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

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1. M. Ajtai, A non-linear time lower bound for Boolean branching programs, in Proc. of 40th FOCS (1999) 60-70.  
2. N. Alon and W. Maass, Meanders and their applications in lower bound arguments. J. Comput. System Sci.37 (1988) 118-129.  
3. P. Beame, M. Saks, X. Sun and E. Vee, Super-linear time-space tradeoff lower bounds for randomized computation, in Proc. of 41st FOCS and ECCC Report TR 00-025 (2000).  
4. J. Bern, C. Meinel and A. Slobodová, Some heuristics for generating tree-like FBDD types. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems15 (1995) 127-130.  
5. 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).  
6. B. Bollig, M. Sauerhoff, D. Sieling and I. Wegener, Hierarchy theorems for k-OBDDs and k-IBDDs. Theoret. Comput. Sci.205 (1998) 45-60.  
7. B. Bollig and I. Wegener, Read-once projections and formal circuit verification with binary decision diagrams, in Proc. of 13th STACS. Springer, Lecture Notes in Comput. Sci.1046 (1996) 491-502.  
8. B. Bollig and I. Wegener, Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. Theory Comput. Syst.32 (1999) 487-503.  
9. B. Bollig and P. Woelfel, A read-once branching program lower bound of $\Omega \left(2^{n/4}\right)$ for integer multiplication using universal hashing, in Proc. of 33rd STOC (to appear).  
10. A. Borodin, A. Razborov and R. Smolensky, On lower bounds for read-k-times branching programs. Comput. Complexity3 (1993) 1-18.  
11. R.E. Bryant, Graph-based algorithms for Boolean manipulation. IEEE Trans. Comput.35 (1986) 677-691.  
12. R.E. Bryant, On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Trans. Comput.40 (1991) 205-213.  
13. J. Gergov, Time-space trade-offs for integer multiplication on various types of input oblivious sequential machines. Inform. Process. Lett.51 (1994) 265-269.  
14. J. Gergov and C. Meinel, Efficient Boolean manipulation with OBDDs can be extended to FBDDs. IEEE Trans. Comput.43 (1994) 1197-1209.  
15. J. Hromkovic, Communication Complexity and Parallel Computing (Springer, 1997).  
16. J. Hromkovic and M. Sauerhoff, Communications with restricted nondeterminism and applications to branching program complexity, in Proc. of 17th STACS. Springer, Lecture Notes in Comput. Sci.1770 (2000) 145-156.  
17. 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.  
18. E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge University Press (1997).  
19. C. Meinel, Polynomial size $\Omega$-branching programs and their computational power. Inform. and Comput.85 (1990) 163-182.  
20. S. Ponzio, A lower bound for integer multiplication with read-once branching programs. SIAM J. Comput.28 (1998) 798-815.  
21. M. Sauerhoff, Computing with restricted nondeterminism: The dependence of the OBDD size on the number of nondeterministic variables, in Proc. 19th FST & TCS. Springer, Lecture Notes in Comput. Sci.1738 (1999) 342-355.  
22. P. Savický and D. Sieling, A hierarchy result for read-once branching programs with restricted parity nondeterminism, in Proc. of 25th MFCS. Springer, Lecture Notes in Comput. Sci.1893 (2000) 650-659.  
23. D. Sieling and I. Wegener, Graph driven BDDs - a new data structure for Boolean functions. Theoret. Comput. Sci.141 (1995) 283-310.  
24. J. Thathachar, On separating the read-k-times branching program hierarchy, in Proc. of 30th Ann. ACM Symposium on Theory of Computing (STOC) (1998) 653-662.  
25. I. Wegener, Branching Programs and Binary Decision Diagrams - Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications (2000).  
26. I. Wegener, The Complexity of Boolean Functions. Wiley-Teubner (1987).  
27. P. Woelfel, New bounds on the OBDD-size of integer multiplication via universal hashing, in Proc. of 18th STACS. Springer, Lecture Notes in Comput. Sci.2010 (2001) 563-574.  

1. Beate Bollig, Complexity theoretical results on nondeterministic graph-driven read-once branching programs
2. Beate Bollig, Complexity Theoretical Results on Nondeterministic Graph-driven Read-Once Branching Programs