99,258 research outputs found
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
Simplifying the mosaic description of DNA sequences
By using the Jensen-Shannon divergence, genomic DNA can be divided into
compositionally distinct domains through a standard recursive segmentation
procedure. Each domain, while significantly different from its neighbours, may
however share compositional similarity with one or more distant
(non--neighbouring) domains. We thus obtain a coarse--grained description of
the given DNA string in terms of a smaller set of distinct domain labels. This
yields a minimal domain description of a given DNA sequence, significantly
reducing its organizational complexity. This procedure gives a new means of
evaluating genomic complexity as one examines organisms ranging from bacteria
to human. The mosaic organization of DNA sequences could have originated from
the insertion of fragments of one genome (the parasite) inside another (the
host), and we present numerical experiments that are suggestive of this
scenario.Comment: 16 pages, 1 figure, Accepted for publication in Phys. Rev.
Exact results for hydrogen recombination on dust grain surfaces
The recombination of hydrogen in the interstellar medium, taking place on
surfaces of microscopic dust grains, is an essential process in the evolution
of chemical complexity in interstellar clouds. The H_2 formation process has
been studied theoretically, and in recent years also by laboratory experiments.
The experimental results were analyzed using a rate equation model. The
parameters of the surface, that are relevant to H_2 formation, were obtained
and used in order to calculate the recombination rate under interstellar
conditions. However, it turned out that due to the microscopic size of the dust
grains and the low density of H atoms, the rate equations may not always apply.
A master equation approach that provides a good description of the H_2
formation process was proposed. It takes into account both the discrete nature
of the H atoms and the fluctuations in the number of atoms on a grain. In this
paper we present a comprehensive analysis of the H_2 formation process, under
steady state conditions, using an exact solution of the master equation. This
solution provides an exact result for the hydrogen recombination rate and its
dependence on the flux, the surface temperature and the grain size. The results
are compared with those obtained from the rate equations. The relevant length
scales in the problem are identified and the parameter space is divided into
two domains. One domain, characterized by first order kinetics, exhibits high
efficiency of H_2 formation. In the other domain, characterized by second order
kinetics, the efficiency of H_2 formation is low. In each of these domains we
identify the range of parameters in which, the rate equations do not account
correctly for the recombination rate. and the master equation is needed.Comment: 23 pages + 8 figure
Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation
We present an efficient proof system for Multipoint Arithmetic Circuit
Evaluation: for every arithmetic circuit of size and
degree over a field , and any inputs ,
the Prover sends the Verifier the values and a proof of length, and
the Verifier tosses coins and can check the proof in about time, with probability of error less than .
For small degree , this "Merlin-Arthur" proof system (a.k.a. MA-proof
system) runs in nearly-linear time, and has many applications. For example, we
obtain MA-proof systems that run in time (for various ) for the
Permanent, Circuit-SAT for all sublinear-depth circuits, counting
Hamiltonian cycles, and infeasibility of - linear programs. In general,
the value of any polynomial in Valiant's class can be certified
faster than "exhaustive summation" over all possible assignments. These results
strongly refute a Merlin-Arthur Strong ETH and Arthur-Merlin Strong ETH posed
by Russell Impagliazzo and others.
We also give a three-round (AMA) proof system for quantified Boolean formulas
running in time, nearly-linear time MA-proof systems for
counting orthogonal vectors in a collection and finding Closest Pairs in the
Hamming metric, and a MA-proof system running in -time for
counting -cliques in graphs.
We point to some potential future directions for refuting the
Nondeterministic Strong ETH.Comment: 17 page
The Complexity of Reverse Engineering Problems for Conjunctive Queries
Reverse engineering problems for conjunctive queries (CQs), such as query by example (QBE) or definability, take a set of user examples and convert them into an explanatory CQ. Despite their importance, the complexity of these problems is prohibitively high (coNEXPTIME-complete). We isolate their two main sources of complexity and propose relaxations of them that reduce the complexity while having meaningful theoretical interpretations. The first relaxation is based on the idea of using existential pebble games for approximating homomorphism tests. We show that this characterizes QBE/definability for CQs up to treewidth k, while reducing the complexity to EXPTIME. As a side result, we obtain that the complexity of the QBE/definability problems for CQs of treewidth k is EXPTIME-complete for each k > 1. The second relaxation is based on the idea of "desynchronizing" direct products, which characterizes QBE/definability for unions of CQs and reduces the complexity to coNP. The combination of these two relaxations yields tractability for QBE and characterizes it in terms of unions of CQs of treewidth at most k. We also study the complexity of these problems for conjunctive regular path queries over graph databases, showing them to be no more difficult than for CQs
Fixed-complexity quantum-assisted multi-user detection for CDMA and SDMA
In a system supporting numerous users the complexity of the optimal Maximum Likelihood Multi-User Detector (ML MUD) becomes excessive. Based on the superimposed constellations of K users, the ML MUD outputs the specific multilevel K-user symbol that minimizes the Euclidean distance with respect to the faded and noise-contaminated received multi-level symbol. Explicitly, the Euclidean distance is considered as the Cost Function (CF). In a system supporting K users employing M-ary modulation, the ML MUD uses MK CF evaluations (CFE) per time slot. In this contribution we propose an Early Stopping-aided Durr-HĂžyer algorithm-based Quantum-assisted MUD (ES-DHA QMUD) based on two techniques for achieving optimal ML detection at a low complexity. Our solution is also capable of flexibly adjusting the QMUD's performance and complexity trade-off, depending on the computing power available at the base station. We conclude by proposing a general design methodology for the ES-DHA QMUD in the context of both CDMA and SDMA systems
Evaluating Datalog via Tree Automata and Cycluits
We investigate parameterizations of both database instances and queries that
make query evaluation fixed-parameter tractable in combined complexity. We show
that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog)
enjoys bilinear-time evaluation on structures of bounded treewidth for programs
of bounded rule size. Such programs capture in particular conjunctive queries
with simplicial decompositions of bounded width, guarded negation fragment
queries of bounded CQ-rank, or two-way regular path queries. Our result is
shown by translating to alternating two-way automata, whose semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
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