We study games with reachability objectives under energy constraints. first prove that strict constraints (either only lower-bound constraint or interval constraint), those are LOGSPACE -equivalent to the same but without objective (i.e., for infinite runs). then consider two relaxations of upper-bound (while keeping strict): in one, called weak upper bound , is absorbing i.e., when reached, ex...

Safety is a critical concern for the next generation of autonomy that likely to rely heavily on deep neural networks perception and control. This paper proposes method repair unsafe ReLU DNNs in safety-critical systems using reachability analysis. Our uses analysis calculate reachable domain DNN, then novel loss function construct its distance safe during retraining process. Since subtle change...

Reachability analysis consists in computing the set of states that are reachable by a dynamical system from all initial and for admissible inputs parameters. It is fundamental problem motivated many applications formal verification, controller synthesis, estimation, to name only few. This article focuses on class methods guaranteed overapproximation continuous hybrid systems, relying predominan...

Timed pushdown automata (tpda) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations tpda expressible in linear arithmetic, generalising Presburger arithmetic and rational arithmetic. The main technical ingredients novel quantifier elimination result for clock constraints (used to simplify the syntax transitions), use diffe...

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those games, it is known that there always exists Nash equilibrium. But sometimes several equilibria may coexist. For instance we can have two equilibria: first where no player reaches his set and an other all the players reach their set. It thus very natural to identify ...

There are numerous applications that need to deal with a large graph, including bioinformatics, social science, link analysis, citation analysis, and collaborative networks. A fundamental query is to query whether a node is reachable from another node in a large graph, which is called a reachability query. In this survey, we discuss several existing approaches to process reachability queries. I...