We develop formal foundations for notions and mechanisms needed to support service-oriented computing. Our work builds on recent theoretical advancements in the algebraic structures that capture the way services are orchestrated and in the processes
that formalize the discovery and binding of services to given client applications by means of logical representations of required and provided services. We show how the denotational and the operational semantics specific to conventional logic programming can be generalized using the theory of institutions to address both static and dynamic aspects of service-oriented computing. Our results rely upon a strong analogy between the discovery of a service that can be bound to an application and the search for a clause that can be used for computing an answer to a query; they explore the manner in which requests for external services can be described as service queries, and explain how the computation of their answers can be performed through service-oriented derivatives of unification and resolution, which characterize the binding of services and the reconfiguration of applications.
This paper presents an approach towards specifying and verifying adaptive distributed systems. We here take fault-handling as an example of adaptive behavior and propose a modeling language Sandal for describing fault-prone message-passing systems. O
ne of the unique mechanisms of the language is a linguistic support for abstracting typical faults such as unexpected termination of processes and random loss of messages. The Sandal compiler translates a model into a set of NuSMV modules. During the compilation process, faults specified in the model will be woven into the output. One can thus enjoy full-automatic exhaustive fault-injection without writing faulty behaviors explicitly. We demonstrate the advantage of the language by verifying a model of the two-phase commit protocol under faulty environment.
Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis. Certifyin
g the loop pipelining algorithm is challenging because there is a huge semantic gap between the input sequential design and the output pipelined implementation making it infeasible to verify their equivalence with automated sequential equivalence checking techniques. We discuss our ongoing effort using ACL2 to certify loop pipelining transformation. The completion of the proof is work in progress. However, some of the insights developed so far may already be of value to the ACL2 community. In particular, we discuss the key invariant we formalized, which is very different from that used in most pipeline proofs. We discuss the needs for this invariant, its formalization in ACL2, and our envisioned proof using the invariant. We also discuss some trade-offs, challenges, and insights developed in course of the project.
In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves on a locale and a commutative C*-algebra, a, within that topos. The Gelfand spectrum of a is a
locale S in this topos, which is equivalent to a bundle over the base locale. We further develop this external presentation of the locale S, by noting that the construction of the Gelfand spectrum in a general topos can be described using geometric logic. As a consequence, the spectrum, seen as a bundle, is computed fibrewise. As a by-product of the geometricity of Gelfand spectra, we find an explicit external description of the spectrum whenever the topos is a functor category. As an intermediate result we show that locally perfect maps compose, so that the externalization of a locally compact locale in a topos of sheaves over a locally compact locale is locally compact, too.
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the component
theories. As such, they extend the sum of two theories, which is just their unrestrained combination. Tensors of theories arise in several contexts; in particular, in the semantics of programming languages, the monad transformer for global state is given by a tensor. We present two main results: we show that the tensor of two monads need not in general exist by presenting two counterexamples, one of them involving finite powerset (i.e. the theory of join semilattices); this solves a somewhat long-standing open problem, and contrasts with recent results that had ruled out previously expected counterexamples. On the other hand, we show that tensors with bounded powerset monads do exist from countable powerset upwards.
We develop a polynomial translation from finite control pi-calculus processes to safe low-level Petri nets. To our knowledge, this is the first such translation. It is natural in that there is a close correspondence between the control flows, enjoys
a bisimulation result, and is suitable for practical model checking.
In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A. Makowsky (2009).
We demonstrate its vast applicability in simplifying known and new non-definability results of graph properties and finding new non-definability results for graph parameters. We also prove a Feferman-Vaught Theorem for the logic CFOL, First Order Logic with the modular counting quantifiers.
Meta SOS is a software framework designed to integrate the results from the meta-theory of structural operational semantics (SOS). These results include deriving semantic properties of language constructs just by syntactically analyzing their rule-ba
sed definition, as well as automatically deriving sound and ground-complete axiomatizations for languages, when considering a notion of behavioural equivalence. This paper describes the Meta SOS framework by blending aspects from the meta-theory of SOS, details on their implementation in Maude, and running examples.
There exists a rich literature of rule formats guaranteeing different algebraic properties for formalisms with a Structural Operational Semantics. Moreover, there exist a few approaches for automatically deriving axiomatizations characterizing strong
bisimilarity of processes. To our knowledge, this literature has never been extended to the setting with data (e.g. to model storage and memory). We show how the rule formats for algebraic properties can be exploited in a generic manner in the setting with data. Moreover, we introduce a new approach for deriving sound and ground-complete axiom schemata for a notion of bisimilarity with data, called stateless bisimilarity, based on intuitive auxiliary function symbols for handling the store component. We do restrict, however, the axiomatization to the setting where the store component is only given in terms of constants.
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a dis
tributive law of T over the powerset monad on categories, one is the preservation by T of exactness of certain squares. Both characterisations are generalisations of the classical results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks. The results presented in this paper enable us to compute predicate liftings of endofunctors of, for example, generalised (ultra)metric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.
