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Summary: Theoretical Computer Science 233 (2000) 247261
www.elsevier.com/locate/tcs
On the cost of recomputing:
Tight bounds on pebbling with faults 1
Yonatan Aumann a;;2
, Judit Bar-Ilan b;3
, Uriel Feige c;4
a Department of Mathematics and Computer Science, Bar-Ilan University, Ramat Gan, Israel
b School of Library, Archive and Information Studies, The Hebrew University Jerusalem 91904, Israel
c Department of Applied Math., The Weizmann Institute, Rehovot, Israel
Received September 1996; revised February 1998
Communicated by D. Peleg
Abstract
We introduce a formal framework to study the time and space complexity of computing
with faulty memory. For the fault-free case, time and space complexities were studied using
the "pebbling game" model. We extend this model to the faulty case, where the content of
memory cells may be erased. The model captures notions such as "check points" (keeping
multiple copies of intermediate results), and "recovery" (partial recomputing in the case of
failure). Using this model, we derive tight bounds on the time and/or space overhead in icted
by faults. As a lower bound, we exhibit cases where f worst-case faults may necessitate an (f)
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