On the Power of Randomized Ordered Branching Programs DRAFT (original) (raw)
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On the Power of Randomized Ordered Branching Programs
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;
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.
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.
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 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 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.
Lower bounds for depth-restricted branching programs
Information and Computation, 1991
We present a new method for proving lower bounds on the complexity of branching programs and consider k-times-only branching programs. While exponential and nearly exponential lower bounds on the complexity of one-timeonly branching programs were proved for many problems, there are still missing methods of proving lower bounds for k-times-only programs (k > 1). We prove exponential lower bounds for k-times-only branching programs which have the additional restriction that the input bits are read k times, yet blockwise and in each block in the same order. This is done both for the algebraic decision problem POLYzd (n E N prime, d<n) whether a given mapping g: IF, + F, is a polynomial over F, of degree at most d, and for the corresponding monotone problem over quadratic Boolean matrices. As a consequence we obtain a sharp bound of order @(n 'log(n)) on the communication complexity of POLY:,, (SE (0, i)).
1995
Recent developments in the eld of digital design and hardware veri cation have found great use for restricted forms of branching programs. In particular, oblivious read-once branching programs (also called \OBDD's") are central to a very common technique for verifying circuits. These programs are useful because they are easily manipulated and compared for equivalence. However, their utility is limited because they cannot compute in polynomial size several simple functions|most notably, integer multiplication. This limitation has prompted the consideration of alternative models, usually restricted classes of branching programs, in the hope of nding one with greater computational power but also easily manipulated and tested for equivalence. Read-once (non-oblivious) branching programs can to some degree be manipulated and tested for equivalence, but it has been an open question whether they can compute integer multiplication in polynomial size. The main result of this thesis ...