing formula satisfaction, arXiv:1204.3413v1 [cs.DS]Google Scholar
- 8.Fischer, E., Lachish, O., Newman, I., Matsliah, A., Yahalom, O.: On the query complexity of testing orientations for being eulerian. TALG (to appear)Google Scholar
- 13.Halevy, S., Lachish, O., Newman, I., Tsur, D.: Testing orientation properties. ECCC (153) (2005)Google Scholar
- 14.Halevy, S., Lachish, O., Newman, I., Tsur, D.: Testing properties of constraint-graphs. In: IEEE Conference on Computational Complexity (2007)Google Scholar
- 18.Ron, D.: Algorithmic and Analysis Techniques in Property Testing (2010)Google Scholar