We show the interconvertibility of context-free-language reachability problems and a class of set-constraint problems: given a context-free-language reachability problem, we show how to construct a set-constraint problem whose answer gives a solution to the reachability problem; given a set-constraint problem, we show how to construct a context-free-language reachability problem whose answer gi...

Petri Nets are a system description and analysis tool. Reachability is one of the most basic properties in Petri Net research. In a sense, reachability research is the foundation study for other dynamic properties of Petri Nets through which many problems involving Petri Nets can be described. Nowadays, there are two mature analysis methods–the matrix equation and the reachability tree. However...

A Self modifying code is that modifies its own instructions during execution time. It nowadays widely used, especially in malware to make the hard analyse and detect by anti-viruses. Thus, analysis of such self programs a big challenge. Pushdown systems (PDSs) natural model extensively used for sequential because they allow accurately procedure calls mimic program’s stack. In this work, we prop...

Saturation is considered the state-of-the-art method for computing fixpoints with decision diagrams. We present a relatively simple diagram operation called REACH that also computes fixpoints. In contrast to saturation, it does not require partitioning of transition relation. give sequential algorithms implementing new both binary and multi-valued diagrams, moreover provide parallel counterpart...

This work studies the reachable space of infinite dimensional control systems which are null controllable in any positive time, typical example being heat equation controlled from boundary or an arbitrary open set. The focus is on robustness with respect to linear nonlinear perturbations generator. More precisely, our first main result asserts that this invariant under small (in appropriate sen...

We address the problem of verifying reachability in programs running under formal model Px86 defined recently by Raad et al. POPL'20 for persistent Intel x86 architecture. prove that this is decidable. To achieve that, we provide a new equivalent to and has feature being well structured system. Deriving result deep investigation properties interplay its components.

Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems’ safety properties. In particular, this work focuses on estimating the forward reachable set of neural feedback loops (closed-loop systems with NN controllers). Recent provides bounds these sets, computationally tractable appr...

The theory of Well Structured Transition Systems, (WSTS) allows the automatical verification of safety properties of infinite-state systems, such that parts of reachability sets can be finitely represented [7, 11, 10]. Termination, boundedness and coverability are decidable for WSTS [4, 5, 9]. As Petri nets are WSTS, the previous properties are decidable. For complete WSTS [10], the Karp and Mi...