 
Summary: Verification of Identities \Lambda
Sridhar Rajagopalan y Leonard J. Schulman z
March 13, 1999
Abstract
We provide an O(n 2 log 1
ffi ) time randomized algorithm to check whether a
given operation ffi : S \Theta S ! S is associative (where n = jSj and ffi ? 0 is the
error probability required of the algorithm.) We prove that (for any constant ffi )
this performance is optimal up to a constant factor even in case the operation
is ``cancellative''. No subn 3 time algorithm was previously known for this task.
More generally we give an O(n c ) time randomized algorithm to check whether
a collection of cary operations satisfy any given ``readonce'' identity.
Key words and phrases: ``Computer Aided Verification'', ``Randomized Al
gorithms''.
AMS subject classification: primary 68Q25, secondary 20N02, 20N05.
Abbreviated title: Verification of Identities.
\Lambda SIAM J. Computing, to appear.
y IBM Almaden Research Center. sridhar@almaden.ibm.com This research was conducted while
the author was a postdoctoral fellow at DIMACS and Princeton University.
z College of Computing, Georgia Institute of Technology, Atlanta GA 303320280.
