This paper proposes a new logic RoCTL* to model robustness in concurrent systems. RoCTL* extends CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure respectively. We pres
ent a number of examples of problems to which RoCTL* can be applied. The core result of this paper is to show that RoCTL* is expressively equivalent to CTL* but is non-elementarily more succinct. We present a translation from RoCTL* into CTL* that preserves truth but may result in non-elementary growth in the length of the translated formula as each nested Robustly operator may result in an extra exponential blowup. However, we show that this translation is optimal in the sense that any equivalence preserving translation will require an extra exponential growth per nested Robustly. We also compare RoCTL* to Quantified CTL* (QCTL*) and hybrid logics.
We present new high spatial resolution (<~ 0.1) 1-5 micron adaptive optics images, interferometric 1.3 mm continuum and 12CO 2-1 maps, and 350 micron, 2.8 and 3.3 mm fluxes measurements of the HV Tau system. Our adaptive optics images reveal an unusu
ally slow orbital motion within the tight HV Tau AB pair that suggests a highly eccentric orbit and/or a large deprojected physical separation. Scattered light images of the HV Tau C edge-on protoplanetary disk suggest that the anisotropy of the dust scattering phase function is almost independent of wavelength from 0.8 to 5 micron, whereas the dust opacity decreases significantly over the same range. The images further reveal a marked lateral asymmetry in the disk that does not vary over a timescale of 2 years. We further detect a radial velocity gradient in the disk in our 12CO map that lies along the same position angle as the elongation of the continuum emission, which is consistent with Keplerian rotation around an 0.5-1 Msun central star, suggesting that it could be the most massive component in the triple system. We use a powerful radiative transfer model to compute synthetic disk observations and use a Bayesian inference method to extract constraints on the disk properties. Each individual image, as well as the spectral energy distribution, of HV Tau C can be well reproduced by our models with fully mixed dust provided grain growth has already produced larger-than-interstellar dust grains. However, no single model can satisfactorily simultaneously account for all observations. We suggest that future attempts to model this source include more complex dust properties and possibly vertical stratification. (Abridged)
