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

Beate Bollig, Stephan Waack, Philipp Woelfel
2006 Theoretical Computer Science  
On the other hand, the problem of proving superpolynomial 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.  ... 
doi:10.1016/j.tcs.2006.05.035 fatcat:xt3jt6e67bhpvi2az54hilq2yu

Parity Graph-Driven Read-Once Branching Programs and An Exponential Lower Bound for Integer Multiplication [chapter]

Beate Bollig, Stephan Waack, Philipp Woelfel
2002 Foundations of Information Technology in the Era of Network and Mobile Computing  
On the other hand, the problem of proving superpolynomial 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.  ... 
doi:10.1007/978-0-387-35608-2_8 dblp:conf/ifipTCS/BolligWW02 fatcat:cii5jh2fizczlhrpahnzonubmq

Restricted Nondeterministic Read-Once Branching Programs and an Exponential Lower Bound for Integer Multiplication [chapter]

Beate Bollig
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.  ... 
doi:10.1007/3-540-44612-5_18 fatcat:zak2tm34vnhadf5igohiptdlue

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

Beate Bollig
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.  ... 
doi:10.1051/ita:2003010 fatcat:5kwlzcpdujfqfmp5avd2uz47q4

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

Beate Bollig
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.  ... 
doi:10.1007/3-540-36494-3_27 fatcat:72jylkrqrrcuhlckyaq52jepua

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

Beate Bollig
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.  ... 
doi:10.1051/ita:2001113 fatcat:yjaouw2vpjboznwowlup3xyb3e

Lower bounds for restricted read-once parity branching programs

Matthias Homeister
2006 Theoretical Computer Science  
We 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  ... 
doi:10.1016/j.tcs.2006.01.052 fatcat:pxhleg5ylvew7lrnhuvqkyswmm

A Lower Bound Technique for Nondeterministic Graph-Driven Read-Once-Branching Programs and Its Applications [chapter]

Beate Bollig, Philipp Woelfel
2002 Lecture Notes in Computer Science  
We present a new 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.  ... 
doi:10.1007/3-540-45687-2_10 fatcat:ehj7iq2iy5euhe66rk2xvf4zz4

A Lower Bound Technique for Nondeterministic Graph-Driven Read-Once-Branching Programs and Its Applications

Beate Bollig, Philipp Woelfel
2004 Theory of Computing Systems  
We present a new 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.  ... 
doi:10.1007/s00224-004-1130-1 fatcat:vkw65xtubjgxpesg2u4c3ifqde

Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs

Henrik Brosenne, Matthias Homeister, Stephan Waack
2002 RAIRO - Theoretical Informatics and Applications  
As a consequence, we derive a 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.  ... 
doi:10.1051/ita:2002011 fatcat:kub7ts4k6bhnxfgki6gubqqqde

Efficient data structures for Boolean functions

Ingo Wegener
1994 Discrete Mathematics  
A 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.  ... 
doi:10.1016/0012-365x(95)90790-r fatcat:xxzf72b4mvh4foatevscaqvivm

Graph driven BDDs — a new data structure for Boolean functions

Detlef Sieling, Ingo Wegener
1995 Theoretical Computer Science  
Since an ordering of the variables may be stored as a list, OBDDs may also be called list 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.  ... 
doi:10.1016/0304-3975(94)00078-w fatcat:q4yroj4gifb5jnbkqzyhkj3t2a

A Lower Bound for Integer Multiplication with Read-Once Branching Programs

Stephen Ponzio
1998 SIAM journal on computing (Print)  
This is the first nontrivial 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.  ... 
doi:10.1137/s0097539795290349 fatcat:e3pq6gvqpzcczcejjuop4j6atu

A lower bound for integer multiplication with read-once branching programs

Stephen Ponzio
1995 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95  
This is the first nontrivial 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.  ... 
doi:10.1145/225058.225098 dblp:conf/stoc/Ponzio95 fatcat:fuueuvpjofbebl76b6jbx2aime

New Lower Bounds and Hierarchy Results for Restricted Branching Programs

Detlef Sieling
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 .  ... 
doi:10.1006/jcss.1996.0050 fatcat:6eomjcq6vbbcnb5ye6cbhziglu
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