Andrea Corradini

Contextual Petri nets, asymmetric event structures, and processes

We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (read-only operations). A basic role is played by asymmetric event structures, a generalization of Winskels prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskels seminal work on safe nets, the truly concurrent event-based semantics of contextual nets is given at categorical level via a chain of coreflections leading from the category SW-CN of semi-weighted contextual nets to the category Dom of finitary prime algebraic domains. First an unfolding construction generates from a contextual net a corresponding occurrence contextual net, from where an asymmetric event structure is extracted. Then the configurations of the asymmetric event structure, endowed with a suitable order, are shown to form a finitary prime algebraic domain. We also investigate the relation between the proposed unfolding semantics and several deterministic process semantics for contextual nets in the literature. In particular, the domain obtained via the unfolding is characterized as the collection of the deterministic processes of the net endowed with a kind of prefix ordering. 2001 Elsevier Science.

A Static Analysis Technique for Graph Transformation Systems

In this paper we introduce a static analysis technique for graph transformation systems. We present an algorithm which, given a graph transformation system and a start graph, produces a finite structure consisting of a hypergraph decorated with transitions (Petri graph) which can be seen as an approximation of the Winskel style unfolding of the graph transformation system. The fact that any reachable graph has an homomorphic image in the Petri graph and the additional causal information provided by transitions allow us to prove several interesting properties of the original system. As an application of the proposed technique we show how it can be used to verify the absence of deadlocks in an infinite-state Dining Philosophers system.

Sesqui-pushout rewriting

Sesqui-pushout (SqPO) rewriting-sesqui means one and a half in Latin-is a new algebraic approach to abstract rewriting in any category. SqPO rewriting is a deterministic and conservative extension of double-pushout (DPO) rewriting, which allows to model deletion in unknown context, a typical feature of single-pushout (SPO) rewriting, as well as cloning. After illustrating the expressiveness of the proposed approach through a case study modelling an access control system, we discuss sufficient conditions for the existence of final pullback complements and we analyze the relationship between SqPO and the classical DPO and SPO approaches.

A conceptual framework for adaptation

In this position paper we present a conceptual vision of adaptation, a key feature of autonomic systems. We put some stress on the role of control data and argue how some of the programming paradigms and models used for adaptive systems match with our conceptual framework.

An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories

We present a categorical characterization of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the well-known characterization of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particular, we show that term graphs over a signature Σ are one-to-one with the arrows of the free gs-monoidal category generated by Σ. Such a category satisfies all the axioms for Cartesian categories but for the naturality of two transformations (the discharger ! and the duplicator ∇), providing in this way an abstract and clear relationship between terms and term graphs. In particular, the absence of the naturality of ∇ and ! has a precise interpretation in terms of explicit sharing and of loss of implicit garbage collection, respectively.

Compositional semantics for open Petri nets based on deterministic processes

In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalisation of the ordinary model where some places, designated as open, represent an interface between the system and the environment. Besides generalising the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the Goltz–Reisig process semantics of Petri nets. We introduce a composition operation over open nets, characterised as a pushout in the corresponding category, suitable for modelling both interaction through open places and synchronisation of transitions. The deterministic process semantics is shown to be compositional with respect to such a composition operation. If a net

Verifying Finite-State Graph Grammars: an Unfolding-Based Approach

Z_3

An algebraic semantics for structured transition systems and its application to logic programs

results as the composition of two nets

Unfolding and Event Structure Semantics for Graph Grammars

Z_1

Compositional SOS and beyond: a coalgebraic view of open systems

and