Lower bounds for depth-restricted branching programs (original) (raw)

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On lower bounds for read-k-times branching programs

Computational Complexity, 1993

Randomized branching programs are a probabilistic model of computation defined in analogy to the well-known probabilistic Turing machines. In this paper, we contribute to the complexity theory of randomized read-k-times branching programs.

A lower bound for read-once-only branching programs

Journal of Computer and System Sciences, 1987

We give a C" lower bound for read-once-only branching programs computing an explicit Boolean function. For n = (;), the function computes the parity of the number of triangles in a graph on v vertices. This improves previous exp(c &) lower bounds for other graph functions by Wegener and Zak. The result implies a linear lower bound for the space complexity of this Boolean function on "eraser machines," i.e., machines that erase each input bit immediately after having read it.

On oblivious branching programs of linear length

Information and Computation, 1991

Input oblivious decision graphs of linear length are considered. Among other concerns the computational complexity of three graph accessibility problems and the word problem of the free group are investigated. Several exponential lower bounds are proved.

A Lower Bound for Integer Multiplication on Randomized Read-Once Branching Programs

Electronic Colloquium on Computational Complexity, 1998

We prove an exponential lower bound 2 (n= logn) on the size of any randomized ordered read-once branching program computing integer multiplication. Our proof depends on proving a new lower bound on Yao's randomized one-way communication complexity of certain boolean functions. It generalizes to some other common models of randomized branching programs. In contrast, we prove that testing integer multiplication, contrary even to nondeterministic situation, can be computed by randomized ordered read-once branching program in polynomial size. It is also known that computing the latter problem with deterministic read-once branching programs is as hard as factoring integers.

A lower bound for integer multiplication on randomized ordered read-once branching programs

Information and Computation, 2003

We prove an exponential lower bound 2 (n= logn) on the size of any randomized ordered read-once branching program computing integer multiplication. Our proof depends on proving a new lower bound on Yao's randomized one-way communication complexity of certain boolean functions. It generalizes to some other common models of randomized branching programs. In contrast, we prove that testing integer multiplication, contrary even to nondeterministic situation, can be computed by randomized ordered read-once branching program in polynomial size. It is also known that computing the latter problem with deterministic read-once branching programs is as hard as factoring integers.

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Electronic Colloquium on Computational Complexity, 1998

We de ne the notion of a randomized branching program in the natural way similar to the de nition of a randomized circuit. We exhibit an explicit boolean function f n : f0;1g n ! f0;1g for which we prove that: 1) f n can be computed by polynomial size randomized read-once ordered branching program with a small one-sided error;

Lower bounds on the complexity of real-time branching programs

RAIRO - Theoretical Informatics and Applications, 1988

Lower bounds on the complexity of real-time branching programs Informatique théorique et applications, tome 22, n o 4 (1988), p. 447-459. http://www.numdam.org/item?id=ITA\_1988\_\_22\_4\_447\_0 © AFCET, 1988, tous droits réservés. L'accès aux archives de la revue « Informatique théorique et applications » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Informatique théorique et Applications/Theoretical Informaties and Applications (vol. 22, n° 4, 1988, p. 447 à 459) LOWER BOUNDS ON THE COMPLEXITY OF REAL-TIME BRANCHING PROGRAMS (*) by Klaus KRIEGEL (*) and Stephan WAACK (*) Communicated by J. BERSTEL Abstract.-A (2 m)" /24 lower bound is given for the real-time décision graph complexity of the Dyck language D *. Furthermore, a 2 n/4 *Jower bound for the real-time branching program complexity of an encoding of the Dyck language DJ is proved. Previously known similar lower bounds are 2 e ", c« 10" 13 , for one-time-only branching programs (a less powerful model), and 2 nt V 5) for realtime branching programs. Résumé.-Dans cet article, nous montrons que le nombre de noeuds d'un arbre de décision en temps réel pour le langage de Dyck D* est borné inférieurement par (2m)" /24. On donne également une borne inférieure en 2" /48 pour la complexité des programmes temps réel pour un codage du langage de Dyck D*-Les bornes précédemment connues étaient en 2 e " avec c«10~1 3 pour les programmes à un seul branchement (un modèle moins puissant) et en 2 n (V n) pour les programmes à branchements temps réel.

On the power of randomized branching programs

1996

The seminar \Structure and Complexity" was the third Dagstuhl Seminar devoted to the structural aspects of Computational Complexity Theory. It was attented by 40 scientists who in 27 talks presented new results in this eld. The following topics were among the main subjects covered by the talks: Kolmogorov complexity, isomorphism theory, resource-bounded measures, relativizations, randomness, leaf language characterizations, circuit theory, logical characterizations of complexity classes, interactive proof systems, oneway functions, and computational models.