Conformant Planning via Symbolic Model Checking

We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation of the search space based on Binary Decision Diagrams (BDDs), which is the basis for search techniques derived from symbolic model checking. The symbolic representation makes it possible to analyze potentially large sets of states and transitions in a single computation step, thus providing for an efficient implementation. Third, we present CMBP (Conformant Model Based Planner), an efficient implementation of the data structures and algorithm described above, directly based on BDD manipulations, which allows for a compact representation of the search layers and an efficient implementation of the search steps. Finally, we present an experimental comparison of our approach with the state-of-the-art conformant planners CGP, QBFPLAN and GPT. Our analysis includes all the planning problems from the distribution packages of these systems, plus other problems defined to stress a number of specific factors. Our approach appears to be the most effective: CMBP is strictly more expressive than QBFPLAN and CGP and, in all the problems where a comparison is possible, CMBP outperforms its competitors, sometimes by orders of magnitude

Formal Design of Asynchronous Fault Detection and Identification Components using Temporal Epistemic Logic

Autonomous critical systems, such as satellites and space rovers, must be able to detect the occurrence of faults in order to ensure correct operation. This task is carried out by Fault Detection and Identification (FDI) components, that are embedded in those systems and are in charge of detecting faults in an automated and timely manner by reading data from sensors and triggering predefined alarms. The design of effective FDI components is an extremely hard problem, also due to the lack of a complete theoretical foundation, and of precise specification and validation techniques. In this paper, we present the first formal approach to the design of FDI components for discrete event systems, both in a synchronous and asynchronous setting. We propose a logical language for the specification of FDI requirements that accounts for a wide class of practical cases, and includes novel aspects such as maximality and trace-diagnosability. The language is equipped with a clear semantics based on temporal epistemic logic, and is proved to enjoy suitable properties. We discuss how to validate the requirements and how to verify that a given FDI component satisfies them. We propose an algorithm for the synthesis of correct-by-construction FDI components, and report on the applicability of the design approach on an industrial case-study coming from aerospace.Comment: 33 pages, 20 figure

On the robustness of the Hβ\beta Lick index as a cosmic clock in passive early-type galaxies

We examine the H$\beta$ Lick index in a sample of $\sim 24000$ massive ($\rm log(M/M_{\odot})>10.75$) and passive early-type galaxies extracted from SDSS at z<0.3, in order to assess the reliability of this index to constrain the epoch of formation and age evolution of these systems. We further investigate the possibility of exploiting this index as "cosmic chronometer", i.e. to derive the Hubble parameter from its differential evolution with redshift, hence constraining cosmological models independently of other probes. We find that the H$\beta$ strength increases with redshift as expected in passive evolution models, and shows at each redshift weaker values in more massive galaxies. However, a detailed comparison of the observed index with the predictions of stellar population synthesis models highlights a significant tension, with the observed index being systematically lower than expected. By analyzing the stacked spectra, we find a weak [NII]$\lambda6584$ emission line (not detectable in the single spectra) which anti-correlates with the mass, that can be interpreted as a hint of the presence of ionized gas. We estimated the correction of the H$\beta$ index by the residual emission component exploiting different approaches, but find it very uncertain and model-dependent. We conclude that, while the qualitative trends of the observed H$\beta$-z relations are consistent with the expected passive and downsizing scenario, the possible presence of ionized gas even in the most massive and passive galaxies prevents to use this index for a quantitative estimate of the age evolution and for cosmological applications.Comment: 20 pages, 11 figures, 1 table. Accepted for publication in MNRAS Main Journa

An improved measurement of baryon acoustic oscillations from the correlation function of galaxy clusters at z∼0.3z \sim 0.3

We detect the peak of baryon acoustic oscillations (BAO) in the two-point correlation function of a spectroscopic sample of $25226$ clusters selected from the Sloan Digital Sky Survey. Galaxy clusters, as tracers of massive dark matter haloes, are highly biased structures. The linear bias $b$ of the sample considered in this work, that we estimate from the projected correlation function, is $b \sigma_8 = 1.72 \pm 0.03$. Thanks to the high signal in the cluster correlation function and to the accurate spectroscopic redshift measurements, we can clearly detect the BAO peak and determine its position, $s_p$, with high accuracy, despite the relative paucity of the sample. Our measurement, $s_p = 104 \pm 7 \, \mathrm{Mpc} \, h^{-1}$, is in good agreement with previous estimates from large galaxy surveys, and has a similar uncertainty. The BAO measurement presented in this work thus provides a new strong confirmation of the concordance cosmological model and demonstrates the power and promise of galaxy clusters as key probes for cosmological applications based on large scale structures.Comment: 10 pages, 7 figure, accepted for publication in MNRA

Listening to galaxies tuning at z ~ 2.5 - 3.0: The first strikes of the Hubble fork

