32 research outputs found
The Complexity of Finding Reset Words in Finite Automata
We study several problems related to finding reset words in deterministic
finite automata. In particular, we establish that the problem of deciding
whether a shortest reset word has length k is complete for the complexity class
DP. This result answers a question posed by Volkov. For the search problems of
finding a shortest reset word and the length of a shortest reset word, we
establish membership in the complexity classes FP^NP and FP^NP[log],
respectively. Moreover, we show that both these problems are hard for
FP^NP[log]. Finally, we observe that computing a reset word of a given length
is FNP-complete.Comment: 16 pages, revised versio
The Complexity of Reasoning for Fragments of Default Logic
Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified
the complexity of the extension existence problem for propositional default
logic as \SigmaPtwo-complete, and the complexity of the credulous and
skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete.
Additionally, he investigated restrictions on the default rules, i.e.,
semi-normal default rules. Selman made in 1992 a similar approach with
disjunction-free and unary default rules. In this paper we systematically
restrict the set of allowed propositional connectives. We give a complete
complexity classification for all sets of Boolean functions in the meaning of
Post's lattice for all three common decision problems for propositional default
logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-,
P-, NL-complete, trivial) for the extension existence problem, while for the
credulous and skeptical reasoning problem we obtain similar classifications
without trivial cases.Comment: Corrected versio
A common algebraic description for probabilistic and quantum computations
AbstractThrough the study of gate arrays we develop a unified framework to deal with probabilistic and quantum computations, where the former is shown to be a natural special case of the latter. On this basis we show how to encode a probabilistic or quantum gate array into a sum-free tensor formula which satisfies the conditions of the partial trace problem, and vice-versa; that is, given a tensor formula F of order n×1 over a semiring S plus a positive integer k, deciding whether the kth partial trace of the matrix valSn,n(F·FT) fulfills a certain property. We use this to show that a certain promise version of the sum-free partial trace problem is complete for the class pr- BPP (promise BPP) for formulas over the semiring (Q+,+,·) of the positive rational numbers, for pr-BQP (promise BQP) in the case of formulas defined over the field (Q+,+,·), and if the promise is given up, then completeness for PP is shown, regardless whether tensor formulas over positive rationals or rationals in general are used. This suggests that the difference between probabilistic and quantum polytime computers may ultimately lie in the possibility, in the latter case, of having destructive interference between computations occurring in parallel. Moreover, by considering variants of this problem, classes like ⊕P, NP, C=P, its complement co-C=P, the promise version of Valiant's class UP, its generalization promise SPP, and unique polytime US can be characterized by carrying the problem properties and the underlying semiring
Kondo effect in coupled quantum dots: a Non-crossing approximation study
The out-of-equilibrium transport properties of a double quantum dot system in
the Kondo regime are studied theoretically by means of a two-impurity Anderson
Hamiltonian with inter-impurity hopping. The Hamiltonian, formulated in
slave-boson language, is solved by means of a generalization of the
non-crossing approximation (NCA) to the present problem. We provide benchmark
calculations of the predictions of the NCA for the linear and nonlinear
transport properties of coupled quantum dots in the Kondo regime. We give a
series of predictions that can be observed experimentally in linear and
nonlinear transport measurements through coupled quantum dots. Importantly, it
is demonstrated that measurements of the differential conductance , for the appropriate values of voltages and inter-dot tunneling
couplings, can give a direct observation of the coherent superposition between
the many-body Kondo states of each dot. This coherence can be also detected in
the linear transport through the system: the curve linear conductance vs
temperature is non-monotonic, with a maximum at a temperature
characterizing quantum coherence between both Kondo states.Comment: 20 pages, 17 figure
The intersection of aging biology and the pathobiology of lung diseases: A joint NHLBI/NIA Workshop.
Death from chronic lung disease is increasing and Chronic Obstructive Pulmonary Disease has become the third leading cause of death in the United States in the past decade. Both chronic and acute lung diseases disproportionately affect elderly individuals, making it likely that these diseases will become more frequent and severe as the worldwide population ages. Chronic lung diseases are associated with substantial morbidity, frequently resulting in exercise limiting dyspnea, immobilization and isolation. Therefore, effective strategies to prevent or treat lung disease are likely to increase healthspan as well as lifespan. This review summarizes the findings of a joint workshop sponsored by the NIA and NHLBI that brought together investigators focused on aging and lung biology. These investigators encouraged the use of genetic systems and aged animals in the study of lung disease and the development of integrative systems-based platforms that can dynamically incorporate datasets that describe the genomics, transcriptomics, epigenomics, metabolomics and proteomics of the aging lung in health and disease. Further research was recommended to integrate benchmark biological hallmarks of aging in the lung with the pathobiology of acute and chronic lung diseases with divergent pathologies for which advanced age is the most important risk factor