REMARKS ON A QUERY-BASED VARIANT OF THE PARALLEL REPETITION THEOREM

2001 ◽  
Vol 12 (04) ◽  
pp. 517-531
Author(s):  
OLEG VERBITSKY
Keyword(s):  
Strong Correlation ◽  
Error Probability ◽  
Cryptographic Protocols ◽  
Parallel Execution ◽  
Proof System ◽  
Interactive Proof ◽  
Parallel Repetition ◽  
Interactive Proof System

The Parallel Repetition Theorem says that n-fold parallel execution of a two-prover one-round interactive proof system reduces the error probability exponentially in n. The bound on the error probability of the parallelized system depends on the error probability and the answer size of the single proof system. It is still unknown whether the theorem holds true with a bound depending only on the query size. This kind of a bound may be preferable whenever the query size is considerably smaller than the answer size, what really happens in some cryptographic protocols. Such a bound is only known in the case that queries to the provers are independent. The present paper extends this result to some cases of strong correlation between queries. In particular, a query-based variant of the Parallel Repetition Theorem is proven when the graph of dependence between queries to the provers is a tree and, in a bit weaker form, when this graph is a cycle.

scholarly journals A parallel repetition theorem for entangled projection games

2015 ◽  
Vol 24 (2) ◽  
pp. 201-254 ◽  
Author(s):  
Irit Dinur ◽  
David Steurer ◽  
Thomas Vidick
Keyword(s):  
Parallel Repetition ◽  
Projection Games
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