We investigate the morphological properties of 494 galaxies selected from the GMASS survey at z>1, primarily in their optical rest frame, using HST images, from the CANDELS survey. We propose that the Hubble sequence of galaxy morphologies takes shape at redshift 2.5<z<3. The fractions of both ellipticals and disks decrease with increasing lookback time at z>1, such that at redshifts z=2.5-2.7 and above, the Hubble types cannot be identified, and most galaxies are classified as irregular. The quantitative morphological analysis shows that, at 1<z<3, morphological parameters are not as effective in distinguishing the different morphological Hubble types as they are at low redshift. No significant morphological k-correction was found to be required for the Hubble type classification, with some exceptions. In general, different morphological types occupy the two peaks of the rest-frame (U-B) colour bimodality of galaxies: most irregulars occupy the blue peak, while ellipticals are mainly found in the red peak, though with some level of contamination. Disks are more evenly distributed than either irregulars and ellipticals. We find that the position of a galaxy in a UVJ diagram is related to its morphological type: the "quiescent" region of the plot is mainly occupied by ellipticals and, to a lesser extent, by disks. We find that only ~33% of all morphological ellipticals in our sample are red and passively evolving galaxies. Blue galaxies morphologically classified as ellipticals show a remarkable structural similarity to red ones. Almost all irregulars have a star-forming galaxy spectrum. In addition, the majority of disks show some sign of star-formation activity in their spectra, though in some cases their red continuum is indicative of old stellar populations. Finally, an elliptical morphology may be associated with either passively evolving or strongly star-forming galaxies.Comment: 27 pages, 16 figures, 5 tables. "Morphological atlas" in the appendix. Revised version accepted for publication in A&

The surface density of Extremely Red Objects in high-z quasar fields

We report on a study of the surface density of Extremely Red Objects (EROs) in the fields of 13 radio-loud quasars at 1.8 < z < 3.0 covering a total area of 61.7 sqr arcmin. There is a large variation in the ERO surface density from field to field, and as many as 30--40 % of the fields have roughly 4--5 times more EROs than what is expected from a random distribution. The average surface density exceeds the value found in large random-field surveys by a factor of 2--3, a result which is significant at the >3 sigma level. Hence, it appears that the quasar lines of sight are biassed towards regions of high ERO density. This might be caused by clusters or groups of galaxies physically associated with the quasars. However, an equally likely possibility is that the observed ERO excess is part of overdensities in the ERO population along the line of sight to the quasars. In this case, the non-randomness of quasar fields with respect to EROs may be explained in terms of gravitational lensing.Comment: 6 pages, 2 figures, to appear in "Radio galaxies: past, present and future", eds. M. Jarvis et al., Leiden, November 200

Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving

Unveiling the inner morphology and gas kinematics of NGC 5135 with ALMA

The local Seyfert 2 galaxy NGC5135, thanks to its almost face-on appearance, a bulge overdensity of stars, the presence of a large-scale bar, an AGN and a Supernova Remnant, is an excellent target to investigate the dynamics of inflows, outflows, star formation and AGN feedback. Here we present a reconstruction of the gas morphology and kinematics in the inner regions of this galaxy, based on the analysis of Atacama Large Millimeter Array (ALMA) archival data. To our purpose, we combine the available $\sim$100 pc resolution ALMA 1.3 and 0.45 mm observations of dust continuum emission, the spectroscopic maps of two transitions of the CO molecule (tracer of molecular mass in star forming and nuclear regions), and of the CS molecule (tracer of the dense star forming regions) with the outcome of the SED decomposition. By applying the $^{\rm 3D}$BAROLO software (3D-Based Analysis of Rotating Object via Line Observations), we have been able to fit the galaxy rotation curves reconstructing a 3D tilted-ring model of the disk. Most of the observed emitting features are described by our kinematic model. We also attempt an interpretation for the emission in few regions that the axisymmetric model fails to reproduce. The most relevant of these is a region at the northern edge of the inner bar, where multiple velocity components overlap, as a possible consequence of the expansion of a super-bubble.Comment: 15 pages, 13 figures, resubmitted to MNRAS after moderate revision

Software Model Checking via Large-Block Encoding

The construction and analysis of an abstract reachability tree (ART) are the basis for a successful method for software verification. The ART represents unwindings of the control-flow graph of the program. Traditionally, a transition of the ART represents a single block of the program, and therefore, we call this approach single-block encoding (SBE). SBE may result in a huge number of program paths to be explored, which constitutes a fundamental source of inefficiency. We propose a generalization of the approach, in which transitions of the ART represent larger portions of the program; we call this approach large-block encoding (LBE). LBE may reduce the number of paths to be explored up to exponentially. Within this framework, we also investigate symbolic representations: for representing abstract states, in addition to conjunctions as used in SBE, we investigate the use of arbitrary Boolean formulas; for computing abstract-successor states, in addition to Cartesian predicate abstraction as used in SBE, we investigate the use of Boolean predicate abstraction. The new encoding leverages the efficiency of state-of-the-art SMT solvers, which can symbolically compute abstract large-block successors. Our experiments on benchmark C programs show that the large-block encoding outperforms the single-block encoding.Comment: 13 pages (11 without cover), 4 figures, 5 table