Given any diagonal cyclic subgroup $\Lambda \subset GL(n+1,k)$ of order $d$, let $I_d\subset k[x_0,\ldots, x_n]$ be the ideal generated by all monomials $\{m_{1},\ldots, m_{r}\}$ degree $d$ which are invariants $\Lambda$. $I_d$ is a monomial Togliatti system, provided $r \leq \binom{d+n-1}{n-1}$, and in this case projective toric variety $X_d$ parameterized $(m_{1},\ldots, m_{r})$ called $GT$-v...

Abstract We introduce a framework for the verification of protocols involving distinguished machine (referred to as leader) orchestrating operation an arbitrary number identical machines followers) in network. At core our is high-level formalism capturing these types together with their network interactions. show that this automatically translates tractable form first-order temporal logic. Chec...

In this paper, two Galerkin projection based reduced basis approaches are investigated for the reduced-order modeling of parameterized incompressible Navier-Stokes equations laminar transient flows. The first approach solves only momentum equation with additional, physics-based approximations dynamics pressure field. On other hand, second both and continuity equations. bases velocity fields gen...

Many aspects of computer systems are naturally modeled as parameterized systems which renders their automatic verification difficult. In wellknown examples such as cache coherence protocols and mutual exclusion protocols, the unbounded parameter is the number of concurrent processes which run the same distributed algorithm. In this paper, we introduce environment abstraction as a tool for the v...

We study Bayesian optimal control of a general class of smoothly parameterized Markov decision problems (MDPs). We propose a lazy version of the so-called posterior sampling method, a method that goes back to Thompson and Strens, more recently studied by Osband, Russo and van Roy. While Osband et al. derived a bound on the (Bayesian) regret of this method for undiscounted total cost episodic, f...

Parameterized systems verification is a long-standing problem, where the challenge is to verify that a property holds for all (infinite) instances of the parameterized system. Existing techniques aim to reduce this problem to checking the properties on smaller systems with a bound on the parameter referred to as the "cut-off " such that if the property holds for system instances of size cut-off...

Real-time systems often have to be able to cope with an unbounded number of components. For example, a real-time operating system scheduler manages arbitrarily many threads or a bus system copes with arbitrarily many connected devices. Such systems can be characterized as parameterized systems. The number of (homogeneous) components is the parameter of these systems. This makes their formal ver...

Ben Henda, N. 2008. Infinite-state Stochastic and Parameterized Systems. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology 76. 281 pp. Uppsala. ISBN 978-91-554-7228-3. A major current challenge consists in extending formal methods in order to handle infinite-state systems. Infiniteness stems from the fact that the system operates on unbounded data ...

We present CheAPS, the checker of asynchronous parameterized communicating systems. It is a set of tools for verification of parameterized families F = {Mn} of finite-state models against LTL specification φ. Each model Mn from a family F is composed of a fixed number of control processes and n processes from a fixed set of prototypes. Given a description of a family F CheAPS generates finite-s...