Stability and Complexity of Minimising Probabilistic Automata

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with floating-point arithmetic. Our algorithm can also be used for "lossy" minimisation with bounded error. We show an application in image compression. In the second part of the paper we study the complexity of the minimisation problem for probabilistic automata. We prove that the problem is NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape

Brzozowski Algorithm Is Generically Super-Polynomial Deterministic Automata

International audienceWe study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than nd tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question

A Kleene theorem for polynomial coalgebras

For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras

HIV/AIDS among Inmates of and Releasees from US Correctional Facilities, 2006: Declining Share of Epidemic but Persistent Public Health Opportunity

Because certain groups at high risk for HIV/AIDS (human immunodeficiency virus/acquired immunodeficiency syndrome) come together in correctional facilities, seroprevalence was high early in the epidemic. The share of the HIV/AIDS epidemic borne by inmates of and persons released from jails and prisons in the United States (US) in 1997 was estimated in a previous paper. While the number of inmates and releasees has risen, their HIV seroprevalence rates have fallen. We sought to determine if the share of HIV/AIDS borne by inmates and releasees in the US decreased between 1997 and 2006. We created a new model of population flow in and out of correctional facilities to estimate the number of persons released in 1997 and 2006. In 1997, approximately one in five of all HIV-infected Americans was among the 7.3 million who left a correctional facility that year. Nine years later, only one in seven (14%) of infected Americans was among the 9.1 million leaving, a 29.3% decline in the share. For black and Hispanic males, two demographic groups with heightened incarceration rates, recently released inmates comprise roughly one in five of those groups' total HIV-infected persons, a figure similar to the proportion borne by the correctional population as a whole in 1997. Decreasing HIV seroprevalence among those admitted to jails and prisons, prolonged survival and aging of the US population with HIV/AIDS beyond the crime-prone years, and success with discharge planning programs targeting HIV-infected prisoners could explain the declining concentration of the epidemic among correctional populations. Meanwhile, the number of persons with HIV/AIDS leaving correctional facilities remains virtually identical. Jails and prisons continue to be potent targets for public health interventions. The fluid nature of incarcerated populations ensures that effective interventions will be felt not only in correctional facilities but also in communities to which releasees return

Position Automaton Construction for Regular Expressions with Intersection

Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible with intersection. The resulting automaton is homogeneous and has the partial derivative automaton as its quotient

Computational and Structural Evidence for Neurotransmitter-mediated Modulation of the Oligomeric States of Human Insulin in Storage Granules

Human insulin is a pivotal protein hormone controlling metabolism, growth and ageing, and whose malfunctioning underlies diabetes, some cancers and neuro-degeneration. Despite its central position in human physiology, the in vivo oligomeric state and conformation of insulin in its storage granules in the pancreas are not known. In contrast, many in vitro structures of hexamers of this hormone are available, which fall into three conformational states: T6, T3Rf3 and R6. As there is strong evidence for accumulation of neurotransmitters, such as serotonin and dopamine, in insulin storage granules in pancreatic β-cells, we probed by molecular dynamics (MD) and protein crystallography (PC) if these endogenous ligands affect and stabilize insulin oligomers. Parallel studies independently converged on the observation that serotonin binds well within the insulin hexamer (site I), stabilizing it in the T3R3 conformation. Both methods indicated serotonin binding on the hexamer surface (site III) as well. MD, but not PC, indicated that dopamine was also a good site III ligand. Some of the PC studies also included arginine, which may be abundant in insulin granules upon processing of pro-insulin, and stable T3R3 hexamers loaded with both serotonin and arginine were obtained. The MD and PC results were supported further by in solution spectroscopic studies with R-state specific chromophore. Our results indicate that the T3R3 oligomer is a plausible insulin pancreatic storage form, resulting from its complex interplay with neurotransmitters, and pro-insulin processing products. These findings may have implications for clinical insulin formulations

Lightweighting design optimisation for additively manufactured mirrors

Design for additive manufacture (AM; 3D printing) is significantly different than design for subtractive machining. Although there are some limitations on the designs that can be printed, the increase in the AM design-space removes some of the existing challenges faced by the traditional lightweight mirror designs; for example, sandwich mirrors are just as easy to fabricate as open-back mirrors via AM, and they provide an improvement in structural rigidity. However, the ability to print a sandwich mirror as a single component does come with extra considerations; such as orientation upon the build plate and access to remove any temporary support material. This paper describes the iterations in optimisation applied to the lightweighting of a small, 84 mm diameter by 20 mm height, spherical concave mirror intended for CubeSat applications. The initial design, which was fabricated, is discussed in terms of the internal lightweighting design and the design constraints that were imposed by printing and post-processing. Iterations on the initial design are presented; these include the use of topology optimisation to minimise the total internal strain energy during mirror polishing and the use of lattices combined with thickness variation i.e. having a thicker lattice in strategic support locations. To assess the suitability of each design, finite element analysis is presented to quantify the print-through of the lightweighting upon the optical surface for a given mass reduction

Opto-mechanical measurement of micro-trap via nonlinear cavity enhanced Raman scattering spectrum

High-gain resonant nonlinear Raman scattering on trapped cold atoms within a high-fineness ring optical cavity is simply explained under a nonlinear opto-mechanical mechanism, and a proposal using it to detect frequency of micro-trap on atom chip is presented. The enhancement of scattering spectrum is due to a coherent Raman conversion between two different cavity modes mediated by collective vibrations of atoms through nonlinear opto-mechanical couplings. The physical conditions of this technique are roughly estimated on Rubidium atoms, and a simple quantum analysis as well as a multi-body semiclassical simulation on this nonlinear Raman process is conducted.Comment: 7 pages, 2 figure