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Lower Bounds on the Randomized Communication Complexity of Read-Once Functions

Nikos Leonardos, Michael Saks
2010 Computational Complexity  
We prove lower bounds on the randomized two-party communication complexity of functions that arise from read-once boolean formulae.  ...  The complexity of the evaluation of general read-once formulae has attracted interest mainly in the decision tree model.  ...  We also thank the anonymous referees of the 24th IEEE Conference on Computational Complexity and the Computational Complexity journal for their corrections and useful suggestions.  ... 
doi:10.1007/s00037-010-0292-2 fatcat:hiy5kdsiibbldhp73h3owfzgu4

Depth-Independent Lower Bounds on the Communication Complexity of Read-Once Boolean Formulas [chapter]

Rahul Jain, Hartmut Klauck, Shengyu Zhang
2010 Lecture Notes in Computer Science  
We show lower bounds of Ω( √ n) and Ω(n 1/4 ) on the randomized and quantum communication complexity, respectively, of all nvariable read-once Boolean formulas.  ...  Our results complement the recent lower bound of Ω(n/8 d ) by Leonardos and Saks [LS09] and Ω(n/2 O(d log d) ) by Jayram, Kopparty and Raghavendra [JKR09] for randomized communication complexity of read-once  ...  Acknowledgments: Research of Rahul Jain and Hartmut Klauck is supported by the internal grants of the Centre for Quantum Technologies (CQT), which is funded by the Singapore Ministry of Education and the  ... 
doi:10.1007/978-3-642-14031-0_8 fatcat:zgw77zfaargctpdjunxxc7tf5q

Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas [article]

Rahul Jain, Hartmut Klauck, Shengyu Zhang
2009 arXiv   pre-print
We show lower bounds of Ω(√(n)) and Ω(n^1/4) on the randomized and quantum communication complexity, respectively, of all n-variable read-once Boolean formulas.  ...  Our results complement the recent lower bound of Ω(n/8^d) by Leonardos and Saks and Ω(n/2^Ω(d d)) by Jayram, Kopparty and Raghavendra for randomized communication complexity of read-once Boolean formulas  ...  Acknowledgments: Research of Rahul Jain and Hartmut Klauck is supported by the internal grants of the Centre for Quantum Technologies (CQT), which is funded by the Singapore Ministry of Education and the  ... 
arXiv:0908.4453v1 fatcat:mhv43mywpjdz7clfnrmnpbdi4e

Approximation of boolean functions by combinatorial rectangles

Martin Sauerhoff
2003 Theoretical Computer Science  
The functions from the main result require only linear size for nondeterministic read-once branching programs and randomized read-once branching programs with two-sided error 1 3 +o(1), while randomized  ...  As applications of this result, the following separation results for read-once branching programs are obtained.  ...  I am further indebted to the anonymous referees for careful reading of the ÿrst version of this paper and valuable suggestions which helped to improve and shorten the paper signiÿcantly, and one referee  ... 
doi:10.1016/s0304-3975(02)00568-6 fatcat:326qtqy2rbe5hij5l2h4zvwi5q

Lower bounds for randomized read-k-times branching programs [chapter]

Martin Sauerhoff
1998 Lecture Notes in Computer Science  
Randomized read-k-times branching programs are thus one of the most general types of branching programs for which an exponential lower bound result could be established.  ...  In this paper, we contribute to the complexity theory of randomized read-k-times branching programs.  ...  Acknowledgement I would like to thank Ingo Wegener and Martin Dietzfelbinger for helpful discussions on the subject of this paper.  ... 
doi:10.1007/bfb0028553 fatcat:rngolkph6ffbpa7uymafwfkzr4

On the Communication Complexity of Read-Once AC^0 Formulae

T.S. Jayram, Swastik Kopparty, Prasad Raghavendra
2009 2009 24th Annual IEEE Conference on Computational Complexity  
We study the 2-party randomized communication complexity of read-once AC 0 formulae.  ...  Our techniques build on and extend the information complexity methodology [4], [5], [3] for proving lower bounds on randomized communication complexity.  ...  communication complexity of the TRIBES functions [3] (where T is a depth-2 read-once formula).  ... 
doi:10.1109/ccc.2009.39 dblp:conf/coco/JayramKR09 fatcat:54jkkbv6h5b2bavpkgx6qrtwb4

A lower bound for integer multiplication on randomized ordered read-once branching programs

Farid Ablayev, Marek Karpinski
2003 Information and Computation  
Our proof depends on proving a new lower bound on Yao's randomized one-way communication complexity of certain Boolean functions. It generalizes to some other models of randomized branching programs.  ...  We prove an exponential lower bound 2 (n/ log n) on the size of any randomized ordered read-once branching program computing integer multiplication.  ...  Acknowledgments We would like to thank Anna Gál, Stephen Ponzio, Sasha Razborov, Thomas Thierauf, and Andy Yao for helpful discussion on the subject of the paper.  ... 
doi:10.1016/s0890-5401(03)00118-4 fatcat:hk36x4iylzbrdd4e5dt2lfiwoi

Finding the Median (Obliviously) with Bounded Space [chapter]

