699 research outputs found
A Congruence for Petri Nets
We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs
Ackermann Encoding, Bisimulations, and OBDDs
We propose an alternative way to represent graphs via OBDDs based on the
observation that a partition of the graph nodes allows sharing among the
employed OBDDs. In the second part of the paper we present a method to compute
at the same time the quotient w.r.t. the maximum bisimulation and the OBDD
representation of a given graph. The proposed computation is based on an
OBDD-rewriting of the notion of Ackermann encoding of hereditarily finite sets
into natural numbers.Comment: To appear on 'Theory and Practice of Logic Programming
Adequacy Issues in Reactive Systems: Barbed Semantics for Mobile Ambients
Reactive systems represent a meta-framework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules.
The aim of this thesis is to address one of the main issues of the framework, concerning the adequacy of the standard observational semantics (the IPO and the saturated one) in modelling the concrete semantics of actual formalisms. The problem is that IPO-bisimilarity (obtained considering only minimal labels) is often too discriminating, while the saturated one (via all labels) may be too coarse, and intermediate proposals should then be put forward.
We then introduce a more expressive semantics for reactive systems which, thanks to its flexibility,
allows for recasting a wide variety of observational, bisimulation-based equivalences. In particular, we propose suitable notions of barbed and weak barbed semantics for reactive systems, and an efficient characterization of them through the IPO-transition systems.
We also propose a novel, more general behavioural equivalence: L-bisimilarity, which is able to recast both its IPO and saturated counterparts, as well as the barbed one. The equivalence is parametric with respect to a set L of reactive systems labels, and it is shown that under mild conditions on L it is a congruence.
In order to provide a suitable test-bed, we instantiate our proposal over the asynchronous CCS and, most importantly, over the mobile ambients calculus, whose semantics is still in a flux
Encoding CSP into CCS
We study encodings from CSP into asynchronous CCS with name passing and
matching, so in fact, the asynchronous pi-calculus. By doing so, we discuss two
different ways to map the multi-way synchronisation mechanism of CSP into the
two-way synchronisation mechanism of CCS. Both encodings satisfy the criteria
of Gorla except for compositionality, as both use an additional top-level
context. Following the work of Parrow and Sj\"odin, the first encoding uses a
centralised coordinator and establishes a variant of weak bisimilarity between
source terms and their translations. The second encoding is decentralised, and
thus more efficient, but ensures only a form of coupled similarity between
source terms and their translations.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634
04241 Abstracts Collection -- Graph Transformations and Process Algebras for Modeling Distributed and Mobile Systems
Recently there has been a lot of research, combining concepts of process algebra with those of the theory of graph grammars and graph transformation systems. Both can be viewed as general frameworks in which one can specify and reason about concurrent and distributed systems. There are many areas where both theories overlap and this reaches much further than just using graphs to give a graphic representation to processes.
Processes in a communication network can be seen in two different ways: as terms in an algebraic theory, emphasizing their behaviour and their interaction with the environment, and as nodes (or edges) in a graph, emphasizing their topology and their connectedness. Especially topology, mobility and dynamic reconfigurations at
runtime can be modelled in a very intuitive way using graph transformation. On the other hand the definition and proof of behavioural equivalences is often easier in the process algebra setting.
Also standard techniques of algebraic semantics for universal constructions, refinement and compositionality can take better advantage of the process algebra representation. An important example where the combined theory is more convenient than both alternatives is for defining the concurrent (noninterleaving), abstract semantics of distributed systems. Here graph transformations lack abstraction and process algebras lack expressiveness.
Another important example is the work on bigraphical reactive systems with the aim of deriving a labelled transitions system from an unlabelled reactive system such that the resulting bisimilarity is a congruence. Here, graphs seem to be a convenient framework, in which this theory can be stated and developed.
So, although it is the central aim of both frameworks to model and reason about concurrent systems, the semantics of processes can have a very different flavour in these theories. Research in this area aims at combining the advantages of both frameworks and translating concepts of one theory into the other. The Dagsuthl Seminar, which took place from 06.06. to 11.06.2004, was aimed at bringing together researchers of the two communities in order to share their ideas and develop new concepts. These proceedings4 of the do not only contain abstracts of the talks given at the seminar, but also summaries of topics of central interest. We would like to thank all participants of the seminar for coming and sharing their ideas and everybody who has contributed to the proceedings
Structural Analysis of Boolean Equation Systems
We analyse the problem of solving Boolean equation systems through the use of
structure graphs. The latter are obtained through an elegant set of
Plotkin-style deduction rules. Our main contribution is that we show that
equation systems with bisimilar structure graphs have the same solution. We
show that our work conservatively extends earlier work, conducted by Keiren and
Willemse, in which dependency graphs were used to analyse a subclass of Boolean
equation systems, viz., equation systems in standard recursive form. We
illustrate our approach by a small example, demonstrating the effect of
simplifying an equation system through minimisation of its structure graph
An Algebra of Hierarchical Graphs and its Application to Structural Encoding
We define an algebraic theory of hierarchical graphs, whose axioms
characterise graph isomorphism: two terms are equated exactly when
they represent the same graph. Our algebra can be understood as
a high-level language for describing graphs with a node-sharing, embedding
structure, and it is then well suited for defining graphical
representations of software models where nesting and linking are key
aspects. In particular, we propose the use of our graph formalism as a
convenient way to describe configurations in process calculi equipped
with inherently hierarchical features such as sessions, locations, transactions,
membranes or ambients. The graph syntax can be seen as an
intermediate representation language, that facilitates the encodings of
algebraic specifications, since it provides primitives for nesting, name
restriction and parallel composition. In addition, proving soundness
and correctness of an encoding (i.e. proving that structurally equivalent
processes are mapped to isomorphic graphs) becomes easier as it can
be done by induction over the graph syntax
Checking bisimilarity for attributed graph transformation
Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.Postprint (published version
DELPHIC: Practical DEL Planning via Possibilities (Extended Version)
Dynamic Epistemic Logic (DEL) provides a framework for epistemic planning
that is capable of representing non-deterministic actions, partial
observability, higher-order knowledge and both factual and epistemic change.
The high expressivity of DEL challenges existing epistemic planners, which
typically can handle only restricted fragments of the whole framework. The goal
of this work is to push the envelop of practical DEL planning, ultimately
aiming for epistemic planners to be able to deal with the full range of
features offered by DEL. Towards this goal, we question the traditional
semantics of DEL, defined in terms on Kripke models. In particular, we propose
an equivalent semantics defined using, as main building block, so-called
possibilities: non well-founded objects representing both factual properties of
the world, and what agents consider to be possible. We call the resulting
framework DELPHIC. We argue that DELPHIC indeed provides a more compact
representation of epistemic states. To substantiate this claim, we implement
both approaches in ASP and we set up an experimental evaluation to compare
DELPHIC with the traditional, Kripke-based approach. The evaluation confirms
that DELPHIC outperforms the traditional approach in space and time
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