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Parity graph-driven read-once branching programs and an exponential lower bound for integer multiplication

2006
*
Theoretical Computer Science
*

On the other hand, the problem of proving superpolynomial

doi:10.1016/j.tcs.2006.05.035
fatcat:xt3jt6e67bhpvi2az54hilq2yu
*lower**bounds**for**parity**read*-*once**branching**programs*is still open. ... Exponential*lower**bounds**for*deterministic and nondeterministic*read*-*once**branching**programs*are known*for*a long time. ... Acknowledgement Thanks to Stefan Droste, Detlef Sieling, and Ingo Wegener*for*fruitful discussions. ...##
###
Parity Graph-Driven Read-Once Branching Programs and An Exponential Lower Bound for Integer Multiplication
[chapter]

2002
*
Foundations of Information Technology in the Era of Network and Mobile Computing
*

On the other hand, the problem of proving superpolynomial

doi:10.1007/978-0-387-35608-2_8
dblp:conf/ifipTCS/BolligWW02
fatcat:cii5jh2fizczlhrpahnzonubmq
*lower**bounds**for**parity**read*-*once**branching**programs*is still open. ... Exponential*lower**bounds**for*deterministic and nondeterministic*read*-*once**branching**programs*are known*for*a long time. ... Acknowledgement Thanks to Stefan Droste, Detlef Sieling, and Ingo Wegener*for*fruitful discussions. ...##
###
Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication
[chapter]

2000
*
Lecture Notes in Computer Science
*

*For*that reason two restricted models of nondeterministic

*read*-

*once*

*branching*

*programs*are defined and a

*lower*

*bound*method is presented. ... Furthermore, the first exponential

*lower*

*bound*

*for*integer multiplication on the size of a nondeterministic nonoblivious

*read*-

*once*

*branching*

*program*model is proven. ... Thanks to Detlef Sieling and Ingo Wegener

*for*fruitful discussions and to Stefan Droste

*for*proofreading. I also would like to thank the anonymous referees

*for*their helpful comments. ...

##
###
Complexity Theoretical Results on Nondeterministic Graph-driven Read-Once Branching Programs

2003
*
RAIRO - Theoretical Informatics and Applications
*

*Branching*

*programs*are a well-established computation model

*for*boolean functions, especially

*read*-

*once*

*branching*

*programs*(BP1s) have been studied intensively. ... Here it is proved that the consistency test is co-NP-complete

*for*nondeterministic (

*parity*)

*graph*-

*driven*BP1s. Moreover, a

*lower*

*bound*technique

*for*nondeterministic

*graph*-

*driven*BP1s is presented. ... The author would like to thank Ingo Wegener

*for*fruitful discussions on the subject of the paper. ...

##
###
Complexity Theoretical Results on Nondeterministic Graph-Driven Read-Once Branching Programs
[chapter]

2003
*
Lecture Notes in Computer Science
*

*Branching*

*programs*are a well-established computation model

*for*boolean functions, especially

*read*-

*once*

*branching*

*programs*(BP1s) have been studied intensively. ... Here it is proved that the consistency test is co-NP-complete

*for*nondeterministic (

*parity*)

*graph*-

*driven*BP1s. Moreover, a

*lower*

*bound*technique

*for*nondeterministic

*graph*-

*driven*BP1s is presented. ... The author would like to thank Ingo Wegener

*for*fruitful discussions on the subject of the paper. ...

##
###
Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication

2001
*
RAIRO - Theoretical Informatics and Applications
*

*For*that reason two restricted models of nondeterministic

*read*-

*once*

*branching*

*programs*are defined and a

*lower*

*bound*method is presented. ... Furthermore, the first exponential

*lower*

*bound*

*for*integer multiplication on the size of a nondeterministic nonoblivious

*read*-

*once*

*branching*

*program*model is proven. ... Acknowledgement Thanks to Ingo Wegener

*for*several valuable hints and fruitful discussions and to Stefan Droste

*for*proofreading. ...

##
###
Lower bounds for restricted read-once parity branching programs

2006
*
Theoretical Computer Science
*

We

doi:10.1016/j.tcs.2006.01.052
fatcat:pxhleg5ylvew7lrnhuvqkyswmm
*generalize*a*lower**bound*by Savický and Sieling (see [P. Savický, D. Sieling, A hierarchy result*for**read*-*once**Branching**programs*with restricted*parity*nondeterminism, Theoret. Comput. ... We prove the first*lower**bounds**for*restricted*read*-*once**parity**branching**programs*with unlimited*parity*nondeterminism where*for*each input the variables may be tested according to several orderings. ... Then every sum of*graph*-*driven*BP1s guided by a sequence of*graph*-orderings G = (G 1 , . . . , G k ) representing the characteristic function of R(r, l) has size*bounded*below by 2 (n 1/2 /2 k ) /(|G 1 ...##
###
A Lower Bound Technique for Nondeterministic Graph-Driven Read-Once-Branching Programs and Its Applications
[chapter]