Paul Beame, Vincent Liew, Mihai Pǎtraşcu
2015 Lecture Notes in Computer Science  
The bound also implies a size lower bound for read-once branching programs computing the low order bit of the median and implies the analog of P = NP ∩ coNP for length o(n log log n) oblivious branching  ...  This bound also applies to the problem of determining whether the median is odd or even.  ...  The use of communication complexity lower bounds in the "best partition" model to derive lower bounds for oblivious algorithms is not new, but the necessity of bounded rounds is.  ... 
doi:10.1007/978-3-662-47672-7_9 fatcat:vw63g5p4m5hpjnsbrv7533qxwu

Computing with Restricted Nondeterminism: The Dependence of the OBDD Size on the Number of Nondeterministic Variables [chapter]

Martin Sauerhoff
1999 Lecture Notes in Computer Science  
It is an open question whether an analogous simulation exists in the context of space-bounded computation. In this paper, a negative answer to this question is given for nondeterministic OBDDs.  ...  This is a consequence of the following main result of the paper.  ...  Thanks to Ingo Wegener for proofreading and improving the upper bound of Theorem 2, to Juraj Hromkovič, Detlef Sieling, and Ingo Wegener for helpful discussions, and finally to the referees for careful  ... 
doi:10.1007/3-540-46691-6_28 fatcat:3onwga6ukbcr3cotoi6hsmjrki

Finding the Median (Obliviously) with Bounded Space [article]

Paul Beame and Vincent Liew and Mihai Pǎtraşcu
2015 arXiv   pre-print
The bound also implies a size lower bound for read-once branching programs computing the low order bit of the median and implies the analog of P NP ∩ coNP for length o(n n) oblivious branching programs  ...  This bound also applies to the problem of determining whether the median is odd or even.  ...  Acknowledgements We thank Anup Rao for suggesting the improved form of Lemma 1 that we include here.  ... 
arXiv:1505.00090v1 fatcat:cywduuecufhjdlm25fepeqfdrq

One-way communication complexity and the Neciporuk lower bound on formula size [article]

Hartmut Klauck
2004 arXiv   pre-print
In this paper the Neciporuk method for proving lower bounds on the size of Boolean formulae is reformulated in terms of one-way communication complexity.  ...  A near quadratic lower bound on quantum formula size, as well as a polynomial separation between the sizes of quantum formulae with and without multiple read random inputs.  ...  The author wishes to thank Gregor Gramlich for a talk on the Nečiporuk method, which inspired this research, and Georg Schnitger for stimulating discussions.  ... 
arXiv:cs/0111062v2 fatcat:ycnaen7igje2pkw75v6syfjukq

Page 9257 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
On the other hand for a special k-stable function, a randomized read-once branch- ing program of polynomial size computing it with zero error is suggested (it is known that any deterministic read-once  ...  Judy Goldsmith (1-KY-C; Lexington, KY) 2002m:68041 68Q15 68Q05 68Q17 68R05 68W20 Sauerhoff, Martin (D-DORT-I2; Dortmund) On the size of randomized OBDDs and read-once branching programs for k-stable functions  ... 

One-Way Communication Complexity and the Nečiporuk Lower Bound on Formula Size

Hartmut Klauck
2007 SIAM journal on computing (Print)  
The Nečiporuk method for proving lower bounds on the size of Boolean formulae is reformulated in terms of one-way communication complexity.  ...  A near quadratic lower bound on quantum formula size, as well as a polynomial separation between the sizes of quantum formulae with and without multiple read random inputs.  ...  The author wishes to thank Gregor Gramlich for a talk on the Nečiporuk method, which inspired this research, and Georg Schnitger for stimulating discussions.  ... 
doi:10.1137/s009753970140004x fatcat:nnlcg6twr5e4tgtftlfip6eiqu

Quantum vs. Classical Read-once Branching Programs [article]

Martin Sauerhoff
2005 arXiv   pre-print
The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs.  ...  that is computable by error-free quantum read-once branching programs of size O(n^3), while each classical randomized read-once branching program and each quantum OBDD for this function with bounded two-sided  ...  Acknowledgment The author wishes to thank Detlef Sieling for proofreading of draft versions of the present paper, several valuable suggestions regarding proof details and presentation, and for a lot of  ... 
arXiv:quant-ph/0504198v2 fatcat:tmnvya6vpbbflaemrelygqldii

Hardness of Function Composition for Semantic Read once Branching Programs

Jeff Edmonds, Venkatesh Medabalimi, Toniann Pitassi, Marc Herbstritt
2018 Computational Complexity Conference  
We prove asymptotically optimal lower bounds for function composition in the setting of nondeterministic read once branching programs, for the syntactic model as well as the stronger semantic model of  ...  While previous super-polynomial lower bounds have been proven for read-once nondeterministic branching programs (for both the syntactic as well as the semantic models), we give the first lower bounds for  ...  For example, lifting theorems in communication complexity reduce lower bounds in communication complexity to query complexity lower bounds, via function composition.  ... 
doi:10.4230/lipics.ccc.2018.15 dblp:conf/coco/EdmondsMP18 fatcat:xhitioiy3nbella7iewr3wkofy
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