Related papers: A concise proof of Commoner's theorem
Van der Aalst's theorem is an important result for the analysis and synthesis of process models. The paper proves the theorem by exhausting perpetual free-choice Petri nets by CP-subnets. The resulting T-systems are investigated by…
The theory of free-choice Petri nets is an established field, initiated in the 1970s by Commoner and Hack at MIT. We revisit well-formed free-choice nets (those admitting markings that are both live and bounded) and provide a new…
Persistence is a strong, global, behavioural property of a Petri net, meaning that no activity can disable a different activity. Persistent permutability is a weaker property, pertaining to individual interleavings of a Petri net and…
Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is the verification of safety and liveness properties in this model; despite the…
We show that the EXPSPACE-hardness result for structural liveness of Petri nets [Jancar and Purser, 2019] holds even for a simple subclass of conservative nets. As our main result, we prove that for structurally live conservative nets, the…
Petri nets proved useful to describe various real-world systems, but many of their properties are very hard to check. To alleviate this difficulty, subclasses are often considered. The class of weighted marked graphs with relaxed place…
Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…
Detectability describes the property of a system whose current and the subsequent states can be uniquely determined after a finite number of observations. In this paper, we developed a novel approach to verifying strong detectability and…
We present a short and self-contained proof of the choosability version of Brooks' theorem.
The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly's and Mac Lane's…
Bipolar synchronization systems (BP-systems) constitute a class of coloured Petri nets, well suited for modeling the control flow of discrete, dynamical systems. Every BP-system has an underlying ordinary Petri net, which is a T-system.…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
In a live and bounded Free Choice Petri net, pick a non-conflicting transition. Then there exists a unique reachable marking in which no transition is enabled except the selected one. For a routed live and bounded Free Choice net, this…
Detectability describes the property of a system to uniquely determine, after a finite number of observations, the current and subsequent states. In this paper, to reduce the complexity of checking the detectability properties in the…
In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set…
The formalism of the models with Petri networks provides a sound theoretical base, supported by powerful mathematical methods able to extract information necessary for the formalism and simulation of the real system that provides features…
This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.
Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to…
A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.