Pseudo-deterministic proofs
Name
LIPIcs-ITCS-2018-17.pdf
Description
Published version
Size
496.5 KB
Format
Adobe PDF
Checksum (MD5)
7bae5bc0530459e900db8e8585537cd7
Author(s)
Goldwasser, Shafi
Grossman, Ofer
Holden, Dhiraj
Date Issued
2018
Citation
"Pseudo-deterministic proofs."
Version
Final published version
Abstract
© Shafi Goldwasser, Ofer Grossman, and Dhiraj Holden. We introduce pseudo-deterministic interactive proofs (psdIP): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with classical interactive proofs, the verifier is a probabilistic polynomial time algorithm interacting with an untrusted powerful prover. We view pseudo-deterministic interactive proofs as an extension of the study of pseudodeterministic randomized polynomial time algorithms: the goal of the latter is to find canonical solutions to search problems whereas the goal of the former is to prove that a solution to a search problem is canonical to a probabilistic polynomial time verifier. Alternatively, one may think of the powerful prover as aiding the probabilistic polynomial time verifier to find canonical solutions to search problems, with high probability over the randomness of the verifier. The challenge is that pseudo-determinism should hold not only with respect to the randomness, but also with respect to the prover: a malicious prover should not be able to cause the verifier to output a solution other than the unique canonical one. The IP = PSPACE characterization implies that psdIP = IP. The challenge is to find constant round pseudo-deterministic interactive proofs for hard search problems. We show a constant round pseudo-deterministic interactive proof for the graph isomorphism problem: on any input pair of isomorphic graphs (G0,G1), there exist a unique isomorphism φ from G0to G1(although many isomorphism many exist) which will be output by the verifier with high probability, regardless of any dishonest prover strategy. In contrast, we show that it is unlikely that psdIP proofs with constant rounds exist for NP-complete problems by showing that if any NP-complete problem has a constant round psdIP protocol, then the polynomial hierarchy collapses.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ITCS.2018.17
