Complexity theoretical results on nondeterministic graph-driven read-once branching programs
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 1, pp. 51-66.

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 BP1s is presented. The method generalizes a technique for the well-structured model and 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).

DOI : https://doi.org/10.1051/ita:2003010
Classification : 68Q05,  68Q15,  94C10
Mots clés : computational complexity, read-once branching programs, nondeterminism, lower bounds
@article{ITA_2003__37_1_51_0,
     author = {Bollig, Beate},
     title = {Complexity theoretical results on nondeterministic graph-driven read-once branching programs},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {51--66},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {1},
     year = {2003},
     doi = {10.1051/ita:2003010},
     zbl = {1084.68049},
     mrnumber = {1991751},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2003__37_1_51_0/}
}
Bollig, Beate. Complexity theoretical results on nondeterministic graph-driven read-once branching programs. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 1, pp. 51-66. doi : 10.1051/ita:2003010. http://www.numdam.org/item/ITA_2003__37_1_51_0/

[1] M. Ajtai, A non-linear time lower bound for boolean branching programs, in Proc. of 40th FOCS (1999) 60-70. | MR 1916185

[2] 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. | MR 1931815

[3] P. Beame and E. Vee, Time-space trade-offs, multiparty communication complexity, and nearest neighbor problems, in Proc. of 34th STOC (2002) 688-697. | MR 2121196

[4] B. Bollig, Restricted nondeterministic read-once branching programs and an exponential lower bound for integer multiplication. RAIRO: Theoret. Informatics Appl. 35 (2001) 149-162. | Numdam | MR 1862460 | Zbl 0992.68057

[5] 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.

[6] 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. | MR 2064452 | Zbl 1014.68504

[7] 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

[8] 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. | MR 1907013 | Zbl 0999.68068

[9] R.E. Bryant, Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35 (1986) 677-691. | Zbl 0593.94022

[10] 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. | MR 1244146 | Zbl 0798.68078

[11] 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

[12] J. Hromkovič, Communication Complexity and Parallel Computing. Springer (1997). | MR 1442518 | Zbl 0873.68098

[13] M. Krause, BDD-based cryptanalysis of keystream generators, in Proc. of EUROCRYT (2002) 222-237. | MR 1975536 | Zbl 1055.94018

[14] E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge University Press (1997). | MR 1426129 | Zbl 0869.68048

[15] 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.

[16] E.I. Nechiporuk, On a boolean function. Soviet Math. Dokl. 7 (1966) 999-1000. | Zbl 0161.00901

[17] 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. | MR 1136069

[18] 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. | MR 1844789 | Zbl 0996.68513

[19] P. Savický and S. Žák, A read-once lower bound and a (1,+k)-hierarchy for branching programs. Theoret. Comput. Sci. 238 (2000) 347-362. | MR 1760487 | Zbl 0947.68056

[20] D. Sieling and I. Wegener, I. (1995). Graph driven BDDs - A new data structure for boolean functions. Theoret. Comput. Sci. 141 (1995) 283-310. | Zbl 0873.68036

[21] D. Sieling and I. Wegener, A comparison of free BDDs and transformed BDDs. Formal Meth. System Design 19 (2001) 223-236. | Zbl 1053.68071

[22] 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. | MR 1715611 | Zbl 1006.68054

[23] I. Wegener, The Complexity of boolean Functions. Wiley-Teubner (1987). | MR 905473 | Zbl 0623.94018

[24] I. Wegener, Branching Programs and Binary Decision Diagrams - Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications (2000). | Zbl 0956.68068

[25] 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. | MR 2050857 | Zbl 1054.68554