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Complexity Theoretical Resultson Nondeterministic Graph-driven Read-Once Branching Programs

Published online by Cambridge University Press:  15 November 2003

Beate Bollig
Beate Bollig*
Affiliation:
FB Informatik, LS2, University Dortmund, 44221 Dortmund, Germany; bollig@ls2.cs.uni-dortmund.de.  Supported in part by DFG We 1066/9.
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Abstract

Branching programs are a well-established computation model for boolean functions,especially read-once branching programs (BP1s) have been studied intensively. Recently two restricted nondeterministic (parity)BP1 models, called nondeterministic (parity) graph-driven BP1s and well-structured nondeterministic (parity) graph-driven BP1s, have been investigated. The consistency test for a BP-model M is the test whether a given BP is really a BP of model M. 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 BP1sis presented. The method generalizes a technique for the well-structured modeland is applied in order to answer in the affirmative the open question whether the model of nondeterministic graph-driven BP1s is a proper restriction of nondeterministic BP1s (with respect to polynomial size).

Keywords

Computational complexityread-once branching programsnondeterminismlower bounds.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 1 , January 2003 , pp. 51 - 66
Copyright
© EDP Sciences, 2003

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References

M. Ajtai, A non-linear time lower bound for boolean branching programs, in Proc. of 40th FOCS (1999) 60-70.
P. Beame, M. Saks, X. Sun and E. Vee, Super-linear time-space tradeoff lower bounds for randomized computation, in Proc. of 41st FOCS (2000) 169-179.
P. Beame and E. Vee, Time-space trade-offs, multiparty communication complexity, and nearest neighbor problems, in Proc. of 34th STOC (2002) 688-697.
Bollig, B., Restricted nondeterministic read-once branching programs and an exponential lower bound for integer multiplication. RAIRO: Theoret. Informatics Appl. 35 (2001) 149-162.
B. Bollig, St. Waack and P. Woelfel, Parity graph-driven read-once branching programs and an exponential lower bound for integer multiplication, in Proc. of 2nd IFIP International Conference on Theoretical Computer Science (2002) 83-94.
B. Bollig and P. Woelfel, A lower bound technique for nondeterministic graph-driven read-once branching programs and its applications, in Proc. of MFCS 2002. Springer, Lecture Notes in Comput. Sci. 2420 (2002) 131-142.
Borodin, A., Razborov, A. and Smolensky, R., On lower bounds for read-k-times branching programs. Comput. Complexity 3 (1993) 1-18. CrossRef
H. Brosenne, M. Homeister and St. Waack, Graph-driven free parity BDDs: Algorithms and lower bounds, in Proc. of MFCS. Springer, Lecture Notes in Comput. Sci. 2136 (2001) 212-223.
Bryant, R.E., Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35 (1986) 677-691. CrossRef
J. Gergov and C. Meinel, Frontiers of feasible and probabilistic feasible boolean manipulation with branching programs, in Proc. of STACS. Springer, Lecture Notes in Comput. Sci. 665 (1993) 576-585.
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).
M. Krause, BDD-based cryptanalysis of keystream generators, in Proc. of EUROCRYT (2002) 222-237.
E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge University Press (1997).
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.
Nechiporuk, E.I., On a boolean function. Soviet Math. Dokl. 7 (1966) 999-1000.
A.A. Razborov, Lower bounds for deterministic and nondeterministic branching programs, in Proc. of FCT. Springer, Lecture Notes in Comput. Sci. 529 (1991) 47-60.
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.
Savický, P. and Zák, S., A read-once lower bound and a (1, +k)-hierarchy for branching programs. Theoret. Comput. Sci. 238 (2000) 347-362. CrossRef
Sieling, D. and Wegener, I., I. (1995). Graph driven BDDs - A new data structure for boolean functions. Theoret. Comput. Sci. 141 (1995) 283-310. CrossRef
Sieling, D. and Wegener, I., A comparison of free BDDs and transformed BDDs. Formal Meth. System Design 19 (2001) 223-236. CrossRef
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.
I. Wegener, The Complexity of boolean Functions. Wiley-Teubner (1987).
I. Wegener, Branching Programs and Binary Decision Diagrams - Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications (2000).
P. Woelfel, A lower bound technique for restricted branching programs and applications, in Proc. of 19th STACS. Springer, Lecture Notes in Comput. Sci. 2285 (2002) 431-442.