Axiomatizing Petri Net Concatenable Processes

The concatenable processes of a Petri net $N$ can be characterized abstractly as the arrows of a symmetric monoidal category $P[N]$. Yet, this is only a partial axiomatization, since $P[N]$ is built on a concrete, ad hoc chosen, category of symmetries. In this paper we give a fully equational description of the category of concatenable processes of $N$, thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets

CCS Dynamic Bisimulation is Progressing

Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g.\ $\alpha.\tau.\beta.nil$ and $\alpha.\beta.nil$ are woc but $\tau.\beta.nil$ and $\beta.nil$ are not. This fact prevents us from characterizing CCS semantics (when $\tau$ is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e.\ run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two characterizations via modal logic in the style of HML, and a complete axiomatization for finite agents. Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents. Thus the title of the paper

Dynamic Congruence vs. Progressing Bisimulation for CCS

Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. \alpha.\tau.\beta.nil and \alpha.\beta.nil are woc but \tau.\beta.nil and \beta.nil are not. This fact prevent us from characterizing CCS semantics (when \tau is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e. run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two logical characterizations via modal logic in the style of HML and a complete axiomatization for finite agents (consisting of the axioms for Strong Observational Congruence and of two of the three Milner's $\tau$-laws). Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents

A bibliography on formal methods for system specification, design and validation

Literature on the specification, design, verification, testing, and evaluation of avionics systems was surveyed, providing 655 citations. Journal papers, conference papers, and technical reports are included. Manual and computer-based methods were employed. Keywords used in the online search are listed

Process versus Unfolding Semantics for Place/Transition Petri Nets

In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification

On the Semantics of Petri Nets: Processes, Unfoldings and Infinite Computations.

PhD Thesi

Identifying Implicit Component Interactions in Distributed Cyber-Physical Systems

Modern distributed systems and networks, like those found in cyber-physical system domains such as critical infrastructures, contain many complex interactions among their constituent software and/or hardware components. Despite extensive testing of individual components, security vulnerabilities resulting from unintended and unforeseen component interactions (so-called implicit interactions) often remain undetected. This paper presents a method for identifying the existence of implicit interactions in designs of distributed cyber-physical systems using the algebraic modeling framework known as Communicating Concurrent Kleene Algebra (C²KA). Experimental results verifying the applicability of C²KA for identifying dependencies in system designs that would otherwise be very hard to find are also presented. More broadly, this research aims to advance the specification, design, and implementation of distributed cyber-physical systems with improved cybersecurity assurance by providing a new way of thinking about the problem of implicit interactions through the application of formal methods