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

Published online by Cambridge University Press:  15 April 2002

Beate Bollig
Beate Bollig*
Affiliation:
FB Informatik, LS2, Univ. Dortmund, 44221 Dortmund, Germany; ([email protected])
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Abstract

Branching programs are a well established computation model for Boolean functions, especially read-once branching programs have been studied intensively. In this paper the expressive power of nondeterministic read-once branching programs, more precisely the class of functions representable in polynomial size, is investigated. 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.

Keywords

Computational complexityread-once branching programsnondeterminisminteger multiplication.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 2 , March 2001 , pp. 149 - 162
Copyright
© EDP Sciences, 2001

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References

M. Ajtai, A non-linear time lower bound for Boolean branching programs, in Proc. of 40 th FOCS (1999) 60-70.
Alon, N. and Maass, W., Meanders and their applications in lower bound arguments. J. Comput. System Sci. 37 (1988) 118-129. CrossRef
P. Beame, M. Saks, X. Sun and E. Vee, Super-linear time-space tradeoff lower bounds for randomized computation, in Proc. of 41 st FOCS and ECCC Report TR 00-025 (2000).
Bern, J., Meinel, C. and Slobodová, A., Some heuristics for generating tree-like FBDD types. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems 15 (1995) 127-130. CrossRef
B. Bollig, M. Sauerhoff, D. Sieling and I. Wegener, Read-k times ordered binary decision diagrams. Efficient algorithms in the presence of null chains. Tech. Report 474. Univ. Dortmund (1993).
Bollig, B., Sauerhoff, M., Sieling, D. and Wegener, I., Hierarchy theorems for k-OBDDs and k-IBDDs. Theoret. Comput. Sci. 205 (1998) 45-60. CrossRef
Bollig, B. and Wegener, I., Read-once projections and formal circuit verification with binary decision diagrams, in Proc. of 13 th STACS. Springer, Lecture Notes in Comput. Sci. 1046 (1996) 491-502. CrossRef
Bollig, B. and Wegener, I., Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. Theory Comput. Syst. 32 (1999) 487-503. CrossRef
B. Bollig and P. Woelfel, A read-once branching program lower bound of $\Omega(2^{n/4})$ for integer multiplication using universal hashing, in Proc. of 33 rd STOC (to appear).
Borodin, A., Razborov, A. and Smolensky, R., On lower bounds for read-k-times branching programs. Comput. Complexity 3 (1993) 1-18. CrossRef
Bryant, R.E., Graph-based algorithms for Boolean manipulation. IEEE Trans. Comput. 35 (1986) 677-691. CrossRef
Bryant, R.E., On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Trans. Comput. 40 (1991) 205-213. CrossRef
Gergov, J., Time-space trade-offs for integer multiplication on various types of input oblivious sequential machines. Inform. Process. Lett. 51 (1994) 265-269. CrossRef
Gergov, J. and Meinel, C., Efficient Boolean manipulation with OBDDs can be extended to FBDDs. IEEE Trans. Comput. 43 (1994) 1197-1209. CrossRef
J. Hromkovic, Communication Complexity and Parallel Computing (Springer, 1997).
Hromkovic, J. and Sauerhoff, M., Communications with restricted nondeterminism and applications to branching program complexity, in Proc. of 17 th STACS. Springer, Lecture Notes in Comput. Sci. 1770 (2000) 145-156. CrossRef
J. Jain, J. Bitner, D.S. Fussell and J.A. Abraham, Functional partitioning for verification and related problems. Brown/MIT VLSI Conference (1992) 210-226.
E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge University Press (1997).
Meinel, C., Polynomial size $\Omega$ -branching programs and their computational power. Inform. and Comput. 85 (1990) 163-182. CrossRef
Ponzio, S., A lower bound for integer multiplication with read-once branching programs. SIAM J. Comput. 28 (1998) 798-815. CrossRef
Sauerhoff, M., Computing with restricted nondeterminism: The dependence of the OBDD size on the number of nondeterministic variables, in Proc. 19 th FST & TCS. Springer, Lecture Notes in Comput. Sci. 1738 (1999) 342-355. CrossRef
Savický, P. and Sieling, D., A hierarchy result for read-once branching programs with restricted parity nondeterminism, in Proc. of 25 th MFCS. Springer, Lecture Notes in Comput. Sci. 1893 (2000) 650-659. CrossRef
Sieling, D. and Wegener, I., Graph driven BDDs - a new data structure for Boolean functions. Theoret. Comput. Sci. 141 (1995) 283-310. CrossRef
J. Thathachar, On separating the read-k-times branching program hierarchy, in Proc. of 30 th Ann. ACM Symposium on Theory of Computing (STOC) (1998) 653-662.
I. Wegener, Branching Programs and Binary Decision Diagrams - Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications (2000).
I. Wegener, The Complexity of Boolean Functions. Wiley-Teubner (1987).
Woelfel, P., New bounds on the OBDD-size of integer multiplication via universal hashing, in Proc. of 18 th STACS. Springer, Lecture Notes in Comput. Sci. 2010 (2001) 563-574. CrossRef