4,401 research outputs found
Verifying proofs in constant depth
In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's
Distinguishing sequences for partially specified FSMs
Distinguishing Sequences (DSs) are used inmany Finite State Machine (FSM) based test techniques. Although Partially Specified FSMs (PSFSMs) generalise FSMs, the computational complexity of constructing Adaptive and Preset DSs (ADSs/PDSs) for PSFSMs has not been addressed. This paper shows that it is possible to check the existence of an ADS in polynomial time but the corresponding problem for PDSs is PSPACE-complete. We also report on the results of experiments with benchmarks and over 8 * 106 PSFSMs. © 2014 Springer International Publishing
Deterministic Rateless Codes for BSC
A rateless code encodes a finite length information word into an infinitely
long codeword such that longer prefixes of the codeword can tolerate a larger
fraction of errors. A rateless code achieves capacity for a family of channels
if, for every channel in the family, reliable communication is obtained by a
prefix of the code whose rate is arbitrarily close to the channel's capacity.
As a result, a universal encoder can communicate over all channels in the
family while simultaneously achieving optimal communication overhead. In this
paper, we construct the first \emph{deterministic} rateless code for the binary
symmetric channel. Our code can be encoded and decoded in time per
bit and in almost logarithmic parallel time of , where
is any (arbitrarily slow) super-constant function. Furthermore, the error
probability of our code is almost exponentially small .
Previous rateless codes are probabilistic (i.e., based on code ensembles),
require polynomial time per bit for decoding, and have inferior asymptotic
error probabilities. Our main technical contribution is a constructive proof
for the existence of an infinite generating matrix that each of its prefixes
induce a weight distribution that approximates the expected weight distribution
of a random linear code
Functional and dynamic programming in the design of parallel prefix networks
A parallel prefix network of width n takes n inputs, a1, a2, . . ., an, and computes each yi = a1 ○ a2 ○ ⋅ ⋅ ⋅ ○ ai for 1 ≤ i ≤ n, for an associative operator ○. This is one of the fundamental problems in computer science, because it gives insight into how parallel computation can be used to solve an apparently sequential problem. As parallel programming becomes the dominant programming paradigm, parallel prefix or scan is proving to be a very important building block of parallel algorithms and applications. There are many different parallel prefix networks, with different properties such as number of operators, depth and allowed fanout from the operators. In this paper, ideas from functional programming are combined with search to enable a deep exploration of parallel prefix network design. Networks that improve on the best known previous results are generated. It is argued that precise modelling in a functional programming language, together with simple visualization of the networks, gives a new, more experimental, approach to parallel prefix network design, improving on the manual techniques typically employed in the literature. The programming idiom that marries search with higher order functions may well have wider application than the network generation described here
Partial DNA Assembly: A Rate-Distortion Perspective
Earlier formulations of the DNA assembly problem were all in the context of
perfect assembly; i.e., given a set of reads from a long genome sequence, is it
possible to perfectly reconstruct the original sequence? In practice, however,
it is very often the case that the read data is not sufficiently rich to permit
unambiguous reconstruction of the original sequence. While a natural
generalization of the perfect assembly formulation to these cases would be to
consider a rate-distortion framework, partial assemblies are usually
represented in terms of an assembly graph, making the definition of a
distortion measure challenging. In this work, we introduce a distortion
function for assembly graphs that can be understood as the logarithm of the
number of Eulerian cycles in the assembly graph, each of which correspond to a
candidate assembly that could have generated the observed reads. We also
introduce an algorithm for the construction of an assembly graph and analyze
its performance on real genomes.Comment: To be published at ISIT-2016. 11 pages, 10 figure
Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs
A read-once oblivious arithmetic branching program (ROABP) is an arithmetic
branching program (ABP) where each variable occurs in at most one layer. We
give the first polynomial time whitebox identity test for a polynomial computed
by a sum of constantly many ROABPs. We also give a corresponding blackbox
algorithm with quasi-polynomial time complexity . In both the
cases, our time complexity is double exponential in the number of ROABPs.
ROABPs are a generalization of set-multilinear depth- circuits. The prior
results for the sum of constantly many set-multilinear depth- circuits were
only slightly better than brute-force, i.e. exponential-time.
Our techniques are a new interplay of three concepts for ROABP: low
evaluation dimension, basis isolating weight assignment and low-support rank
concentration. We relate basis isolation to rank concentration and extend it to
a sum of two ROABPs using evaluation dimension (or partial derivatives).Comment: 22 pages, Computational Complexity Conference, 201
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