Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

Narrow Band Halpha Photometry of the Super-Earth GJ 1214b with GTC/OSIRIS Tunable Filters

The super-earth planet GJ 1214b has recently been the focus of several studies, using the transit spectroscopy technique, trying to determine the nature of its atmosphere. Here we focus on the Halpha line as a tool to further restrict the nature of GJ1214's atmosphere. We used the Gran Telescopio Canarias (GTC) OSIRIS instrument to acquire narrow band photometry with tunable filters. With our observations, we were able to observe the primary transit of the super-Earth GJ 1214b in three bandpasses: two centered in the continuum around Halpha (653.5 nm and 662.0 nm) and one centered at the line core (656.3 nm). We measure the depth of the planetary transit at each wavelength interval.By fitting analytic models to the measured light curves we were able to compute the depth of the transit at the three bandpasses. Taking the difference in the computed planet to star radius ratio between the line and the comparison continuum filters, we find Delta (Rp/Rstar)_{Halpha-653.5} = (6.60 +/- 3.54) 10^-3 and Delta (Rp/Rstar)_{Halpha-662.0} = (3.30 +/- 3.61) 10^-3. Although the planet radius is found to be larger in the Halpha line than in the surrounding continuum, the quality of our observations and the sigma level of the differences (1.8 and 1.0, respectively) does not allow us to claim an Halpha excess in GJ1214's atmosphere. Further observations will be needed to resolve this issue.Comment: Accepted for publication in A&A, language and typos correcte

WASP-4b Arrived Early for the TESS Mission

The Transiting Exoplanet Survey Satellite (TESS) recently observed 18 transits of the hot Jupiter WASP-4b. The sequence of transits occurred 81.6 $\pm$ 11.7 seconds earlier than had been predicted, based on data stretching back to 2007. This is unlikely to be the result of a clock error, because TESS observations of other hot Jupiters (WASP-6b, 18b, and 46b) are compatible with a constant period, ruling out an 81.6-second offset at the 6.4$\sigma$ level. The 1.3-day orbital period of WASP-4b appears to be decreasing at a rate of $\dot{P} = -12.6 \pm 1.2$ milliseconds per year. The apparent period change might be caused by tidal orbital decay or apsidal precession, although both interpretations have shortcomings. The gravitational influence of a third body is another possibility, though at present there is minimal evidence for such a body. Further observations are needed to confirm and understand the timing variation.Comment: AJ accepte

KELT-12b: A P ~ 5 day, Highly Inflated Hot Jupiter Transiting A Mildly Evolved Hot Star

We announce the discovery of KELT-12b, a highly inflated Jupiter-mass planet transiting the mildly evolved, V = 10.64 host star TYC 2619-1057-1. We followed up the initial transit signal in the KELT-North survey data with precise ground-based photometry, high-resolution spectroscopy, precise radial velocity measurements, and high-resolution adaptive optics imaging. Our preferred best-fit model indicates that the host star has = 6279 ± 51 K, = 3.89 ± 0.05,[Fe/H] = , = , and = 2.37 ± 0.17 . The planetary companion has = 0.95 ± 0.14 , = , = , and density = g cm −3 , making it one of the most inflated giant planets known. Furthermore, for future follow-up, we report a high-precision time of inferior conjunction in of 2,457,083.660459 ± 0.000894 and period of days. Despite the relatively large separation of ∼0.07 au implied by its ∼5.03-day orbital period, KELT-12b receives significant flux of erg s −1 cm −2 from its host. We compare the radii and insolations of transiting gas giant planets around hot ( K) and cool stars, noting that the observed paucity of known transiting giants around hot stars with low insolation is likely due to selection effects. We underscore the significance of long-term ground-based monitoring of hot stars and space-based targeting of hot stars with the Transiting Exoplanet Survey Satellite to search for inflated gas giants in longer-period orbits

KELT-20b: A Giant Planet With A Period Of P ~ 3.5 Days Transiting The V ~ 7.6 Early A Star HD 185603

We report the discovery of KELT-20b, a hot Jupiter transiting a early A star, HD 185603, with an orbital period of days. Archival and follow-up photometry, Gaia parallax, radial velocities, Doppler tomography, and AO imaging were used to confirm the planetary nature of KELT-20b and characterize the system. From global modeling we infer that KELT-20 is a rapidly rotating ( ) A2V star with an effective temperature of K, mass of , radius of , surface gravity of , and age of . The planetary companion has a radius of , a semimajor axis of au, and a linear ephemeris of . We place a upper limit of on the mass of the planet. Doppler tomographic measurements indicate that the planetary orbit normal is well aligned with the projected spin axis of the star ( ). The inclination of the star is constrained to , implying a three-dimensional spin–orbit alignment of . KELT-20b receives an insolation flux of , implying an equilibrium temperature of of ∼2250 K, assuming zero albedo and complete heat redistribution. Due to the high stellar , KELT-20b also receives an ultraviolet (wavelength nm) insolation flux of , possibly indicating significant atmospheric ablation. Together with WASP-33, Kepler-13 A, HAT-P-57, KELT-17, and KELT-9, KELT-20 is the sixth A star host of a transiting giant planet, and the third-brightest host (in V ) of a transiting planet

