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In process discovery, the goal is to find, for a given event log, the model describing the underlying process. While process models can be represented in a variety of ways, Petri nets form a theoretically well-explored description language…
In this paper we deal with additional control structures for decorated PT Nets. The main contribution are inhibitor arcs and priorities. The first ensure that a marking can inhibit the firing of a transition. Inhibitor arcs force that 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…
The theory of Petri Nets provides a general framework to specify the behaviors of real-time reactive systems and Time Petri Nets were introduced to take also temporal specifications into account. We present in this paper a forward…
Causal nets (CNs) are Petri nets where causal dependencies are modelled via inhibitor arcs. They play the role of occurrence nets when representing the behaviour of a concurrent and distributed system, even when reversibility is considered.…
The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper,…
We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer…
Petri nets and their variants are often considered through their interleaved semantics, i.e. considering executions where, at each step, a single transition fires. This is clearly a miss, as Petri nets are a true concurrency model. This…
In this work, we analyse Petri nets where places are allowed to have a negative number of tokens. For each net we build its correspondent category of executions, which is compact closed, and prove that this procedure is functorial. We…
Graph transformation systems (GTS) have been successfully proposed as a general, theoretically sound model for concurrency. Petri nets (PN), on the other side, are a central and intuitive formalism for concurrent or distributed systems,…
Modelling, specifying and reasoning about complex systems requires to process in an integrated fashion declarative and procedural aspects of the target domain. The paper reports on an experiment conducted with a propositional version of…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
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…
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…
In this paper, we introduce Path Integral Networks (PI-Net), a recurrent network representation of the Path Integral optimal control algorithm. The network includes both system dynamics and cost models, used for optimal control based…
In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$…
The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…
In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets…
Transformer models bring propelling advances in various NLP tasks, thus inducing lots of interpretability research on the learned representations of the models. However, we raise a fundamental question regarding the reliability of the…