This paper introduces reachability logic, a language-independent seven-rule proof system for deriving reachability properties of systems. The key ingredients of reachability logic are its sentences, which are called reachability rules and generalize the transitions of operational semantics and the Hoare triples of axiomatic semantics, and the Circularity proof rule, which generalizes invariant ...

Fortier et al. proposed several research problems on packing arborescences and settled some of them. Others were later solved by Matsuoka Tanigawa Gao Yang. The last open problem is in this article. We show how to turn an inductive idea used the latter two articles into a simple proof technique that allows relate previous results arborescence packings. prove strong version Edmonds’ theorem span...

Reachability analysis is the most general approach to the analysis of Petri nets. Due to the wellknown problem of state-space explosion, generation of the reachability set and reachability graph with the known approaches often becomes intractable even for moderately sized nets. This paper presents a new method to generate and represent the reachability set and reachability graph of large Petri ...

This paper is showing the solution for two open problems about decidability of vector reachability problem in a finitely generated semigroup of matrices from SL(2,Z) and the point to point reachability (over rational numbers) for fractional linear transformations, where associated matrices are form SL(2,Z). The approach of solving reachability problems is based on analysis of reachability paths...

It is well known that positive linear systems have differences in the concepts and characterizations of the structural properties of reachability and controllability. In this paper, the reachability indices of a positive system are defined and consequently they are studied. For that, a canonical form of the reachability indices is given by positive similarity. From that canonical form, it is es...

Undecidability of the reachability problem is ubiquitous in the context of hybrid automata. Being mostly based on either bounded reachability or on the notion of simulation preorder, current techniques for the approximated reachability analysis force to choose between underand over-approximations. In this paper, we introduce a novel method for the reachability analysis of hybrid automata featur...

Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such games is PSPACE-complete, although it is fixed-parameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory r...

Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such games is PSPACE-complete, although it is fixed-parameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory r...