We present a symbolic analysis technique for Lotos programs with integer variables on which only linear expressions are allowed. The technique is applicable to models generated by the Lotos compiler of the CCsar-Ald ebaran toolbox which are Petri nets extended with guarded commands. It allows to compute a predicate on variables characterizing the set of the reachable states or an upper approxim...

We give a new characterization of primitive permutation groups tied to the notion completely reachable automata. Also, we introduce sync-maximal state complexity set synchronizing words certain associated automata and show that they are contained between 2-homogeneous groups. Lastly, define k-reachable in analogy with motivated by our But results group degree n \(6 \le k - 6\) is either alterna...

This paper introduces a method for approximate reachability, for linear discrete time systems, based on homothety and set invariance. The proposed method utilizes two particular families of sets, more precisely their members, and particular forms of the approximation maps to obtain simple inner and outer approximate reachable sets/tubes. The resulting set–dynamics, induced by the uncertainty se...

The problem of estimating reachable sets of nonlinear dynamical control systems with quadratic nonlinearity and with uncertainty in initial states is studied. We assume that the uncertainty is of a set-membership kind when we know only the bounding set for unknown items and any additional statistical information on their behavior is not available. We present approaches that allow finding ellips...

This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states, the algorithm employs a linear matrix inequality approach to compute both upper and lower bounds on reachable regions. Rather than performing computations in the state-space, this method uses...

This contribution treats the estimation of reachable states for time invariant hybrid systems. Using the framework provided by Willems’ behavioural systems theory, we suggest a method based on l-complete approximations, which can be realized by finite state machines. The approximating behaviour is a superset of the original behaviour. Hence, the estimate of reachable states based on an l-comple...

In this paper we propose an algorithm for approximating the reachable sets of systems defined by polynomial differential equations. Such systems can be used to model a variety of physical phenomena. We first derive an integration scheme that approximates the state reachable in one time step by applying some polynomial map to the current state. In order to use this scheme to compute all the stat...

Term Rewriting Systems are now commonly used as a modeling language for programs or systems. On those rewriting based models, reachability analysis, i.e. proving or disproving that a given term is reachable from a set of input terms, provides an efficient verification technique. For disproving reachability (i.e. proving non reachability of a term) on non terminating and non confluent rewriting ...

Term rewriting systems are now commonly used as a modeling language for programs or systems. On those rewriting based models, reachability analysis, i.e. proving or disproving that a given term is reachable from a set of input terms, provides an efficient verification technique. For disproving reachability (i.e. proving non reachability of a term) on non terminating and non confluent rewriting ...

This contribution treats the estimation of reachable states for time invariant hybrid systems. Using the framework provided by Willems’ behavioural systems theory, we suggest a method based on -complete approximations, which can be realized by finite state machines. The approximating behaviour is a superset of the original behaviour. Hence, the estimate of reachable states based on an -complete...