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Com S 631: Lower bounds and Separation Results Lecture 14 Scribe: Ankit Agrawal
 

Summary: Com S 631: Lower bounds and Separation Results
Lecture 14 Scribe: Ankit Agrawal
In circuit lower bounds, our goal is to explicitly exhibit a function that requires large
circuits. Even though we believe that NP requires super polynomial size circuits, we do not
even know how to show that NP does not have n2
size circuits. In the last lecture, we showed
that a larger class 3 does not have n2
-size circuits. Today we will improve upon this result.
We will first show that 2 does not have n2
-size circuits. Finally, we show that ZPPNP
does
not have a n2
size circuit.
Theorem 1 (Kannan). There is a language in 2 that does not have a n2
-size circuit.
Proof. First consider the case when NP does not have polynomial size circuits. This implies
that k, SAT does not have nk
-size circuits. And as we know that NP 2, so 2 also does
not have any n2
-size circuits.

  

Source: Aduri, Pavan - Department of Computer Science, Iowa State University

 

Collections: Computer Technologies and Information Sciences