Canonical Graph Shapes

Abstract. Graphs are an intuitive model for states of a (software) system that include pointer structures — for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary in order to arrive at a tractable model. In this paper we propose a decidable fragment of first-order graph logic that we call local shape logic (LSL) as a possible abstraction mechanism, inspired by previous work of Sagiv, Reps and Wilhelm. An LSL formula constrains the multiplicities of nodes and edges in state graphs; abstraction is achieved by reasoning not about individual, concrete state graphs but about their characteristic shape properties. We go on to define the concept of the canonical shape of a state graph, which is expressed in a monomorphic sub-fragment of LSL, for which we define a graphical representation. We show that the canonical shapes give rise to an automatic finite abstraction of the state space of a software system, and we give an upper bound to the size of this abstract state space

Portable and platform‐independent MR pulse sequence programs

Purpose: To introduce a new sequence description format for vendor‐independent MR sequences that include all calculation logic portably. To introduce a new MRI sequence development approach which utilizes flexibly reusable modules. Methods: The proposed sequence description contains a sequence module hierarchy for loop and group logic, which is enhanced by a novel strategy for performing efficient parameter and pulse shape calculation. These calculations are powered by a flow graph structure. By using the flow graph, all calculations are performed with no redundancy and without requiring preprocessing. The generation of this interpretable structure is a separate step that combines MRI techniques while actively considering their context. The driver interface is slim and highly flexible through scripting support. The sequences do not require any vendor‐specific compiling or processing step. A vendor‐independent frontend for sequence configuration can be used. Tests that ensure physical feasibility of the sequence are integrated into the calculation logic. Results: The framework was used to define a set of standard sequences. Resulting images were compared to respective images acquired with sequences provided by the device manufacturer. Images were acquired using a standard commercial MRI system. Conclusions: The approach produces configurable, vendor‐independent sequences, whose configurability enables rapid prototyping. The transparent data structure simplifies the process of sharing reproducible sequences, modules, and techniques

Graph Abstraction and Abstract Graph Transformation

Many important systems like concurrent heap-manipulating programs, communication networks, or distributed algorithms are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation of states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs supporting abstract graph transformation. The abstraction method naturally generalises previous approaches to abstract graph transformation. The set of possible abstract graphs is finite. This has the pleasant consequence of generating a finite transition system for any start graph and any finite set of transformation rules. Moreover, abstraction preserves a simple logic for expressing properties on graph nodes. The precision of the abstraction can be adjusted according to properties expressed in this logic to be verified

COSMICAH 2005: workshop on verification of COncurrent Systems with dynaMIC Allocated Heaps (a Satellite event of ICALP 2005) - Informal Proceedings

Lisboa Portugal, 10 July 200