Strictly Positive Definite Kernels on a Product of Spheres II

We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286-301, arXiv:1505.03695]

Capillary rising damp in Venetian context : state of the art and numerical simulation

The fragility of Venice and its buildings are linked to the floods, observed since ancient times and emphasized in recent years: the periodic sea level rise, accompanied by rising damp, are the main causes of the alteration. In particular, the rising damp causes a series of complex diseases in the historic buildings, such as physical decay, chemical or biological, with loss of aesthetic and economic value. In addition, greater heat dispersion and reduced thermal comfort can also occur in interior spaces, with consequent risks for human health. This is a sign of “Sick Building Syndrome”. It is very important to develop models for assessing the vulnerability of assets and to manage sustainable plans related to maintenance processes and activities, satisfying the requirements of effectiveness and compatibility.Basing on numerical models performed with the WUFI 2D software, the paper analyses the different behavior of rising damp in relation to materials or masonry structures. In particular, the construction techniques and typical materials used in Venetian buildings were investigated, such as clay brick walls, lime plaster, Marmorino and Cocciopesto, adopted mainly to limit the capillary rise also caused by the phenomenon of “acqua alta”

THE ADDITION OF TEMPORAL NEIGHBORHOOD MAKES THE LOGIC OF PREFIXES AND SUB-INTERVALS EXPSPACE-COMPLETE

A classic result by Stockmeyer [Sto74] gives a non-elementary lower bound to the emptiness problem for generalized ∗-free regular expressions. This result is intimately connected to the satisfiability problem for the interval temporal logic of the chop modality under the homogeneity assumption [HMM83]. The chop modality can indeed be viewed as the inverse of the concatenation operator of regular languages, and such a correspondence enables reductions between the two problems. In this paper, we study the complexity of the satisfiability problem for suitable weakenings of the chop interval temporal logic, that can be equivalently viewed as fragments of Halpern and Shoham interval logic. We first introduce the logic BDhom featuring modalities B (for begins), corresponding to the prefix relation on pairs of intervals, and D (for during), corresponding to the infix relation, whose satisfiability problem, under the homogeneity assumption, has been recently shown to be PSpace-complete [BMPS21b]. The homogeneous models of BDhom naturally correspond to languages defined by restricted forms of generalized *-free regular expressions, that feature operators for union, complementation, and the inverses of the prefix and infix relations. Then, we study the extension of BDhom with the temporal neighborhood modality A, corresponding to the Allen relation Meets, and prove that such an addition increases both the expressiveness and the complexity of the logic. In particular, we show that the resulting logic BDAhom is ExpSpace-complete

The addition of temporal neighborhood makes the logic of prefixes and sub-intervals EXPSPACE-complete

A classic result by Stockmeyer gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably for formulas that make use of the so-called chop operator. Such an operator can indeed be interpreted as the inverse of the concatenation operation on regular languages, and this correspondence enables reductions between non-emptiness of star-free generalized regular expressions and satisfiability of formulas of the interval temporal logic of chop under the homogeneity assumption. In this paper, we study the complexity of the satisfiability problem for suitable weakenings of the chop interval temporal logic, that can be equivalently viewed as fragments of Halpern and Shoham interval logic. We first consider the logic $\mathsf{BD}_{hom}$ featuring modalities $B$, for \emph{begins}, corresponding to the prefix relation on pairs of intervals, and $D$, for \emph{during}, corresponding to the infix relation. The homogeneous models of $\mathsf{BD}_{hom}$ naturally correspond to languages defined by restricted forms of regular expressions, that use union, complementation, and the inverses of the prefix and infix relations. Such a fragment has been recently shown to be PSPACE-complete . In this paper, we study the extension $\mathsf{BD}_{hom}$ with the temporal neighborhood modality $A$ (corresponding to the Allen relation \emph{Meets}), and prove that it increases both its expressiveness and complexity. In particular, we show that the resulting logic $\mathsf{BDA}_{hom}$ is EXPSPACE-complete.Comment: arXiv admin note: substantial text overlap with arXiv:2109.0832

PSPACE-completeness of the temporal logic of sub-intervals and suffixes

In this paper, we prove PSPACE-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality 〈E〉, for the “suffix” relation on pairs of intervals, and modality 〈D〉, for the “sub-interval” relation, under the homogeneity assumption. The result significantly improves the EXPSPACE upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (〈E〉) or, symmetrically, the modality for prefixes (〈B〉) to the logic of sub-intervals (featuring only 〈D〉)

On a temporal logic of prefixes and infixes

A classic result by Stockmeyer [16] gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably for formulas that make use of the so-called chop operator. Such an operator can indeed be interpreted as the inverse of the concatenation operation on regular languages, and this correspondence enables reductions between non-emptiness of star-free generalized regular expressions and satisfiability of formulas of the interval temporal logic of the chop operator under the homogeneity assumption [5]. In this paper, we study the complexity of the satisfiability problem for a suitable weakening of the chop interval temporal logic, that can be equivalently viewed as a fragment of Halpern and Shoham interval logic featuring the operators B, for \u201cbegins\u201d, corresponding to the prefix relation on pairs of intervals, and D, for \u201cduring\u201d, corresponding to the infix relation. The homogeneous models of the considered logic naturally correspond to languages defined by restricted forms of regular expressions, that use union, complementation, and the inverses of the prefix and infix relations