Recherche et téléchargement d’archives de revues mathématiques numérisées

  Table des matières de ce fascicule | Article précédent | Article suivant
Bollig, Beate
Restricted nondeterministic read-once branching programs and an exponential lower bound for integer multiplication. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, 35 no. 2 (2001), p. 149-162
Texte intégral djvu | pdf | Analyses MR 1862460 | Zbl 0992.68057 | 1 citation dans Numdam
Class. Math.: 68Q05, 68Q10, 68Q15, 94C10
Mots clés: computational complexity, read-once branching programs, nondeterminism, integer multiplication

URL stable:


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.


[1] M. Ajtai, A non-linear time lower bound for Boolean branching programs, in Proc. of 40$^{th}$ FOCS (1999) 60-70.  MR 1916185
[2] N. Alon and W. Maass, Meanders and their applications in lower bound arguments. J. Comput. System Sci. 37 (1988) 118-129.  MR 979114 |  Zbl 0664.68045
[3] 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).  MR 1931815
[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 Systems 15 (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.  MR 1638628 |  Zbl 0913.68078
[7] B. Bollig and I. Wegener, 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.  MR 1462120
[8] B. Bollig and I. Wegener, Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams. Theory Comput. Syst. 32 (1999) 487-503.  MR 1693395 |  Zbl 0934.68048
[9] 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).  MR 2120342
[10] A. Borodin, A. Razborov and R. Smolensky, On lower bounds for read-$k$-times branching programs. Comput. Complexity 3 (1993) 1-18.  MR 1220075 |  Zbl 0777.68043
[11] R.E. Bryant, Graph-based algorithms for Boolean manipulation. IEEE Trans. Comput. 35 (1986) 677-691.  Zbl 0593.94022
[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.  MR 1094031
[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.  MR 1294705
[14] J. Gergov and C. Meinel, Efficient Boolean manipulation with OBDDs can be extended to FBDDs. IEEE Trans. Comput. 43 (1994) 1197-1209.  Zbl 1063.68573
[15] J. Hromkovič, Communication Complexity and Parallel Computing (Springer, 1997).  MR 1442518 |  Zbl 0873.68098
[16] J. Hromkovič and M. Sauerhoff, 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.  MR 1781728 |  Zbl 0959.68522
[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).  MR 1426129 |  Zbl 0869.68048
[19] C. Meinel, Polynomial size $\Omega $-branching programs and their computational power. Inform. and Comput. 85 (1990) 163-182.  MR 1044460 |  Zbl 0705.68052
[20] S. Ponzio, A lower bound for integer multiplication with read-once branching programs. SIAM J. Comput. 28 (1998) 798-815.  MR 1643441 |  Zbl 0918.68025
[21] M. Sauerhoff, Computing with restricted nondeterminism: The dependence of the OBDD size on the number of nondeterministic variables, in Proc. 19$^{th}$ FST & TCS. Springer, Lecture Notes in Comput. Sci. 1738 (1999) 342-355.  MR 1776806 |  Zbl 0958.68062
[22] P. Savický and D. Sieling, 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.  MR 1844789 |  Zbl 0996.68513
[23] D. Sieling and I. Wegener, Graph driven BDDs – a new data structure for Boolean functions. Theoret. Comput. Sci. 141 (1995) 283-310.  Zbl 0873.68036
[24] 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.  MR 1715611 |  Zbl 1006.68054
[25] I. Wegener, Branching Programs and Binary Decision Diagrams – Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications (2000).  Zbl 0956.68068
[26] I. Wegener, The Complexity of Boolean Functions. Wiley-Teubner (1987).  MR 905473 |  Zbl 0623.94018
[27] P. Woelfel, 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.  MR 1892342 |  Zbl 0976.68510
Copyright Cellule MathDoc 2014 | Crédit | Plan du site