3,608 research outputs found

    Adequacy Issues in Reactive Systems: Barbed Semantics for Mobile Ambients

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    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

    Bialgebraic Semantics for Logic Programming

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    Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic programs as reactive systems and exploit abstract techniques developed in that setting. First we use saturation to model the operational semantics of logic programs as coalgebrae on presheaves. Then, we make explicit the underlying algebraic structure by using bialgebrae on presheaves. The resulting semantics turns out to be compositional with respect to conjunction and term substitution. Also, it encodes a parallel model of computation, whose soundness is guaranteed by a built-in notion of synchronisation between different threads

    On Barbs and Labels in Reactive Systems

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    Reactive systems (RSs) represent a meta-framework aimed at deriving behavioral congruences for those computational formalisms whose operational semantics is provided by reduction rules. RSs proved a flexible specification device, yet so far most of the efforts dealing with their behavioural semantics focused on idem pushouts (IPOs) and saturated (also known as dynamic) bisimulations. In this paper we introduce a novel, intermediate behavioural equivalence: L-bisimilarity, which is able to recast both its IPO and saturated counterparts. The equivalence is parametric with respect to a set L of RSs labels, and it is shown that under mild conditions on L it is indeed a congruence. Furthermore, L-bisimilarity can also recast the notion of barbed semantics for RSs, proposed by the same authors in a previous paper. In order to provide a suitable test-bed, we instantiate our proposal by addressing the semantics of (asynchronous) CCS and of the calculus of mobile ambients

    Full Semantics Preservation in Model Transformation – A Comparison of Proof Techniques

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    Model transformation is a prime technique in modern, model-driven software design. One of the most challenging issues is to show that the semantics of the models is not affected by the transformation. So far, there is hardly any research into this issue, in particular in those cases where the source and target languages are different.\ud \ud In this paper, we are using two different state-of-the-art proof techniques (explicit bisimulation construction versus borrowed contexts) to show bisimilarity preservation of a given model transformation between two simple (self-defined) languages, both of which are equipped with a graph transformation-based operational semantics. The contrast between these proof techniques is interesting because they are based on different model transformation strategies: triple graph grammars versus in situ transformation. We proceed to compare the proofs and discuss scalability to a more realistic setting.\u

    Towards an Effective Decision Procedure for LTL formulas with Constraints

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    This paper presents an ongoing work that is part of a more wide-ranging project whose final scope is to define a method to validate LTL formulas w.r.t. a program written in the timed concurrent constraint language tccp, which is a logic concurrent constraint language based on the concurrent constraint paradigm of Saraswat. Some inherent notions to tccp processes are non-determinism, dealing with partial information in states and the monotonic evolution of the information. In order to check an LTL property for a process, our approach is based on the abstract diagnosis technique. The concluding step of this technique needs to check the validity of an LTL formula (with constraints) in an effective way. In this paper, we present a decision method for the validity of temporal logic formulas (with constraints) built by our abstract diagnosis technique.Comment: Part of WLPE 2013 proceedings (arXiv:1308.2055

    Sequent Calculus in the Topos of Trees

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    Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of trees. We show that the semantics of the propositional fragment of this logic can be given by linear converse-well-founded intuitionistic Kripke frames, so this logic is a marriage of the intuitionistic modal logic KM and the intermediate logic LC. We therefore call this logic KMlin\mathrm{KM}_{\mathrm{lin}}. We give a sound and cut-free complete sequent calculus for KMlin\mathrm{KM}_{\mathrm{lin}} via a strategy that decomposes implication into its static and irreflexive components. Our calculus provides deterministic and terminating backward proof-search, yields decidability of the logic and the coNP-completeness of its validity problem. Our calculus and decision procedure can be restricted to drop linearity and hence capture KM.Comment: Extended version, with full proof details, of a paper accepted to FoSSaCS 2015 (this version edited to fix some minor typos