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

A Giant Planet Undergoing Extreme-Ultraviolet Irradiation By Its Hot Massive-Star Host

The amount of ultraviolet irradiation and ablation experienced by a planet depends strongly on the temperature of its host star. Of the thousands of extrasolar planets now known, only six have been found that transit hot, A-type stars (with temperatures of 7,300–10,000 kelvin), and no planets are known to transit the even hotter B-type stars. For example, WASP-33 is an A-type star with a temperature of about 7,430 kelvin, which hosts the hottest known transiting planet, WASP-33b (ref. 1); the planet is itself as hot as a red dwarf star of type M (ref. 2). WASP-33b displays a large heat differential between its dayside and nightside2, and is highly inflated–traits that have been linked to high insolation3,4. However, even at the temperature of its dayside, its atmosphere probably resembles the molecule-dominated atmospheres of other planets and, given the level of ultraviolet irradiation it experiences, its atmosphere is unlikely to be substantially ablated over the lifetime of its star. Here we report observations of the bright star HD 195689 (also known as KELT-9), which reveal a close-in (orbital period of about 1.48 days) transiting giant planet, KELT-9b. At approximately 10,170 kelvin, the host star is at the dividing line between stars of type A and B, and we measure the dayside temperature of KELT-9b to be about 4,600 kelvin. This is as hot as stars of stellar type K4 (ref. 5). The molecules in K stars are entirely dissociated, and so the primary sources of opacity in the dayside atmosphere of KELT-9b are probably atomic metals. Furthermore, KELT-9b receives 700 times more extreme-ultraviolet radiation (that is, with wavelengths shorter than 91.2 nanometres) than WASP-33b, leading to a predicted range of mass-loss rates that could leave the planet largely stripped of its envelope during the main-sequence lifetime of the host star (ref. 6)

KELT-18b: Puffy Planet, Hot Host, Probably Perturbed

We report the discovery of KELT-18b, a transiting hot Jupiter in a 2.87-day orbit around the bright ( V = 10.1), hot, F4V star BD+60 1538 (TYC 3865-1173-1). We present follow-up photometry, spectroscopy, and adaptive optics imaging that allow a detailed characterization of the system. Our preferred model fits yield a host stellar temperature of K and a mass of , situating it as one of only a handful of known transiting planets with hosts that are as hot, massive, and bright. The planet has a mass of , a radius of , and a density of , making it one of the most inflated planets known around a hot star. We argue that KELT-18b’s high temperature and low surface gravity, which yield an estimated ∼600 km atmospheric scale height, combined with its hot, bright host, make it an excellent candidate for observations aimed at atmospheric characterization. We also present evidence for a bound stellar companion at a projected separation of ∼1100 au, and speculate that it may have contributed to the strong misalignment we suspect between KELT-18\u27s spin axis and its planet’s orbital axis. The inferior conjunction time is 2457542.524998 ± 0.000416 (BJD TDB ) and the orbital period is 2.8717510 ± 0.0000029 days. We encourage Rossiter–McLaughlin measurements in the near future to confirm the suspected spin–orbit misalignment of this system

Learning Moore Machines from Input-Output Traces

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample

An Unusual Transmission Spectrum for the Sub-Saturn KELT-11b Suggestive of a Sub-Solar Water Abundance

We present an optical-to-infrared transmission spectrum of the inflated sub-Saturn KELT-11b measured with the Transiting Exoplanet Survey Satellite (TESS), the Hubble Space Telescope (HST) Wide Field Camera 3 G141 spectroscopic grism, and the Spitzer Space Telescope (Spitzer) at 3.6 $\mu$m, in addition to a Spitzer 4.5 $\mu$m secondary eclipse. The precise HST transmission spectrum notably reveals a low-amplitude water feature with an unusual shape. Based on free retrieval analyses with varying molecular abundances, we find strong evidence for water absorption. Depending on model assumptions, we also find tentative evidence for other absorbers (HCN, TiO, and AlO). The retrieved water abundance is generally $\lesssim 0.1\times$ solar (0.001--0.7$\times$ solar over a range of model assumptions), several orders of magnitude lower than expected from planet formation models based on the solar system metallicity trend. We also consider chemical equilibrium and self-consistent 1D radiative-convective equilibrium model fits and find they too prefer low metallicities ($[M/H] \lesssim -2$, consistent with the free retrieval results). However, all the retrievals should be interpreted with some caution since they either require additional absorbers that are far out of chemical equilibrium to explain the shape of the spectrum or are simply poor fits to the data. Finally, we find the Spitzer secondary eclipse is indicative of full heat redistribution from KELT-11b's dayside to nightside, assuming a clear dayside. These potentially unusual results for KELT-11b's composition are suggestive of new challenges on the horizon for atmosphere and formation models in the face of increasingly precise measurements of exoplanet spectra.Comment: Accepted to The Astronomical Journal. 31 pages, 20 figures, 7 table