What Are the Limits of Interactive Proofs: Why Does MIP Fall Within NEXP?

  • Thread starter Thread starter Dragonfall
  • Start date Start date
  • Tags Tags
    Proof
AI Thread Summary
Interactive proofs (IP) are shown to be contained within PSPACE by analyzing the decision tree of the prover, which can be managed with polynomial space. However, the scenario changes with multiple provers, where traversing multiple trees simultaneously leads to the conclusion that MIP is contained within NEXP. This raises questions about the limitations of interactive proofs when scaling to multiple provers. The discussion emphasizes the complexity differences between single and multiple prover systems. Understanding these distinctions is crucial for theoretical computer science.
Dragonfall
Messages
1,023
Reaction score
5
You can prove that \mathbf{IP} \subset \mathbf{PSPACE} by traversing the exponentially large decision tree of the prover, which takes only polynomial amount of space at a time.

Why can't you do the same in the case of multiple provers? You'd traverse polynomially many trees at a time instead of one, but that should only require poly space. Instead, \mathbf{MIP} \subset \mathbf{NEXP}.
 
Mathematics news on Phys.org
I'd have posted this in the CS subforums, but this is more of a theoretical question.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Why does an object initially at rest begin to fall?
Replies
24
Views
4K
I Why should a Fourier transform not be a change of basis?
Replies
43
Views
7K
Job Skills [Career] - What kind of life does a career in physics entail?
Replies
2
Views
3K
A Schrödinger's original interpretation
Replies
21
Views
4K
Logical Proof That Black Holes Can't Exist
Replies
3
Views
2K
Is Mathematics a Belief System?
Replies
22
Views
4K
Challenge Math Challenge - October 2018
2
Replies
71
Views
12K
I The standard model from loop quantum gravity via spinors octonions
Replies
26
Views
4K
What does a temporally infinite universe imply?
Replies
1
Views
2K
What Is Gravity and How Does It Relate to Space-Time and Mass?
Replies
16
Views
3K

Hot Threads

Recent Insights

Back
Top