In recent years there has been a lot of interest in the definition of so-called weakly-relational numeric domains, whose complexity and precision are in between the (non-relational) abstract domain of intervals [9] and the (relational) abstract domain of convex polyhedra [10]. The first weakly-relational domain proposed in the literature is based on systems of constraints of the form x−y ≤ c an...

Evaluators, also called \interpreters", play a variety of roles in the study of programming languages. Given this, it's surprising that we don't have a better framework for developing evaluators and specifying their relationship to each other. This paper shows that type classes in HASKELL provide an excellent framework for exploring relationships between evaluators, using abstract interpretatio...

The abstract Cauchy problem for the non-stationary bulk queue M(t)|M[k, B]|1 Abstract We derived state probability equations describing the queue M (t)| M [k, B]|1 and formulated as an abstract Cauchy problem to investigate by means of the semi-group theory of bounded linear operators in functional analysis. With regard to the abstract Cauchy problem of this queue, we determined the eigenfuncti...

Ordering optimisations are optimisations that can be applied to a concurrent logic program when the atoms of a clause are known to be ordered. In this paper ordering optimisations are reviewed, reformulated and refined. The paper explains how ordering optimisations can be realised in terms of abstract interpretation and shows that by, building on schedule analysis, simple, efficient and accurat...

Evaluators, also called \interpreters", play a variety of roles in the study of programming languages. Given this, it's surprising that we don't have a better framework for developing evaluators and specifying their relationship to each other. This paper shows that type classes in HASKELL provide an excellent framework for exploring relationships between evaluators, using abstract interpretatio...

For an operator of a certain class in Hilbert space, we introduce axioms of an abstract intersection theory, which we prove to be equivalent to the Riemann Hypothesis concerning the spectrum of that operator. In particular if the nontrivial zeros of the Riemann zeta-function arise from an operator of this class, the original Riemann Hypothesis is equivalent to the existence of an abstract inter...

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We report on several abstract interpretation strategies that are designed to improve the performance of HyTech, a symbolic model checker for linear hybrid systems. We (1) simultaneously compute the target region from di erent directions, (2) conservatively approximate the target region by dropping constraints, and (3) iteratively re ne the approximation until su cient precision is obtained. We ...

The well-founded semantics for normal logic programs is deened in a constructive way through the use of a xpoint operator and in general is not computable. We propose an approach for approximating through abstract interpretation the concrete behavior of normal logic programs described by the well-founded semantics. We provide also an abstract well-founded semantics scheme, based on an abstract ...

pack-declarator:noptr-abstract-pack-declaratorptr-operator abstract-pack-declarator