264 research outputs found
Acyclic Solos and Differential Interaction Nets
We present a restriction of the solos calculus which is stable under
reduction and expressive enough to contain an encoding of the pi-calculus. As a
consequence, it is shown that equalizing names that are already equal is not
required by the encoding of the pi-calculus. In particular, the induced solo
diagrams bear an acyclicity property that induces a faithful encoding into
differential interaction nets. This gives a (new) proof that differential
interaction nets are expressive enough to contain an encoding of the
pi-calculus. All this is worked out in the case of finitary (replication free)
systems without sum, match nor mismatch
Formalising the pi-calculus using nominal logic
We formalise the pi-calculus using the nominal datatype package, based on
ideas from the nominal logic by Pitts et al., and demonstrate an implementation
in Isabelle/HOL. The purpose is to derive powerful induction rules for the
semantics in order to conduct machine checkable proofs, closely following the
intuitive arguments found in manual proofs. In this way we have covered many of
the standard theorems of bisimulation equivalence and congruence, both late and
early, and both strong and weak in a uniform manner. We thus provide one of the
most extensive formalisations of a process calculus ever done inside a theorem
prover.
A significant gain in our formulation is that agents are identified up to
alpha-equivalence, thereby greatly reducing the arguments about bound names.
This is a normal strategy for manual proofs about the pi-calculus, but that
kind of hand waving has previously been difficult to incorporate smoothly in an
interactive theorem prover. We show how the nominal logic formalism and its
support in Isabelle accomplishes this and thus significantly reduces the tedium
of conducting completely formal proofs. This improves on previous work using
weak higher order abstract syntax since we do not need extra assumptions to
filter out exotic terms and can keep all arguments within a familiar
first-order logic.Comment: 36 pages, 3 figure
Saturated Transition Systems for Presheaf Models
La presente tesi propone una tecnica sistematica per la rappresentazione coalgebrica di sistemi di transizione in cui la bisimilarità è una congruenza, adoperando categorie di coalgebre su presheaves. Si investigano le condizioni di rappresentabilità e si forniscono esempi applicativi
A Fully Abstract Symbolic Semantics for Psi-Calculi
We present a symbolic transition system and bisimulation equivalence for
psi-calculi, and show that it is fully abstract with respect to bisimulation
congruence in the non-symbolic semantics.
A psi-calculus is an extension of the pi-calculus with nominal data types for
data structures and for logical assertions representing facts about data. These
can be transmitted between processes and their names can be statically scoped
using the standard pi-calculus mechanism to allow for scope migrations.
Psi-calculi can be more general than other proposed extensions of the
pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion
calculus, or the concurrent constraint pi-calculus.
Symbolic semantics are necessary for an efficient implementation of the
calculus in automated tools exploring state spaces, and the full abstraction
property means the semantics of a process does not change from the original
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
Psi-calculi: a framework for mobile processes with nominal data and logic
The framework of psi-calculi extends the pi-calculus with nominal datatypes
for data structures and for logical assertions and conditions. These can be
transmitted between processes and their names can be statically scoped as in
the standard pi-calculus. Psi-calculi can capture the same phenomena as other
proposed extensions of the pi-calculus such as the applied pi-calculus, the
spi-calculus, the fusion calculus, the concurrent constraint pi-calculus, and
calculi with polyadic communication channels or pattern matching. Psi-calculi
can be even more general, for example by allowing structured channels,
higher-order formalisms such as the lambda calculus for data structures, and
predicate logic for assertions. We provide ample comparisons to related calculi
and discuss a few significant applications. Our labelled operational semantics
and definition of bisimulation is straightforward, without a structural
congruence. We establish minimal requirements on the nominal data and logic in
order to prove general algebraic properties of psi-calculi, all of which have
been checked in the interactive theorem prover Isabelle. Expressiveness of
psi-calculi significantly exceeds that of other formalisms, while the purity of
the semantics is on par with the original pi-calculus.Comment: 44 page
Modal Logics for Nominal Transition Systems
We define a uniform semantic substrate for a wide variety of process calculi where states and action labels can be from arbitrary nominal sets. A Hennessy-Milner logic for these systems is introduced, and proved adequate for bisimulation equivalence. A main novelty is the use of finitely supported infinite conjunctions. We show how to treat different bisimulation variants such as early, late and open in a systematic way, and make substantial comparisons with related work. The main definitions and theorems have been formalized in Nominal Isabelle
Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming
In this paper we compare three different formalisms that can be used in the
area of models for distributed, concurrent and mobile systems. In particular we
analyze the relationships between a process calculus, the Fusion Calculus,
graph transformations in the Synchronized Hyperedge Replacement with Hoare
synchronization (HSHR) approach and logic programming. We present a translation
from Fusion Calculus into HSHR (whereas Fusion Calculus uses Milner
synchronization) and prove a correspondence between the reduction semantics of
Fusion Calculus and HSHR transitions. We also present a mapping from HSHR into
a transactional version of logic programming and prove that there is a full
correspondence between the two formalisms. The resulting mapping from Fusion
Calculus to logic programming is interesting since it shows the tight analogies
between the two formalisms, in particular for handling name generation and
mobility. The intermediate step in terms of HSHR is convenient since graph
transformations allow for multiple, remote synchronizations, as required by
Fusion Calculus semantics.Comment: 44 pages, 8 figures, to appear in a special issue of Theory and
Practice of Logic Programming, minor revisio
Observational equivalences for linear logic CC languages
Linear logic Concurrent Constraint programming (LCC) is an extension of
concurrent constraint programming (CC) where the constraint system is based on
Girard's linear logic instead of the classical logic. In this paper we address
the problem of program equivalence for this programming framework. For this
purpose, we present a structural operational semantics for LCC based on a label
transition system and investigate different notions of observational
equivalences inspired by the state of art of process algebras. Then, we
demonstrate that the asynchronous \pi-calculus can be viewed as simple
syntactical restrictions of LCC. Finally we show LCC observational equivalences
can be transposed straightforwardly to classical Concurrent Constraint
languages and Constraint Handling Rules, and investigate the resulting
equivalences.Comment: 17 page
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