TY - GEN

T1 - Proofs of proximity for context-free languages and read-once branching programs

AU - Goldreich, Oded

AU - Gur, Tom

AU - Rothblum, Ron D.

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.

PY - 2015

Y1 - 2015

N2 - Proofs of proximity are probabilistic proof systems in which the verifier only queries a sub-linear number of input bits, and soundness only means that, with high probability, the input is close to an accepting input. In their minimal form, called Merlin-Arthur proofs of proximity (MAP), the verifier receives, in addition to query access to the input, also free access to an explicitly given short (sub-linear) proof. A more general notion is that of an interactive proof of proximity (IPP), in which the verifier is allowed to interact with an all-powerful, yet untrusted, prover. MAPs and IPPs may be thought of as the NP and IP analogues of property testing, respectively. In this work we construct proofs of proximity for two natural classes of properties: (1) context-free languages, and (2) languages accepted by small read-once branching programs. Our main results are: 1. MAPs for these two classes, in which, for inputs of length n, both the verifier’s query complexity and the length of the MAP proof are Õ(√ n). 2. IPPs for the same two classes with constant query complexity, polylogarithmic communication complexity, and logarithmically many rounds of interaction.

AB - Proofs of proximity are probabilistic proof systems in which the verifier only queries a sub-linear number of input bits, and soundness only means that, with high probability, the input is close to an accepting input. In their minimal form, called Merlin-Arthur proofs of proximity (MAP), the verifier receives, in addition to query access to the input, also free access to an explicitly given short (sub-linear) proof. A more general notion is that of an interactive proof of proximity (IPP), in which the verifier is allowed to interact with an all-powerful, yet untrusted, prover. MAPs and IPPs may be thought of as the NP and IP analogues of property testing, respectively. In this work we construct proofs of proximity for two natural classes of properties: (1) context-free languages, and (2) languages accepted by small read-once branching programs. Our main results are: 1. MAPs for these two classes, in which, for inputs of length n, both the verifier’s query complexity and the length of the MAP proof are Õ(√ n). 2. IPPs for the same two classes with constant query complexity, polylogarithmic communication complexity, and logarithmically many rounds of interaction.

UR - http://www.scopus.com/inward/record.url?scp=84950105883&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-662-47672-7_54

DO - https://doi.org/10.1007/978-3-662-47672-7_54

M3 - منشور من مؤتمر

SN - 9783662476710

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 666

EP - 677

BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings

A2 - Halldorsson, Magnus M.

A2 - Kobayashi, Naoki

A2 - Speckmann, Bettina

A2 - Iwama, Kazuo

T2 - 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

Y2 - 6 July 2015 through 10 July 2015

ER -