278 research outputs found
Tree morphisms and bisimulations
A category of (action labelled) trees is defined that can be used to model unfolding of labelled transition systems and to study behavioural relations over them. In this paper we study five different equivalences based on bisimulation for our model. One, that we called resource bisimulation, amounts essentially to three isomorphism. Another, its weak counterpart, permits abstracting from silent actions while preserving the tree structure. The other three are the well known strong, branching and weak bisimulation equivalence. For all bisimulations, but weak, canonical representatives are constructed and it is shown that they can be obtained via enriched functors over our categories of trees, with and without silent actions. Weak equivalence is more problematic; a canonical minimal representative for it cannot be denned by quotienting our trees. The common framework helps in understanding the relationships between the various equivalences and the results provide support to the claim that branching bisimulation is the natural generalization of strong bisimulation to systems with silent moves and that resource and weak resource have an interest of their own
Bisimilarity is not Borel
We prove that the relation of bisimilarity between countable labelled
transition systems is -complete (hence not Borel), by reducing the
set of non-wellorders over the natural numbers continuously to it.
This has an impact on the theory of probabilistic and nondeterministic
processes over uncountable spaces, since logical characterizations of
bisimilarity (as, for instance, those based on the unique structure theorem for
analytic spaces) require a countable logic whose formulas have measurable
semantics. Our reduction shows that such a logic does not exist in the case of
image-infinite processes.Comment: 20 pages, 1 figure; proof of Sigma_1^1 completeness added with
extended comments. I acknowledge careful reading by the referees. Major
changes in Introduction, Conclusion, and motivation for NLMP. Proof for Lemma
22 added, simpler proofs for Lemma 17 and Theorem 30. Added references. Part
of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logic
GSOS for non-deterministic processes with quantitative aspects
Recently, some general frameworks have been proposed as unifying theories for
processes combining non-determinism with quantitative aspects (such as
probabilistic or stochastically timed executions), aiming to provide general
results and tools. This paper provides two contributions in this respect.
First, we present a general GSOS specification format (and a corresponding
notion of bisimulation) for non-deterministic processes with quantitative
aspects. These specifications define labelled transition systems according to
the ULTraS model, an extension of the usual LTSs where the transition relation
associates any source state and transition label with state reachability weight
functions (like, e.g., probability distributions). This format, hence called
Weight Function SOS (WFSOS), covers many known systems and their bisimulations
(e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS,
Segala-GSOS, among others).
The second contribution is a characterization of these systems as coalgebras
of a class of functors, parametric on the weight structure. This result allows
us to prove soundness of the WFSOS specification format, and that
bisimilarities induced by these specifications are always congruences.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Bisimulations and Unfolding in P-Accessible Categorical Models
In this paper, we propose a categorical framework for bisimulations and unfoldings that unifies the classical approach from Joyal and al. via open maps and unfoldings. This is based on a notion of categories accessible with respect to a subcategory of path shapes, i.e., for which one can define a nice notion of trees as glueing of paths. We prove that transitions systems and pre sheaf models are a particular case of our framework. We also prove that in our framework, several characterizations of bisimulation coincide, in particular an "operational one" akin to the standard definition in transition systems. Also, accessibility is preserved by coreflexions. We then design a notion of unfolding, which has good properties in the accessible case: its is a right adjoint and is a universal covering, i.e., initial among the morphisms that have the unique lifting property with respect to path shapes. As an application, we prove that the universal covering of a groupoid, a standard construction in algebraic topology, coincides with an unfolding, when the category of path shapes is well chosen
Full abstraction for fair testing in CCS (expanded version)
In previous work with Pous, we defined a semantics for CCS which may both be
viewed as an innocent form of presheaf semantics and as a concurrent form of
game semantics. We define in this setting an analogue of fair testing
equivalence, which we prove fully abstract w.r.t. standard fair testing
equivalence. The proof relies on a new algebraic notion called playground,
which represents the `rule of the game'. From any playground, we derive two
languages equipped with labelled transition systems, as well as a strong,
functional bisimulation between them.Comment: 80 page
Coalgebraic Methods for Object-Oriented Specification
This thesis is about coalgebraic methods in software specification and verification. It extends known techniques of coalgebraic specification to a more general level to pave the way for real world applications of software verification. There are two main contributions of the present thesis: 1. Chapter 3 proposes a generalisation of the familiar notion of coalgebra such that classes containing methods with arbitrary types (including binary methods) can be modelled with these generalised coalgebras. 2. Chapter 4 presents the specification language CCSL (short for Coalgebraic Class Specification Language), its syntax, its semantics, and a prototype compiler that translates CCSL into higher-order logic.Die Dissertation beschreibt coalgebraische Mittel und Methoden zur Softwarespezifikation und -verifikation. Die Ergebnisse dieser Dissertation vereinfachen die Anwendung coalgebraischer Spezifikations- und Verifikationstechniken und erweitern deren Anwendbarkeit. Damit werden Softwareverifikation im Allgemeinen und im Besonderen coalgebraische Methoden zur Softwareverifikation der praktischen Anwendbarkeit ein Stück nähergebracht. Diese Dissertation enthält zwei wesentliche Beiträge: 1. Im Kapitel 3 wird eine Erweiterung des klassischen Begriffs der Coalgebra vorgestellt. Diese Erweiterung erlaubt die coalgebraische Modellierung von Klassenschnittstellen mit beliebigen Methodentypen (insbesondere mit binären Methoden). 2. Im Kapitel 4 wird die coalgebraische Spezifikationssprache CCSL (Coalgebraic Class Specification Language) vorgestellt. Die Bescheibung umfasst Syntax, Semantik und einen Prototypcompiler, der CCSL Spezifikationen in Logik höherer Ordnung (passend für die Theorembeweiser PVS und Isabelle/HOL) übersetzt
An expressive completeness theorem for coalgebraic modal mu-calculi
Generalizing standard monadic second-order logic for Kripke models, we
introduce monadic second-order logic interpreted over coalgebras for an
arbitrary set functor. We then consider invariance under behavioral equivalence
of MSO-formulas. More specifically, we investigate whether the coalgebraic
mu-calculus is the bisimulation-invariant fragment of the monadic second-order
language for a given functor. Using automatatheoretic techniques and building
on recent results by the third author, we show that in order to provide such a
characterization result it suffices to find what we call an adequate uniform
construction for the coalgebraic type functor. As direct applications of this
result we obtain a partly new proof of the Janin-Walukiewicz Theorem for the
modal mu-calculus, avoiding the use of syntactic normal forms, and bisimulation
invariance results for the bag functor (graded modal logic) and all exponential
polynomial functors (including the "game functor"). As a more involved
application, involving additional non-trivial ideas, we also derive a
characterization theorem for the monotone modal mu-calculus, with respect to a
natural monadic second-order language for monotone neighborhood models.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0721
History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps
We show that history-preserving bisimilarity for higher-dimensional automata
has a simple characterization directly in terms of higher-dimensional
transitions. This implies that it is decidable for finite higher-dimensional
automata. To arrive at our characterization, we apply the open-maps framework
of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.Comment: Minor updates in accordance with reviewer comments. Submitted to MFPS
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