Generalized Strong Preservation by Abstract Interpretation

Standard abstract model checking relies on abstract Kripke structures which approximate concrete models by gluing together indistinguishable states, namely by a partition of the concrete state space. Strong preservation for a specification language L encodes the equivalence of concrete and abstract model checking of formulas in L. We show how abstract interpretation can be used to design abstract models that are more general than abstract Kripke structures. Accordingly, strong preservation is generalized to abstract interpretation-based models and precisely related to the concept of completeness in abstract interpretation. The problem of minimally refining an abstract model in order to make it strongly preserving for some language L can be formulated as a minimal domain refinement in abstract interpretation in order to get completeness w.r.t. the logical/temporal operators of L. It turns out that this refined strongly preserving abstract model always exists and can be characterized as a greatest fixed point. As a consequence, some well-known behavioural equivalences, like bisimulation, simulation and stuttering, and their corresponding partition refinement algorithms can be elegantly characterized in abstract interpretation as completeness properties and refinements

KAPASITAS LENTUR, TOUGHNESS, DAN STIFFNESS BALOK BETON BERSERAT POLYETHYLENE

Abstract The common problems of concrete are brittle failure and low of tension. Fiber reinforced plastic concrete is one of the alternatives to solve the problems. This research aim is to demonstrate a contribution of Polyethylene to revise the weakness of its properties. An experiment has been conducted to observe compressive strength, toughness, modulus of rupture and stiffness of fiber-polyethylene-reinforced concrete. The results show that by adding Polyethylene as a fiber in concrete material, compressive strength increases to 120.36%, moment capacity of beam increases to 115.79% and toughness increases to 318.6% compared with normal concrete. Hence, it can be stated that the addition of Polyethylene fiber has a significant contribution to increase the concrete performances. Keywords: concrete, fiber, polyethylene, stiffness, toughness

Abstract Objects in a Metaphysical Perspective

The article presents an unconventional although not absolutely unprecedented view on abstract objects defending the position of metaphysical realism. It is argued that abstract objects taken in purely ontological sense are the forms of objects. The forms possess some common characteristics of abstract objects, they can exist not in physical space and time and play a grounding role in their relation to concrete objects. It is stated that commonly discussed abstract objects – properties, kinds, mathematical objects – are forms

Soundness, idempotence and commutativity of set-sharing

It is important that practical data-flow analyzers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined and sound with respect to the concrete semantics. In logic programming, the abstract domain Sharing is a standard choice for sharing analysis for both practical work and further theoretical study. In spite of this, we found that there were no satisfactory proofs for the key properties of commutativity and idempotence that are essential for Sharing to be well-defined and that published statements of the soundness of Sharing assume the occurs-check. This paper provides a generalization of the abstraction function for Sharing that can be applied to any language, with or without the occurs-check. Results for soundness, idempotence and commutativity for abstract unification using this abstraction function are proven

Engineering design in a different way: cognitive perspective on the contact and channel model approach

Engineering design often involves the integration of new design ideas into existing products, requiring designers to think simultaneously about abstract properties and functions as well as concrete solution constraints. Often designers struggle to reason with functional descriptions, while not fixating on existing solutions. This paper introduces the Contact & Channel Model (C&CM) approach, which combines abstract functional models of technical systems with the concrete geometric descriptions that many designers are familiar with. By locating functions at working surface pairs, they receive a concrete location in mental models. The C&CM approach can be applied to analyze existing product descriptions and synthesize creative new solutions for parts of the system or for entire new systems. At the moment the approach is being developed into an complete modeling and problem solving approach. C&CM has been used for several years in undergraduate engineering teaching at the University of Karlsruhe (TH) and is increasingly being introduced into industry by its use in research and development projects, by its students and its alumni

Abstract Interpretation for Probabilistic Termination of Biological Systems

In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. In this paper, we refine the approach in order to address probabilistic termination properties. More in details, we introduce a refinement of the abstract LTS semantics and we abstract the probabilistic semantics using a variant of Interval Markov Chains. The abstract probabilistic model safely approximates a set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination

Synthesising Graphical Theories

In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum mechanics, or "Quantum Picturalism", aims to turn concrete features of quantum theory into abstract structural properties, expressed in the form of diagrammatic identities. One way we search for these properties is to start with a concrete model (e.g. a set of linear maps or finite relations) and start composing generators into diagrams and looking for graphical identities. Naively, we could automate this procedure by enumerating all diagrams up to a given size and check for equalities, but this is intractable in practice because it produces far too many equations. Luckily, many of these identities are not primitive, but rather derivable from simpler ones. In 2010, Johansson, Dixon, and Bundy developed a technique called conjecture synthesis for automatically generating conjectured term equations to feed into an inductive theorem prover. In this extended abstract, we adapt this technique to diagrammatic theories, expressed as graph rewrite systems, and demonstrate its application by synthesising a graphical theory for studying entangled quantum states.Comment: 10 pages, 22 figures. Shortened and one theorem adde