Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, counter values, run lengths). Some of these features can be checked in exponential space by using Rackoff’s proof or its variants, combined with Savitch’s Theorem. However, the question is still open for many others, e.g., regularity detection p...

Channel boundedness is a necessary condition for a message-passing system to exhibit regular, finite-state behaviour at the global level. For Message Sequence Graphs (MSGs), the most basic form of Highlevel Message Sequence Charts (HMSCs), channel boundedness can be characterized in terms of structural conditions on the underlying graph. We consider MSGs enriched with timing constraints between...

We study an extension of classical Petri nets where tokens carry values from a countable data domain, that can be tested for equality upon firing transitions. These Unordered Data Petri Nets (UDPN) are well-structured and therefore allow generic decision procedures for several verification problems including coverability and boundedness. We show how to construct a finite representation of the c...

Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using Rackoff’s proof or its variants, combined with Savitch’s theorem. However, the question is still open for many others, e.g., reversal-boundedness. In the paper, we ...

Since the theory of pseudo-differential operators was established in 1970’s, the L-boundedness of them with symbols in the Hörmander class S ρ,δ has been well investigated by many authors. Among them, Calderón-Vaillancourt [5] first treated the boundedness for the class S 0,0, which means that the boundedness of all the derivatives of symbols assures the L-boundedness of the corresponding opera...

Reachability and boundedness problems have been shown decidable for Vector Addition Systems with one zero-test. Surprisingly, place-boundedness remained open. We provide here a variation of the Karp-Miller algorithm to compute a basis of the downward closure of the reachability set which allows to decide place-boundedness. This forward algorithm is able to pass the zero-tests thanks to a finer ...

This paper completes the proof of the Lp-boundedness of bilinear operators associated to nonsmooth symbols or multipliers begun in Part I, our companion paper [8], by establishing the corresponding Lp-boundedness of time-frequency paraproducts associated with tiles in phase plane. The affine invariant structure of such operators in conjunction with the geometric properties of the associated pha...

We establish a weighted Lp boundedness of a parametric Marcinkiewicz integral operator ρ Ω,h if Ω is allowed to be in the block space B (0,−1/2) q (Sn−1) for some q > 1 and h satisfies a mild integrability condition. We apply this conclusion to obtain the weighted Lp boundedness for a class of the parametric Marcinkiewicz integral operators ∗,ρ Ω,h,λ and ρ Ω,h,S related to the Littlewood-Paley ...

The very classical structural boundedness and repetitiveness properties for discrete and untimed models are reconsidered for timed continuous Petri nets (TCPN), under infinite server semantics. The timing is here involved in the analysis, by taking advantage of its matricial characterization and properties analogous to conservativeness and consistency are defined. It is shown that such properti...

For the classical gradient method xt+1 = xt − γt∇f(xt) and several deterministic and stochastic variants, we discuss the issue of convergence of the gradient sequence ∇f(xt) and the attendant issue of stationarity of limit points of xt. We assume that ∇f is Lipschitz continuous, and that the stepsize γt diminishes to 0 and satisfies standard stochastic approximation conditions. We show that eit...