303 research outputs found
Enhanced Coalgebraic Bisimulation
International audienceWe present a systematic study of bisimulation-up-to techniques for coalgebras. This enhances the bisimulation proof method for a large class of state based systems, including labelled transition systems but also stream systems and weighted automata. Our approach allows for compositional reasoning about the soundness of enhancements. Applications include the soundness of bisimulation up to bisimilarity, up to equivalence and up to congruence. All in all, this gives a powerful and modular framework for simplified coinductive proofs of equivalence
Up-To Techniques for Generalized Bisimulation Metrics
Bisimulation metrics allow us to compute distances between the behaviors of probabilistic systems. In this paper we present enhancements of the proof method based on bisimulation metrics, by extending the theory of up-to techniques to (pre)metrics on discrete probabilistic concurrent processes.
Up-to techniques have proved to be a powerful proof method for showing that two systems are bisimilar, since they make it possible to build (and thereby check) smaller relations in bisimulation proofs. We define soundness conditions for up-to techniques on metrics, and study compatibility properties that allow us to safely compose up-to techniques with each other. As an example, we derive the soundness of the up-to-bisimilarity-metric-and-context technique.
The study is carried out for a generalized version of the bisimulation metrics, in which the Kantorovich lifting is parametrized with respect to a distance function. The standard bisimulation metrics, as well as metrics aimed at capturing multiplicative properties such as differential privacy, are specific instances of this general definition
Equations, Contractions, and Unique Solutions
International audienceOne of the most studied behavioural equivalences is bisimilarity. Its success is much due to the associated bisimulation proof method, which can be further enhanced by means of 'bisimulation up-to' techniques such as 'up-to context'. A different proof method is discussed, based on unique solution of special forms of inequations called contractions, and inspired by Milner's theorem on unique solution of equations. The method is as powerful as the bisimulation proof method and its 'up-to context' enhancements. The definition of contraction can be transferred onto other behavioural equivalences , possibly contextual and non-coinductive. This enables a coinduc-tive reasoning style on such equivalences, either by applying the method based on unique solution of contractions, or by injecting appropriate contraction preorders into the bisimulation game. The techniques are illustrated on CCS-like languages; an example dealing with higher-order languages is also shown
Presenting Distributive Laws
Distributive laws of a monad T over a functor F are categorical tools for
specifying algebra-coalgebra interaction. They proved to be important for
solving systems of corecursive equations, for the specification of well-behaved
structural operational semantics and, more recently, also for enhancements of
the bisimulation proof method. If T is a free monad, then such distributive
laws correspond to simple natural transformations. However, when T is not free
it can be rather difficult to prove the defining axioms of a distributive law.
In this paper we describe how to obtain a distributive law for a monad with an
equational presentation from a distributive law for the underlying free monad.
We apply this result to show the equivalence between two different
representations of context-free languages
Bisimulations up-to: beyond first-order transition systems
International audienceThe bisimulation proof method can be enhanced by employing 'bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on the notion of compatible function for fixed-point theory. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references
Modular coinduction up-to for higher-order languages via first-order transition systems
The bisimulation proof method can be enhanced by employing âbisimulations up-toâ techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the Ï-calculus, the λ-calculus, and a (call-by-value) λ-calculus with references
Coinduction up to in a fibrational setting
Bisimulation up-to enhances the coinductive proof method for bisimilarity,
providing efficient proof techniques for checking properties of different kinds
of systems. We prove the soundness of such techniques in a fibrational setting,
building on the seminal work of Hermida and Jacobs. This allows us to
systematically obtain up-to techniques not only for bisimilarity but for a
large class of coinductive predicates modelled as coalgebras. By tuning the
parameters of our framework, we obtain novel techniques for unary predicates
and nominal automata, a variant of the GSOS rule format for similarity, and a
new categorical treatment of weak bisimilarity
A framework for proof certificates in finite state exploration
Model checkers use automated state exploration in order to prove various
properties such as reachability, non-reachability, and bisimulation over state
transition systems. While model checkers have proved valuable for locating
errors in computer models and specifications, they can also be used to prove
properties that might be consumed by other computational logic systems, such as
theorem provers. In such a situation, a prover must be able to trust that the
model checker is correct. Instead of attempting to prove the correctness of a
model checker, we ask that it outputs its "proof evidence" as a formally
defined document--a proof certificate--and that this document is checked by a
trusted proof checker. We describe a framework for defining and checking proof
certificates for a range of model checking problems. The core of this framework
is a (focused) proof system that is augmented with premises that involve "clerk
and expert" predicates. This framework is designed so that soundness can be
guaranteed independently of any concerns for the correctness of the clerk and
expert specifications. To illustrate the flexibility of this framework, we
define and formally check proof certificates for reachability and
non-reachability in graphs, as well as bisimulation and non-bisimulation for
labeled transition systems. Finally, we describe briefly a reference checker
that we have implemented for this framework.Comment: In Proceedings PxTP 2015, arXiv:1507.0837
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