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Parity graph-driven read-once branching programs and an exponential lower bound for integer multiplication
2006
Theoretical Computer Science
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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]
2002
Foundations of Information Technology in the Era of Network and Mobile Computing
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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]
2000
Lecture Notes in Computer Science
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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
2003
RAIRO - Theoretical Informatics and Applications
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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]
2003
Lecture Notes in Computer Science
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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
2001
RAIRO - Theoretical Informatics and Applications
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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
2006
Theoretical Computer Science
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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]
2002
Lecture Notes in Computer Science
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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
2004
Theory of Computing Systems
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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
2002
RAIRO - Theoretical Informatics and Applications
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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
1994
Discrete Mathematics
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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
1995
Theoretical Computer Science
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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
1998
SIAM journal on computing (Print)
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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
1995
Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
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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
1996
Journal of computer and system sciences (Print)
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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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