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Lower bounds on the complexity of real-time branching programs. (English) Zbl 0664.68046
Author’s summary: “A \((2m)^{n/24}\) lower bound is given for the real- time decision graph complexity of the Dyck language \(D_ m^*\). Furthermore, a \(2^{n/48}\) lower bound for the real-time branching program complexity of an encoding of the Dyck language \(D^*_ 2\) is proved. Previously known similar lower bounds are \(2^{c\cdot n}\), \(c\approx 10^{-13}\), for one-time-only branching programs (a less powerful model), and \(2^{\Omega (\sqrt{n})}\) for real-time branching programs.”
Reviewer: D.Lucanu

68Q25 Analysis of algorithms and problem complexity
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
68Q45 Formal languages and automata
Full Text: DOI EuDML
[1] 1. M. AJTAI, L. BABAI, P. HAJNAL, J. KOMLOS, P. PUDLAK, V. RÖDEL, E. SZEMEREDI and G. TURAN, Two lower bounds for branching programs, 18th ACM STOC, 1986, pp. 30-39.
[2] 2. A. BORODIN, D. DOLEV, F. E. FICH and W. PAUL, Bounds for width two branching programs, 15th ACM STOC, 1983, pp. 87-93. · Zbl 0589.68034
[3] 3. L. BUDACH, Lower bounds for the number of nodes in a decision tree, EIK 21, 1985, No 4/5, pp.221-228. MR824578
[4] 4. A. K. CHANDRA, M. L. FURST and R. J. LIPTON, Multiparty protocols, 15th ACM STOC, 1983, pp.94-99.
[5] 5. P. E. DUNNE, Lower bounds on the complexity of 1-time-only branching programs, FCT Proc., Lect. Notes in Comp. Sci.,Vol. 199, 1985, pp. 90-99. Zbl0575.68064 MR821228 · Zbl 0575.68064
[6] 6. R. J. LIPTON and Y. ZALCSTEIN, Word problems solvable in logspace, Journal of the ACM, Vol. 24, No.3, 1977, pp. 522-526. Zbl0359.68049 MR445901 · Zbl 0359.68049 · doi:10.1145/322017.322031
[7] 7. E. I. NECHIPORUK, On a Boolean function, Dokl. Akad. Nauk USSR, Vol. 169, No. 4, 1966, pp.765-766. Zbl0161.00901 MR218148 · Zbl 0161.00901
[8] 8. P. PUDLAK, A lower bound on the complexity of branching programs, Preprint, Univ. Prague, 1983. MR783479
[9] 9. U. VISHKIN and A. WIGDERSON, Trode-offs between depth and width in parallel computation, SIAM J. Comput, Vol. 14, No.2, 1985, pp. 303-314. Zbl0573.68015 MR784739 · Zbl 0573.68015 · doi:10.1137/0214024
[10] 10. I. WEGENER, On the complexity of branching programs and decision trees for clique fonctions, Univ. of Frankfurt, Fachbereich Informatik, Interner Bericht, 5/84, 1984. · Zbl 0592.94025
[11] 11. A. C. YAO, Lower bounds by probabilistic arguments, 24th IEEE FOCS, 1983, pp. 420-428.
[12] 12. S. ZAK, An exponential lower bound for one-time-only branching programs, MFCS Proc., Lect. Notes in Comp. Sci., Vol. 176, 1984, pp. 562-566. Zbl0558.68044 MR783488 · Zbl 0558.68044
[13] 13. S. ZAK, An exponential lower bound for real-time branching programs, manuscript.
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