TY - GEN
T1 - Testing formula satisfaction
AU - Fischer, Eldar
AU - Goldhirsh, Yonatan
AU - Lachish, Oded
N1 - Funding Information: Research supported in part by an ERC-2007-StG grant number 202405.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84863109355&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-31155-0_33
DO - 10.1007/978-3-642-31155-0_33
M3 - منشور من مؤتمر
SN - 9783642311543
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 376
EP - 387
BT - Algorithm Theory, SWAT 2012 - 13th Scandinavian Symposium and Workshops, Proceedings
T2 - 13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012
Y2 - 4 July 2012 through 6 July 2012
ER -