Revision #6 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Accepted on: 7th July 2021 17:30

Downloads: 24

Keywords:

Suppose Alice and Bob are communicating in order to compute some function $f$, but instead of a conventional communication channel, they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$, where every round one of the players sends a bit, and the other receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkies instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). The motivation for this kind of communication model comes from the study of the KRW conjecture. We show that for some definitions, this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds. We also prove lower bounds for these models using both combinatorial and information-theoretic methods.

In the previous versions on this paper including the conference version we claimed better lower bounds for $IP_n$ in all tree half-duplex models based on an information theoretic approach.

Unfortunately, proofs of these results (Theorems 18, 21, and 24) contain a critical flaw (Lemma~13 in is not true).

Moreover, as far as we know, this flaw can not be fixed --- there is an upper bound of $n/2+2$ on half-duplex complexity of $IP_n$ with silence (proven by Tatiana Gladysh) that matches the lower bound proven here up to an additive constant $2$.

This upper bound contradicts the lower bound claimed in the previous versions of the paper.

All these theorems were removed from the paper preserving numeration of other theorems.

Revision #5 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Accepted on: 1st August 2020 00:35

Downloads: 129

Keywords:

Suppose Alice and Bob are communicating in order to compute some function $f$, but instead of a conventional communication channel, they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$, where every round one of the players sends a bit, and the other receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkies instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). The motivation for this kind of communication model comes from the study of the KRW conjecture. We show that for some definitions, this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds. We also prove lower bounds for these models using both combinatorial and information-theoretic methods.

The theorem numbering changed - now it is synchronized with the ISAAC publication.

Revision #4 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Accepted on: 24th July 2020 01:36

Downloads: 98

Keywords:

Suppose Alice and Bob are communicating in order to compute some function $f$, but instead of a conventional communication channel, they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$, where every round one of the players sends a bit, and the other receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkies instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). The motivation for this kind of communication model comes from the study of the KRW conjecture. We show that for some definitions, this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds. We also prove lower bounds for these models using both combinatorial and information-theoretic methods.

+ Acknowledgement

Revision #3 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Accepted on: 22nd July 2020 02:32

Downloads: 104

Keywords:

Suppose Alice and Bob are communicating bits to each other in order to compute some function $f$, but instead of a classical communication channel they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$ where each round one player sends bit and the other one receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkie instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). We show that for some definitions this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds. We also introduce round elimination technique for proving lower bounds in this setting and use it to prove lower bounds for some Boolean functions.

The proof of Theorem 9 was simplified.

Revision #2 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Accepted on: 21st July 2018 21:02

Downloads: 494

Keywords:

Suppose Alice and Bob are communicating in order to compute some function $f$, but instead of a classical communication channel they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$ where each round one player sends a bit and the other one receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkies instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). The motivation for this kind of a communication model comes from the study of the KRW conjecture. We show that for some definitions this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds. We also prove lower bounds for these models using both combinatorial and information theoretic methods.

New lower bounds via theoretical information methods.

Revision #1 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Accepted on: 16th May 2018 12:28

Downloads: 369

Keywords:

Suppose Alice and Bob are communicating bits to each other in order to compute some function $f$, but instead of a classical communication channel they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$ where each round one player sends bit and the other one receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkie instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). We show that for some definitions this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds.

We introduce round elimination technique for proving lower bounds in this setting and use it to prove lower bounds for some Boolean functions. We also apply information theoretic methods to prove

better lower bounds for one of the models.

We apply information theoretic methods to prove lower bounds on the half-duplex complexity with adversary.

TR18-089 Authors: Kenneth Hoover, Russell Impagliazzo, Ivan Mihajlin, Alexander Smal

Publication: 1st May 2018 22:03

Downloads: 818

Keywords:

Suppose Alice and Bob are communicating bits to each other in order to compute some function $f$, but instead of a classical communication channel they have a pair of walkie-talkie devices. They can use some classical communication protocol for $f$ where each round one player sends bit and the other one receives it. The question is whether talking via walkie-talkie gives them more power? Using walkie-talkie instead of a classical communication channel allows players two extra possibilities: to speak simultaneously (but in this case they do not hear each other) and to listen at the same time (but in this case they do not transfer any bits). We show that for some definitions this non-classical communication model is, in fact, more powerful than the classical one as it allows to compute some functions in a smaller number of rounds. We also introduce round elimination technique for proving lower bounds in this setting and use it to prove lower bounds for some Boolean functions.