Verification of parallel systems via decomposition

Recently, Milner and Moller have presented several decomposition results for processes. Inspired by these, we investigate decomposition techniques for the verification of parallel systems. In particular, we consider those of the form q j (I) where p i and q j are (finite) state systems. We provide a decomposition procedure for all p i and q j and give criteria that must be checked on the decomposed processes to see whether (I) does or does not hold. We analyse the complexity of our procedure and show that it is polynomial in n, m and the sizes of p i and q j if there is no communication. We also show that with communication the verification of (I) is co-NP hard, which makes it very unlikely that a polynomial complexity bound exists. But by applying our decomposition technique to Milner's cyclic scheduler we show that verification can become polynomial in space and time for practical examples, where standard techniques are exponential. Note: The authors are supported by the European Communities under ESPRIT Basic Research Action 3006 (CONCUR)

Refining SCJ Mission Specifications into Parallel Handler Designs

Safety-Critical Java (SCJ) is a recent technology that restricts the execution and memory model of Java in such a way that applications can be statically analysed and certified for their real-time properties and safe use of memory. Our interest is in the development of comprehensive and sound techniques for the formal specification, refinement, design, and implementation of SCJ programs, using a correct-by-construction approach. As part of this work, we present here an account of laws and patterns that are of general use for the refinement of SCJ mission specifications into designs of parallel handlers used in the SCJ programming paradigm. Our notation is a combination of languages from the Circus family, supporting state-rich reactive models with the addition of class objects and real-time properties. Our work is a first step to elicit laws of programming for SCJ and fits into a refinement strategy that we have developed previously to derive SCJ programs.Comment: In Proceedings Refine 2013, arXiv:1305.563

Graphical Verification of a Spatial Logic for the Graphical Verification of a Spatial Logic for the pi-calculus

The paper introduces a novel approach to the verification of spatial properties for finite [pi]-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of pi-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula)

Parallelization of Modular Algorithms

In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional ideal and describe their parallel implementation in SINGULAR. Our modular algorithms to solve problems over Q mainly consist of three parts, solving the problem modulo p for several primes p, lifting the result to Q by applying Chinese remainder resp. rational reconstruction, and a part of verification. Arnold proved using the Hilbert function that the verification part in the modular algorithm to compute Gr\"obner bases can be simplified for homogeneous ideals (cf. \cite{A03}). The idea of the proof could easily be adapted to the local case, i.e. for local orderings and not necessarily homogeneous ideals, using the Hilbert-Samuel function (cf. \cite{Pf07}). In this paper we prove the corresponding theorem for non-homogeneous ideals in case of a global ordering.Comment: 16 page