    Abstract Semantics by Observable Contexts

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    The operational behavior of interactive systems is usually given in terms of transition systems labeled with actions, which, when visible, represent both observations and interactions with the external world. The abstract semantics is given in terms of behavioral equivalences, which depend on the action labels and on the amount of branching structure considered. Behavioural equivalences are often congruences with respect to the operations of the language, and this property expresses the compositionality of the abstract semantics. A simpler approach, inspired by classical formalisms like pi-calculus, Petri nets, term and graph rewriting, and pioneered by the Chemical Abstract Machine [13], defines operational semantics by means of structural axioms and reaction rules. Process calculi representing complex systems, in particular those able to generate and communicate names, are often defined in this way, since structural axioms give a clear idea of the intended structure of the states while reaction rules, which are often non-conditional, give a direct account of the possible steps. Transitions caused by reaction rules, however, are not labeled, since they represent evolutions of the system without interactions with the external world. Thus reduction semantics in itself is neither abstract nor compositional. One standard solution, pioneered in [89], is that of defining a saturated transition system as follows: a process p can do a move with label C[-] and become q, iff C[p]--> q. Saturated semantics, i.e., the abstract semantics defined over the saturated transition system, are always congruences, but they are usually untractable since they have to tackle all possible contexts of which there are usually an infinite number. Moreover, in several paradigmatic cases, saturated semantics are too coarse. For example, in Milner's Calculus of Communicating Systems (CCS), saturated bisimilarity cannot distinguish "always divergent processes" and for this reason Milner and Sangiorgi introduced barbs. These are observations on the states representing the ability to interact over some channels. Sewell introduced a different approach that consists in deriving a transition system where labels are not all contexts but just the minimal ones allowing a system to reach a rule. In such a way, one obtains two advantages: firstly one avoids considering all contexts, and secondly, labels precisely represent interactions, i.e., the portion of environment that is really needed to react. This idea was then refined by Leifer and Milner in the theory of reactive systems, where the categorical notion of idem relative pushout precisely captures this idea of minimal context. In this thesis, we show that in some cases this approach works well (e.g., CCS) but often, the resulting abstract semantics are too strict. In our opinion, they are not really observational since the observer can know exactly how much structure a process needs to reach a specific rule, and thus the observation depends on the rules. One result of the thesis is that of providing evidence of this through several interesting formalisms modeled as reactive systems: Logic Programming, a fragment of open pi-calculus, and an interactive version of Petri nets. Moreover, we introduce two alternative definitions of bisimilarity that efficiently characterize saturated bisimilarity, namely semi-saturated bisimilarity and symbolic bisimilarity. These allow us to reason about saturated semantics without considering all contexts, but saturated semantics are in several cases too coarse. In order to have a framework that is suitable for many formalisms, we add to the above approach observations. Indeed, in our opinion, labels cannot represent both interactions and observations, because these two concepts are in general different, like for example, in the asynchronous calculi where receiving is not observable. Thus, we believe that some notion of observation, either on transitions or on states (e.g. barbs), is necessary. A further result of the thesis is that of providing a generalization of the above theory starting not just from purely reaction rules, but from transition systems labeled with observations. Here we can easily reuse saturated transition systems by defining them as follows: a process p can do a move with context C[-] and observation o and become q iff C[p] --o--> q. Again, saturated semantics, i.e. abstract semantics defined over the above transition systems, are congruences. Analogously to the case of reactive systems, we can define semi-saturated bisimilarity and symbolic bisimilarity as efficient characterizations of saturated semantics. The definition of symbolic bisimilarity which arises from this generalization is similar to the abstract semantics of several works. Here we consider open and asynchronous pi-calculus, by showing that their abstract semantics are instances of our general concepts of saturated and symbolic semantics. We also apply our approach to open Petri nets (that are an interactive version of P/T Petri nets) obtaining a new symbolic semantics for them, that efficiently characterizes their abstract semantics. We round up the thesis with a coalgebraic characterization for saturated, semi-saturated and symbolic bisimilarity. Universal Coalgebra provides a categorical framework where abstract semantics of interactive systems are described as morphisms to their minimal representatives. More precisely, if the category of coalgebras has final object 1, then the unique morphisms from a certain coalgebra to 1 equates all the bisimilar states. In other words, the final object can be seen as a universe of abstract behaviors and the unique morphism as a function assigning to each system its abstract behavior. This characterization of abstract semantics is not only theoretically interesting, but also pragmat- ically useful, since it suggests an algorithm which can check the equivalence: one computes the image of some coalgebras through the unique morphism (that for the finite lts corresponds to the list partitioning algorithm by Kanellakis and Smolka), and these coalgebras are behaviorally equivalent if their images are the same. Ordinary labeled transition systems can be represented as coalgebras, and the resulting abstract semantics exactly coincides with canonical bisimilarity. Then, providing a coalgebraic characterization of saturated bisimilarity is almost straightforward. The case of semi-saturated and symbolic bisimilarities are more complicated because their definitions are asymmetric. In order to properly characterizes semi-saturated and symbolic cases, we first introduce a new notion of redundancy on transitions and then normalized coalgebras: a special kind of coalgebras without redundant transitions. We prove that the category of normalized coalgebras is isomorphic to the category of saturated coalgebras (the coalgebras containing all the redundant transitions), where the large saturated transition system can be directly modelled. In doing this, we use the notions of normalization that throws away all the redundant transitions, and of saturation that adds all the redundant transitions. Both are natural transformations between the endofunctors (defining the two categories of coalgebras) and one is the inverse of the other. As a corollary of the isomorphism theorem, saturated bisimilarity can be characterized as bisimilarity in the category of normalized coalgebras, i.e., abstracting away from redundant transitions. This is interesting because, on the one hand, it provides us with a canonical representatives for ~S without redundant transitions (and then much smaller with respect to the saturated ones), on the other hand, it suggests a minimization algorithm for "efficiently" computing ~S

    Behavioural equivalences for timed systems

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    Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical characterisation of timed transition systems and their behavioural theory is still missing. We introduce the first uniform framework for timed behavioural models that encompasses known behavioural equivalences such as timed bisimulations, timed language equivalences as well as their weak and time-abstract counterparts. All these notions of equivalences are naturally organised by their discriminating power in a spectrum. We prove that this result does not depend on the type of the systems under scrutiny: it holds for any generalisation of timed transition system. We instantiate our framework to timed transition systems and their quantitative extensions such as timed probabilistic systems

    A domain equation for refinement of partial systems

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