2002
*
Lecture Notes in Computer Science
*

We present a new

doi:10.1007/3-540-45687-2_10
fatcat:ehj7iq2iy5euhe66rk2xvf4zz4
*lower**bound*technique*for*a restricted*Branching**Program*model, namely*for*nondeterministic*graph*-*driven**read*-*once**Branching**Programs*(g.d.-BP1s). ... (*For*ω = ⊕ an exponential*lower**bound*was already obtained in [5] by using a different technique.) ... Acknowledgment We would like to thank Martin Sauerhoff and Ingo Wegener*for*fruitful discussions about the subject of this paper and helpful comments. ...##
###
A Lower Bound Technique for Nondeterministic Graph-Driven Read-Once-Branching Programs and Its Applications

2004
*
Theory of Computing Systems
*

We present a new

doi:10.1007/s00224-004-1130-1
fatcat:vkw65xtubjgxpesg2u4c3ifqde
*lower**bound*technique*for*a restricted*Branching**Program*model, namely*for*nondeterministic*graph*-*driven**read*-*once**Branching**Programs*(g.d.-BP1s). ... (*For*ω = ⊕ an exponential*lower**bound*was already obtained in [5] by using a different technique.) ... Acknowledgment We would like to thank Martin Sauerhoff and Ingo Wegener*for*fruitful discussions about the subject of this paper and helpful comments. ...##
###
Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs

2002
*
RAIRO - Theoretical Informatics and Applications
*

As a consequence, we derive a

doi:10.1051/ita:2002011
fatcat:kub7ts4k6bhnxfgki6gubqqqde
*lower**bound*criterion and prove an exponential*lower**bound**for*certain linear code functions. ... We investigate well-structured*graph*-*driven**parity*-FBDDs, which strictly*generalize*the two well-known models*parity*OBDDs and well-structured*graph*-*driven*FBDDs. ... The authors are indebted to Beate Bollig and the referees*for*their helpful suggestions and comments. ...##
###
Efficient data structures for Boolean functions

1994
*
Discrete Mathematics
*

A

doi:10.1016/0012-365x(95)90790-r
fatcat:xxzf72b4mvh4foatevscaqvivm
*generalized*data structure called*graph*-*driven*binary decision diagram is presented. ... Efficient algorithms*for*the operations on*graph**driven*BDDs are outlined. ' Supported in part by DFG grant No We 106617-I. 0012-365X/94/$07.00 0 1994-Elsevier Science B.V. ... Acknowledgement The author thanks Stefan Arnborg (Stockholm)*for*a stimulating discussion leading to Theorem 1. ...##
###
Graph driven BDDs — a new data structure for Boolean functions

1995
*
Theoretical Computer Science
*

Since an ordering of the variables may be stored as a list, OBDDs may also be called list

doi:10.1016/0304-3975(94)00078-w
fatcat:q4yroj4gifb5jnbkqzyhkj3t2a
*driven*BDDs. Two new*generalized*models of*graph**driven*BDDs are presented. ... The above mentioned and many other functions can be represented in small polynomial size in this model and the usual operations on OBDDs can be performed efficiently also*for**graph**driven*BDDs. ... Furthermore, we have proved that the clever*lower**bound*technique due to Bryant [9] works only*for*list*driven*BDDs and not*for**graph**driven*BDDs or*for**read*-*once**branching**programs*. ...##
###
A Lower Bound for Integer Multiplication with Read-Once Branching Programs

1998
*
SIAM journal on computing (Print)
*

This is the first nontrivial

doi:10.1137/s0097539795290349
fatcat:e3pq6gvqpzcczcejjuop4j6atu
*lower**bound**for*multiplication on*branching**programs*that are not oblivious. ... We prove that*read*-*once**branching**programs*computing integer multiplication require size 2 Ω( √ n) . ... Thanks to Mikael Goldmann*for*pointing out the reductions in [We93] , to Mauricio Karchmer and Ravi Sundaram*for*discussions, and to Allan Borodin*for*his seminar in which I learned of this problem. ...##
###
A lower bound for integer multiplication with read-once branching programs

1995
*
Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
*

This is the first nontrivial

doi:10.1145/225058.225098
dblp:conf/stoc/Ponzio95
fatcat:fuueuvpjofbebl76b6jbx2aime
*lower**bound**for*multiplication on*branching**programs*that are not oblivious. ... We prove that*read*-*once**branching**programs*computing integer multiplication require size 2 Ω( √ n) . ... Thanks to Mikael Goldmann*for*pointing out the reductions in [We93] , to Mauricio Karchmer and Ravi Sundaram*for*discussions, and to Allan Borodin*for*his seminar in which I learned of this problem. ...##
###
New Lower Bounds and Hierarchy Results for Restricted Branching Programs

1996
*
Journal of computer and system sciences (Print)
*

*Graph*

*driven*binary decision diagrams (Sieling and Wegener [12] , Gergov and Meinel [9] ) are

*read*-

*once*

*branching*

*programs*

*for*which a

*generalized*variable ordering is given. ...

*Graph*

*driven*binary decision diagrams have the same expressive power as

*read*-

*once*

*branching*

*programs*and the most important operations can be performed efficiently. ... If k=O(log 1&= n)

*for*some =>0, we can apply Theorem 8 and get the superpolynomial

*lower*

*bound*2 0(log 2 n)

*for*the size of each OBDD +(k&1)

*for*f k . ...

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