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Lower bounds on probabilistic linear decision trees

Marc Snir
1985 Theoretical Computer Science  
It is shown that the standard arguments used to prove lower bounds on deterministic linear decision trees apply to probabilistic linear decision trees as well.  ...  The power of probabilistic linear decision trees is examined.  ...  Lower bounds on probabilistic decision trees 75 Once again we can use Theorem 3.1 to extend this lower bound to the cost of probabilistic decision trees.  ... 
doi:10.1016/0304-3975(85)90210-5 fatcat:xnhbumzz2zbyjlorkx3xeb55vi

Applications of Ramsey's theorem to decision tree complexity

Shlomo Moran, Marc Snir, Udi Manber
1985 Journal of the ACM  
All the lower bounds mentioned above are shown to hold for nondeterministic and probabilistic decision trees as well.  ...  A decision tree is called k-bounded if each query depends on at most k variables. No further assumptions on the type of queries are made.  ...  Manber and Tompa [9] extended several lower bounds to nondeterministic and probabilistic models of decision trees (see also [8] and [ 181).  ... 
doi:10.1145/4221.4259 fatcat:twqmzjpvpzbs5k2kjnyeekqbwq

Page 1266 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
The underlying computation model is a restricted linear decision tree, where each decision is based on the sign of a linear combina- tion of at most r variables.  ...  This (non-uniform) bound is almost matched by a simple (uniform) algorithm. In the general nonuni- form linear decision tree model, an upper bound O(n‘*log(n)) is known.  ... 

Page 4916 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
Summary: “We investigate decision trees for decision tables. We present some upper and lower bounds on the minimal decision tree depth.  ...  (RS-NZNV-AM; Nizhnii Novgorod) Decision trees for decision tables.  ... 

Page 3831 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Meyer auf der Heide, A polynomial linear search algorithm for the n-dimensional knapsack problem (pp. 70-79); M. Ben-Or, Lower bounds for algebraic computation trees (pp. 80-86); A. Borodin, D.  ...  Kurtz, On the random oracle hypothesis (pp. 224-230); Stephen Cook and Cynthia Dwork, Bounds on the time for parallel RAMs to compute simple functions (pp. 231-233); Udi Manber and Martin Tompa, Probabilistic  ... 

Page 5789 of Mathematical Reviews Vol. , Issue 86m [page]

1986 Mathematical Reviews  
Author summary: “This work generalizes decision trees in order to study lower bounds on the running times of algorithms that allow probabilistic, nondeterministic, or alternating control.  ...  Two geometric techniques from the literature for proving lower bounds on the time required by ordinary decision trees are shown to be special cases of one unified technique that, in fact, applies to nondeterministic  ... 


Mikio Kubo, Hiroshi Kasugai
1992 Journal of the Operations Research Society of Japan  
IVe also derive the lower bounding procedure using the probabilistic extensions of valid inequalities which, by combining the linear programming technique and the cutting plane procedure, induce the lower  ...  ; thus inserting probabilistic elements to the problem setting is important for the strategic planning in the middle or IQng term decision models.  ...  by solving the linear programming relaxation; we get the improved lower bound E[c-] =:for deriving the upper and lower bounds of the expected network design costs over all possible instances generated  ... 
doi:10.15807/jorsj.35.256 fatcat:4t5kpoqgvbamlgm7ewqpbgb7ra

On the power of circuits with gates of low L1 norms

Vince Grolmusz
1997 Theoretical Computer Science  
Then we present several applications of this theorem for circuit lower bounds (both for bounded-and unbounded depth), and a decision-tree lower bound.  ...  (both deterministic and probabilistic) communication complexity [9,20,30].  ...  Griiger and Turan [I 11 proved a linear lower bound for the depth of decision trees with linear threshold test functions.  ... 
doi:10.1016/s0304-3975(96)00290-3 fatcat:evlgn22tdbbk5iq6p56kv3uyc4

On the Probabilistic Degree of an n-variate Boolean Function [article]

Srikanth Srinivasan, S. Venkitesh
2021 arXiv   pre-print
Our understanding of this complexity measure is significantly weaker than those above: for instance, we do not even know the probabilistic degree of the OR function, the best-known bounds put it between  ...  This was improved to a tight (log n - O(1)) bound by Chiarelli, Hatami and Saks (Combinatorica 2020).  ...  Putting together Simon's bound on the sensitivity of a truly n-variate function with known probabilistic degree lower bounds [16] , one can show a lower bound of (log log n) 1/2−o (1) .  ... 
arXiv:2107.03171v1 fatcat:2vfnlnbhfbcdhbt5dv3xzsn2eu

Page 461 of Mathematical Reviews Vol. , Issue 89A [page]

1989 Mathematical Reviews  
This is the decision problem for the threshold language L,. Our lower bound is tight. For PRIORITY with m shared memory cells we prove an Q(g(n)/m) lower bound.  ...  For probabilistic PRIORITY without ROM we prove a tight Q(n/m) lower bound.  ... 

Stochastic Constraint Programming with And-Or Branch-and-Bound

Behrouz Babaki, Tias Guns, Luc de Raedt
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
The resulting approach searches over the And-Or search tree directly, and we investigate tight bounds on the expected utility objective.  ...  Stochastic constraint programming was proposed as a way to formulate and solve such decision problems, involving arbitrary constraints over both decision and random variables.  ...  Conclusion and Future Work We presented a novel stochastic constraint programming method with three distinguishing features: a novel bound that works on the And-Or search space directly; the use of (nontrivial  ... 
doi:10.24963/ijcai.2017/76 dblp:conf/ijcai/BabakiGR17 fatcat:bonaixzrmnhjbpokfidnuhokom

Cumulative subject index volumes 60–63

1984 Information and Control  
, determination of nonlinear lower bounds, 60, 1 similarity and duality, 62, 109 single-tape Turing machine, simulation by fast probabilistic random access machines, 63, 67 Computing distributed  ...  dynamic logic, 63, 11 Decisions equivalence between DPDA and linear DPDA, with intermediate machine technique, 62, 26 trees, optimal, for symmetric Boolean functions, 62, 129 Decoding complete  ... 
doi:10.1016/s0019-9958(84)80017-0 fatcat:cnws7odqjre33jn42n3t72h46y

Arthur–Merlin Games in Boolean Decision Trees

Ran Raz, Gábor Tardos, Oleg Verbitsky, Nikolai Vereshchagin
1999 Journal of computer and system sciences (Print)  
It is well known that probabilistic boolean decision trees cannot be much more powerful than deterministic ones (N. Nisan, SIAM Journal on Computing, 20(6):999{1007, 1991.  ...  prove some lower bounds.  ...  It is useful to get more broad view of the situation by pre xing some lower bounds on ip(f) to (3) .  ... 
doi:10.1006/jcss.1999.1654 fatcat:nishbztdu5huhkovpzha4r62au

Page 2762 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
So far these lower bounds have been proved only for deterministic algebraic decision trees and for randomized linear decision trees. The proof method is combinatorial: Main theorem.  ...  This paper introduces a new method for proving lower bounds on randomized and deterministic analytic decision trees. It also gives applications for geometric problems.  ... 

Page 6317 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
Our main result is a (tight) linear lower bound on the randomized decision tree comlexity of any function in RO-TC®.  ...  “This relationship between threshold circuits and decision trees bears significance on both models of computation.  ... 
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