Reachability Analysis of Time Basic Petri Nets: a Time Coverage Approach

We introduce a technique for reachability analysis of Time-Basic (TB) Petri nets, a powerful formalism for real- time systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are functions of marking's time description. The technique consists of building a symbolic reachability graph relying on a sort of time coverage, and overcomes the limitations of the only available analyzer for TB nets, based in turn on a time-bounded inspection of a (possibly infinite) reachability-tree. The graph construction algorithm has been automated by a tool-set, briefly described in the paper together with its main functionality and analysis capability. A running example is used throughout the paper to sketch the symbolic graph construction. A use case describing a small real system - that the running example is an excerpt from - has been employed to benchmark the technique and the tool-set. The main outcome of this test are also presented in the paper. Ongoing work, in the perspective of integrating with a model-checking engine, is shortly discussed.Comment: 8 pages, submitted to conference for publicatio

Approximation of the Helfrich's functional via Diffuse Interfaces

We give a rigorous proof of the approximability of the so-called Helfrich's functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the Gauss-rigidity

Why not in your Backyard? On the Location and Size of a Public Facility

In this paper, we tackle the issue of locating a public facility which provides a public good in a closed and populated territory. This facility generates differentiated benefits to neighborhoods depending on their distance from it. In the case of a Nimby facility, the smaller is the distance, the lower is the individual benefit. The opposite is true in the case of an anti-Nimby facility. We first characterize the optimal location which would be chosen by a social planner. Then we introduce a common-agency lobbying game, where agents attempt to influence the location and provision decisions by the government. Some interesting results arise in the case where only a subset of neighborhoods lobby. First, the solution of the lobbying game can replicate the optimal solution. Second, under-provision and over-provision of the public good may be obtained both in the Nimby and the anti-Nimby cases. The provision outcome depends on the presence of either a congestion effect or an agglomeration effect. Third, some non-lobbying neighborhoods may be better off than in the case where all neighborhoods lobby, which raises the possibility of free-riding at the lobbying stage.

Quasi-potentials of the entropy functionals for scalar conservation laws

We investigate the quasi-potential problem for the entropy cost functionals of non-entropic solutions to scalar conservation laws with smooth fluxes. We prove that the quasi-potentials coincide with the integral of a suitable Einstein entropy.Comment: 26 pages, 4 figure