Using a Partial Order and a Metric to Analyze a Recursive Trace Set Equation

In Trace Theory the notion of a process is defined in terms of a set of finite-length traces over an alphabet. These processes are used as the semantics for a program notation. The program text for a recursive component naturally gives rise to an equation over trace sets. This paper takes two approaches at the analysis of that equation. The first approach is based on a partial order and it concentrates on the projection operator for processes. This yields a condition under which the greatest solution of that equation can be approximated by iteration. The second approach introduces a metric on the process domain. Application of Banach\u27s Contraction Theorem results in a condition under which there exists a unique solution that can be approximated by iteration starting anywhere

Rank Order Filters and Priority Queues

A derivation of a parallel algorithm for rank order filtering is presented. Both derivation and result differ from earlier designs: the derivations are less complicated and the result allows a number of different implementations. The same derivation is used to design a collection of priority queues. Both filters and priority queues are highly efficient: they have constant response time and small latency

The Mathematics of Directed Specifications

In this paper we lay a mathematical foundation for processes that communicate via directed communication channels. We start from a collection of primitive specifications. Particular correctness concerns partition this collection into equivalence classes, which can serve as abstract specifications. The theory is illustrated by taking as correctness concern absence of computation interference. In this case the abstract specification space can be identified with the space of delay-insensitive specifications

The Specification Statement Refined

In this paper, we present a rigorous treatment of so-called logical constants, which are used to relate the values of program variables between the precondition and the postcondition of a program. In order to do so, we generalize the latest proof rule for procedures and give a new definition for the specification statement. We show that the specification statement with this definition is the greatest lower bound of all its implementations under the usual refinement ordering and that it is A-distributive. We also demonstrate that a previous treatment of logical constants in specification statements does not have these properties

Quicksort in Constant Space

An in situ sorting algorithm, based on Quicksort, is presented with its proof of correctness. The proof illustrates a concise and elegant way to represent a sequence that has been partially sorted by Quicksort. A list representation turns out to be well suited to this purpose, and the discussion is entirely in terms of lists

Strategic allocation of cyclically arriving container vessels to inter-related terminals

We consider a port consisting of a cluster of inter-related terminals, where container vessels arrive cyclically. The problem is to strategically assign a terminal and a time interval of berthing to each of the vessels in the cycle. Restricting properties are terminal quay lengths and quay crane capacity. Conflicting objectives are i) minimizing the number of required quay cranes, ii) minimizing the amount of inter-terminal traffic and iii) minimizing the total weighted deviation from desired berthing intervals. We formulate both a straightforward and an alternative mixed integer linear program to model this system. Results show that the alternative model is much faster solvable and enables to optimize real-life problems within a couple of hours

On the benefit of modifying the strategic allocation of cyclically calling vessels for multi-terminal container operators

We present a case study based on a multi-terminal container operation in Antwerp, Belgium, where a set of cyclically calling container vessels is processed. The operator faces the problem of strategically allocating a terminal, a berthing interval, and a variable number of quay cranes to the vessels in the set. Restricting properties are terminal quay lengths, number of quay cranes and storage capacities. Currently, the operator's objective is to satisfy the preferences of the vessel lines, with respect to a terminal and berthing time, as much as possible. We are interested in the benefit of modifying a given allocation, i.e. the potential crane and inter-terminal costs savings if specific changes to a given allocation are allowed. An MILP is implemented in a two-step optimization, which enables us to efficiently investigate the benefit of modification. Experimental results suggest that small changes in a given allocation may lead to significant cost savings