2399426
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 $cDecOcc$, 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.
11646095
PMaude: Rewrite-based Specification Language for Probabilistic Object Systems
We introduce a rewrite-based specification language for modelling probabilistic concurrent and distributed systems. The language, based on PMaude, has both a rigorous formal basis and the characteristics of a high-level rule-based programming language. Furthermore, we provide tool support for performing discrete-event simulations of models written in PMaude, and for statistically analyzing various quantitative aspects of such models based on the samples that are generated through discrete-event simulation. Because distributed and concurrent communication protocols can be modelled using actors (concurrent objects with asynchronous message passing), we provide an actor PMaude module. The module aids writing specifications in a probabilistic actor formalism. This allows us to easily write specifications that are purely probabilistic - and not just non-deterministic. The absence of such (un-quantified) non-determinism in a probabilistic system is necessary for a form of statistical analysis that we also discuss. Specifically, we introduce a query language called Quantitative Temporal Expressions (or QuaTEx in short), to query various quantitative aspects of a probabilistic model. We also describe a statistical technique to evaluate QuaTEx expressions for a probabilistic model.
1438509
Algebraic Theories for Contextual Pre-nets
The algebraic models of computation for contextual nets that have been proposed in the literature either rely on a non-free monoid of objects, or introduce too many fictitious behaviors that must be somewhat filtered out. In this paper, we exploit partial membership equational logic to define a suitable theory of models, where the meaningful concurrent computations can be selected by means of membership predicates.
1787436
Proving termination of membership equational programs
Advanced typing, matching, and evaluation strategy features, as well as very general conditional rules, are routinely used in equational programming languages such as, for example, <sc>ASF+SDF</sc>, <sc>OBJ</sc>, <sc>CafeOBJ</sc>, <sc>Maude</sc>, and equational subsets of <sc>ELAN</sc> and <sc>CASL</sc>. Proving termination of equational programs having such expressive features is important but nontrivial, because some of those features may not be supported by standard termination methods and tools, such as <sc>muterm</sc>, <sc>C<i>i</i>ME</sc>, <sc>AProVE</sc>, <sc>TTT</sc>, <sc>Termptation</sc>, etc. Yet, use of the features may be essential to ensure termination. We present a sequence of theory transformations that can be used to bridge the gap between expressive equational programs and termination tools, prove the correctness of such transformations, and discuss a prototype tool performing the transformations on <sc>Maude</sc> equational programs and sending the resulting transformed theories to some of the aforementioned tools.
14145609
Functorial semantics for Petri nets under the individual token philosophy
Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of nets
1768436
Modular Rewriting Semantics in Practice
We present a general method to achieve modularity of semantic definitions of programming languages specified as rewrite theories, so that semantic rules do not have to be redefined in language extensions. We illustrate the practical use of this method by means of two language case studies: two different semantics for CCS, and three different semantics for the GNU bc language.
27956868
Using Maude