63 research outputs found
Width Hierarchy for k-OBDD of Small Width
In this paper was explored well known model k-OBDD. There are proven width
based hierarchy of classes of boolean functions which computed by k-OBDD. The
proof of hierarchy is based on sufficient condition of Boolean function's non
representation as k-OBDD and complexity properties of Boolean function SAF.
This function is modification of known Pointer Jumping (PJ) and Indirect
Storage Access (ISA) functions.Comment: 8 page
On the power of randomized multicounter machines
AbstractOne-way two-counter machines represent a universal model of computation. Here we consider the polynomial-time classes of multicounter machines with a constant number of reversals and separate the computational power of nondeterminism, randomization and determinism. For instance, we show that polynomial-time one-way multicounter machines, with error probability tending to zero with growing input length, can recognize languages that cannot be accepted by polynomial-time nondeterministic two-way multicounter machines with a bounded number of reversals. A similar result holds for the comparison of determinism and one-sided-error randomization, and of determinism and Las Vegas randomization
Pseudorandomness for Regular Branching Programs via Fourier Analysis
We present an explicit pseudorandom generator for oblivious, read-once,
permutation branching programs of constant width that can read their input bits
in any order. The seed length is , where is the length of the
branching program. The previous best seed length known for this model was
, which follows as a special case of a generator due to
Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of
for arbitrary branching programs of size ). Our techniques
also give seed length for general oblivious, read-once branching
programs of width , which is incomparable to the results of
Impagliazzo et al.Our pseudorandom generator is similar to the one used by
Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite
different; ours is based on Fourier analysis of branching programs. In
particular, we show that an oblivious, read-once, regular branching program of
width has Fourier mass at most at level , independent of the
length of the program.Comment: RANDOM 201
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Pseudorandomness for Regular Branching Programs via Fourier Analysis
We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is , where n is the length of the branching program. The previous best seed length known for this model was , which follows as a special case of a generator due to Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of for arbitrary branching programs of size s). Our techniques also give seed length for general oblivious, read-once branching programs of width , which is incomparable to the results of Impagliazzo et al.
Our pseudorandom generator is similar to the one used by Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite different; ours is based on Fourier analysis of branching programs. In particular, we show that an oblivious, read-once, regular branching program of width w has Fourier mass at most at level k, independent of the length of the program.Engineering and Applied Science
Quantum vs. Classical Read-once Branching Programs
The paper presents the first nontrivial upper and lower bounds for
(non-oblivious) quantum read-once branching programs. It is shown that the
computational power of quantum and classical read-once branching programs is
incomparable in the following sense: (i) A simple, explicit boolean function on
2n input bits is presented that is computable by error-free quantum read-once
branching programs of size O(n^3), while each classical randomized read-once
branching program and each quantum OBDD for this function with bounded
two-sided error requires size 2^{\Omega(n)}. (ii) Quantum branching programs
reading each input variable exactly once are shown to require size
2^{\Omega(n)} for computing the set-disjointness function DISJ_n from
communication complexity theory with two-sided error bounded by a constant
smaller than 1/2-2\sqrt{3}/7. This function is trivially computable even by
deterministic OBDDs of linear size. The technically most involved part is the
proof of the lower bound in (ii). For this, a new model of quantum
multi-partition communication protocols is introduced and a suitable extension
of the information cost technique of Jain, Radhakrishnan, and Sen (2003) to
this model is presented.Comment: 35 pages. Lower bound for disjointness: Error in application of info
theory corrected and regularity of quantum read-once BPs (each variable at
least once) added as additional assumption of the theorem. Some more informal
explanations adde
Typically-Correct Derandomization for Small Time and Space
Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n * poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n * poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. As an immediate corollary, there is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique
Методическое пособие по предмету "Алгоритмы и структуры данных в построении и анализе СБИС"
Пособие предназначено для студентов, изучающих программную дисциплину "Алгоритмы и структуры данных в построении и анализе СБИС", а также для преподавателей, ведущих занятия по данному курсу.58Алгоритмы и структуры данных в построении и анализе СБИ
Equivalences on Phase Type Processes
In this thesis, we introduce Phase Type Processes (PTPs), a novel stochastic modeling approach that can express probabilistic and nondeterministic choices as well as random delays following phase type distributions, a generalization of exponential distributions. Action-labeled transitions are used to react on external stimuli and they are clearly separated from phase type transitions. The semantics of PTPs are defined in terms of path probabilities with respect to schedulers that resolve nondeterministic choices based on the timed process history. The main emphasis of this work is to analyze a variety of notions of equivalence for PTPs and classify them with respect to their distinguishing power. Amongst others, we define bisimulation, trace and testing equivalence as well as extensions of failure trace equivalence. Moreover, the contribution includes a discussion of parallel composition in the context of a partial memoryless property and the examination of a mapping from PTPs to the subclass of single phased processes in which all random delays are exponentially distributed
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