. In this paper we describe an approach to model the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. The basic idea is to use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are however combined by means of a synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. To formally model this kind of graph rewriting, however, we do not adopt the classical graph rewriting style but a more general framework, called the tile model, which allows for a clear separation between sequential rewriting and synchronization. Then, since the problem of satisfying the synchronization requirements may be a complex combinatorial pro...

Recently there has been a growing interest towards algebraic structures that are able to express formalisms different from the standard, tree-like presentation of terms. Many of these approaches reveal a specific interest towards their application in the "distributed and concurrent systems" field, but an exhaustive comparison between them is difficult because their presentations can be quite dissimilar. This work is a first step towards a unified view, which is able to recast all those formalisms into a more general one, where they can be easily compared. We introduce a general schema for describing a characteristic normal form for many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable concrete monoidal categories.

In this paper we provide both an operational and an abstract concurrent semantics for zero-safe nets under the individual token philosophy. The main feature of zero-safe nets is a primitive notion of transition synchronization. Besides ordinary places, called stable places, zero-safe nets come equipped with zero places, which are empty in any stable marking. Connected transactions represent basic atomic computations of the system between stable markings. They must satisfy two main requirements: 1) to model interacting activities which cannot be decomposed into disjoint sub-activities, and 2) not to consume stable tokens which were generated in the same transaction. Zero tokens acts as triggers for the firings of the transitions which compose the transaction. The abstract counterpart of a zero-safe net consists of a P/T net where each transition locates a distinguished transaction. In the second part of the paper, following the Petri nets are monoids approach, we make use of catego...

In [12] we introduced the tile model, a framework encompassing a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting and of concurrency theory, and our formalism recollects many properties of these sources. For example, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Moreover, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and side-effects to determine the actual behaviour of a system. In this work we narrow our scope, presenting a restricted version of our tile model and focussing our attention on its expressive power. To this aim, we recall the basic definitions of the process algebras paradigm [3,24], centering the paper on the recasting of this framework in our formalism.

. Tile logic extends rewriting logic by taking into account sideeffects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and "the rest of the world". Since rewriting logic is the semantic basis of several language implementation efforts, an executable specification of tile systems can be obtained by mapping tile logic back into rewriting logic, in a conservative way. However, a correct rewriting implementation of tile logic requires the development of a metalayer to control rewritings, i.e., to discard computations that do not correspond to any deduction in tile logic. We show how such methodology can be applied to term tile systems that cover and extend a wide-class of SOS formats for the specification of process calculi. The well-known case-study of full CCS, where the term tile format is needed to deal with recursion (in the form of the replicator operator), is di...

The definition of sos formats ensuring that bisimilarity on closed terms is a congruence has received much attention in the last two decades. For dealing with open system specifications, the congruence is usually lifted from closed terms to open terms by instantiating the free variables in all possible ways; the only alternatives considered in the literature relying on Larsen and Xinxin's context systems and Rensink's conditional transition systems. We propose a different approach based on tile logic, where both closed and open terms are managed analogously. In particular, we analyze the `bisimilarity as congruence' property for several tile formats that accomplish di erent concepts of subterm sharing.

Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.

Maude's language design and implementation make systematic use of the fact that rewriting logic is reflective. This makes the metatheory of rewriting logic accessible to the user in a clear and principled way, and makes possible many advanced metaprogramming applications, including user-definable strategy languages, language extensions by new module composition operations, development of theorem proving tools, and reifications of other languages and logics within rewriting logic. A naive implementation of reflection can be computationally very expensive. We explain the semantic principles and implementation techniques through which efficient ways of performing reflective computations are achieved in Maude through its predefined META-LEVEL module.

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We introduce a notion of bisimulation for graph rewriting systems, allowing us to prove observational equivalence for dynamically evolving graphs and networks. We use the framework of synchronized graph rewriting with mobility which we describe in two different, but operationally equivalent ways: on graphs defined as syntactic judgements and by using tile logic. One of the main results of the paper says that bisimilarity for synchronized graph rewriting is a congruence whenever the rewriting rules satisfy the basic source property. Furthermore we introduce an up-to technique simplifying bisimilarity proofs and use it in an example to show the equivalence of a communication network and its specification.