Chomsky hierarchy and communication complexity

2005 ◽  
pp. 12-18 ◽  
Author(s):  
Galina Jirásková
Keyword(s):  
Communication Complexity ◽  
Chomsky Hierarchy

scholarly journals Solving Problems in a DistributedWay in Membrane Computing: dP Systems

2010 ◽  
Vol 5 (2) ◽  
pp. 238 ◽  
Author(s):  
Gheorghe Păun ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Parallel Computing ◽  
Regular Language ◽  
Communication Complexity ◽  
Membrane Computing ◽  
P Systems ◽  
Constant Number ◽  
Distributed Architecture ◽  
Chomsky Hierarchy ◽  
Distributed Parallel Computing

Although P systems are distributed parallel computing devices, no explicit way of handling the input in a distributed way in this framework was considered so far. This note proposes a distributed architecture (based on cell-like P systems, with their skin membranes communicating through channels as in tissue-like P systems, according to specified rules of the antiport type), where parts of a problem can be introduced as inputs in various components and then processed in parallel. The respective devices are called dP systems, with the case of accepting strings called dP automata. The communication complexity can be evaluated in various ways: statically (counting the communication rules in a dP system which solves a given problem), or dynamically (counting the number of communication steps, of communication rules used in a computation, or the number of objects communicated). For each measure, two notions of “parallelizability" can be introduced. Besides (informal) definitions, some illustrations of these idea are provided for dP automata: each regular language is “weakly parallelizable" (i.e., it can be recognized in this framework, using a constant number of communication steps), and there are languages of various types with respect to Chomsky hierarchy which are “efficiently parallelizable" (they are parallelizable and, moreover, are accepted in a faster way by a dP automaton than by a single P automaton). Several suggestions for further research are made.

Lower Bounds in Communication Complexity

2007 ◽  
Author(s):  
T. Lee ◽  
A. Shraibman
Keyword(s):  
Lower Bounds ◽  
Communication Complexity

Nondeterministic and Randomized Boolean Hierarchies in Communication Complexity

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Toniann Pitassi ◽  
Morgan Shirley ◽  
Thomas Watson
Keyword(s):  
Communication Complexity

scholarly journals Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marcin Wieśniak
Keyword(s):  
Communication Complexity ◽  
Quantum Communication ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Complexity Reduction ◽  
Main Difficulty ◽  
Quantum Communication Complexity ◽  
Number Of Particles ◽  
Dicke States

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

scholarly journals Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiaoqing Zhong ◽  
Feihu Xu ◽  
Hoi-Kwong Lo ◽  
Li Qian
Keyword(s):  
Communication Complexity ◽  
Single Photon ◽  
Simultaneous Detection ◽  
Minimum Amount ◽  
Photon Detectors ◽  
Communication Time ◽  
Quantum Communication Complexity ◽  
Detection Of Signals ◽  
Coherent Quantum ◽  
Quantum Fingerprinting

AbstractQuantum communication complexity explores the minimum amount of communication required to achieve certain tasks using quantum states. One representative example is quantum fingerprinting, in which the minimum amount of communication could be exponentially smaller than the classical fingerprinting. Here, we propose a quantum fingerprinting protocol where coherent states and channel multiplexing are used, with simultaneous detection of signals carried by multiple channels. Compared with an existing coherent quantum fingerprinting protocol, our protocol could consistently reduce communication time and the amount of communication by orders of magnitude by increasing the number of channels. Our proposed protocol can even beat the classical limit without using superconducting-nanowire single photon detectors. We also report a proof-of-concept experimental demonstration with six wavelength channels to validate the advantage of our protocol in the amount of communication. The experimental results clearly prove that our protocol not only surpasses the best-known classical protocol, but also remarkably outperforms the existing coherent quantum fingerprinting protocol.

scholarly journals Communication Complexity of Byzantine Agreement, Revisited

2019 ◽  
Author(s):  
Ittai Abraham ◽  
T-H. Hubert Chan ◽  
Danny Dolev ◽  
Kartik Nayak ◽  
Rafael Pass ◽  
...  
Keyword(s):  
Communication Complexity ◽  
Byzantine Agreement
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