We construct a double category [Dscr] of proof-nets in multiplicative linear logic (MLL). Its horizontal arrows are MLL modules (subnets of well-formed nets), its vertical arrows model side-effects, and its double cells interpret the cut-elimination procedure. The categorical model is modular in the sense that every computation of a composite module (π1; π2) factors out as the separate and interacting computations of the two subcomponents π1 and π2. This enables us to trace MLL modules in the course of cut-elimination, and analyze their behaviour in time.

This paper describes a family of logics whose categorical semantics is based on functors with structure rather than on categories with structure. This allows the consideration of logics that contain possibly distinct logical subsystems whose interactions are mediated by functorial mappings. For example, within one unified framework, we shall be able to handle logics as diverse as modal logic, ordinary linear logic, and the ‘noncommutative logic’ of Abrusci and Ruet, a variant of linear logic that has both commutative and noncommutative connectives.

Although this paper will not consider in depth the categorical basis of this approach to logic, preferring instead to emphasise the syntactic novelties that it generates in the logic, we shall focus on the particular case when the logics are based on a linear functor, in order to give a definite presentation of these ideas. However, it will be clear that this approach to logic has considerable generality.

Frequently, mathematical structures of a certain type and their morphisms fail to form a category for lack of composability of the morphisms; one example of this problem is the class of probabilistic automata when equipped with morphisms that allow restriction as well as relabelling. The proper mathematical framework for this situation is provided by a generalisation of category theory in the shape of the so-called precategories, which are introduced and studied in this paper. In particular, notions of adjointness, weak adjointness and partial adjointness for precategories are presented and justified in detail. This makes it possible to use universal properties as characterisations of well-known basic constructions in the theory of (generative) probabilistic automata: we show that accessible automata and decision trees, respectively, form coreflective subprecategories of the precategory of probabilistic automata. Moreover, the aggregation of two automata is identified as a partial product, whereas restriction and interconnection of automata are recognised as Cartesian lifts.

Graph rewriting has been used extensively to model the behaviour of concurrent systems and to provide a formal semantics for them. In this paper, we investigate processes for Local Action Systems (LAS); LAS generalize several types of graph rewriting based on node replacement and embedding. An important difference between processes for Local Action Systems and the process notions that have been introduced for other systems, for example, Petri nets, is the presence of a component describing the embedding mechanism. The aim of the paper is to develop a methodology for dealing with this embedding mechanism: we introduce a suitable representation (a dynamic structure) for it, and then investigate the algebraic properties of this representation. This leads to a simple characterization of the configurations of a process and to a number of equational laws for dynamic structures. We illustrate the use of these laws by providing an equational proof of one of the basic results for LAS processes, namely that the construction yielding the result graph of a process behaves well with respect to the sequential composition of processes.

Graph pattern matching is a central problem in many application fields. Since it is NP-complete, we cannot expect to find algorithms with a good worst-case performance. However, there is still room for general procedures with a good average performance. In this paper we explore four different solving approaches within the constraint satisfaction framework, and introduce a new algorithm, which we call nRF+. The algorithm is a refinement of really full look ahead that takes advantage of the problem structure in order to enhance the look ahead procedure. We give a formal proof that nRF+ is superior to the other approaches in terms of number of visited nodes. An additional contribution of this paper is the introduction of a new benchmark for testing algorithms in this domain. It is formed by a large set of well-defined graphs of very diverse nature. In this benchmark, we show that nRF+ can efficiently solve a broad range of problems, while still leaving many problem instances unsolved. The use of this challenging benchmark is encouraged for future algorithms evaluation.

Graph transitions represent an extension of the DPO approach to graph transformation for the specification of reactive systems. In this paper, we develop the theory of concurrency for graph transitions. In particular, we prove a local Church–Rosser theorem and define a notion of shift-equivalence that allows us to represent both intra-concurrency (within the specified subsystem) and inter-concurrency (between subsystem and environment). Via an implementation of transitions in terms of DPO transformations with context rules, a second, more restrictive notion of equivalence is defined that captures, in addition, the extra-concurrency (between operations of the environment). As a running example and motivation, we show how the concepts of this paper provide a formal model for distributed information systems.

This paper details a partial order semantics for families of scenarios represented by High-Level Message Sequence Charts (HMSCs): graph grammars generating event structures are used to represent HMSCs. A decision procedure for HMSC equivalence is then described. This can be considered as a first step towards the formal manipulation of scenarios.

This paper discusses a technique for identifying the joint parameters of a modular robot in order to study the dynamic characteristics of the whole structure and to realise dynamic control. A method for identifying the joint parameters of the structure applying fuzzy logic combined with a genetic algorithm has been studied using a 9-DOF modular redundant robot. A Genetic Algorithm was used in the fuzzy optimisation, which helped to avoid converging to locally optimal solutions and made the results identified much more reasonable. The joint parameters of a 9-DOF modular redundant robot have been identified.

This article focuses on research at the MEC, giving three examples of areas of concerted activities at the Centre: intelligent manufacturing, concurrent engineering and rapid manufacturing.

Let {Av}v∈V be a finite collection of events and G = (V, E) be a chordal graph. Our main result – the chordal graph sieve – is a Bonferroni-type inequality where the selection of intersections in the estimates is determined by a chordal graph G. It interpolates between Boole's inequality (G empty) and the sieve formula (G complete). By varying G, several inequalities both well-known and new are obtained in a concise and unified way.

We show that the limiting distribution of the number of comparisons used by Hoare's quickselect algorithm when given a random permutation of n elements for finding the mth-smallest element, where m = o(n), is the Dickman function. The limiting distribution of the number of exchanges is also derived.

Planar parallel manipulators, with potential applications in high speed, high acceleration tasks such as electronic component placement, would be subject to mechanical vibration due to high inertial forces acting on the linkages and other components. To achieve high throughput capability, such motion induced vibration would have to be damped quickly, to reduce settling time of the platform position and orientation. This paper develops a two-time scale dynamic model of a three-degree-of-freedom planar parallel manipulator with structurally flexible linkages. Based on the two-time scale model, a composite controller, consisting of a computed torque controller for the slow time-scale or rigid body subsystem dynamics, and a linear-quadratic state-feedback regulator for the fast time-scale flexible dynamic subsystem, is designed. Simulation results show that the composite control scheme permits the parallel manipulator platform to follow a given desired trajectory, while damping structural vibration arising due to excitation from inertial forces.

We show that, if G is a graph of order n with maximal degree Δ(G) and minimal degree δ(G) whose complement contains no K2,s, s [ges ] 2, then G contains every tree T of order n−s+1 whose maximal degree is at most Δ(G) and whose vertex of second-largest degree is at most δ(G). We then show that this result implies that special cases of two conjectures are true. We verify that the Erdös–Sós conjecture, which states that a graph whose average degree is larger than k−1 contains every tree of order k+1, is true for graphs whose complement does not contain a K2,4, and the Komlós–Sós conjecture, which states that every graph of median degree at least k contains every tree of order k+1, is true for graphs whose complement does not contain a K2,3.

Consider a finite alphabet Ω and patterns which consist of characters from Ω. For a given pattern w, let cor(w) denote its autocorrelation, which can be seen as a measure of the amount of overlap in w. Letting aw(n) denote the number of strings over Ω of length n which do not contain w as a substring, the main result of this paper is: If cor(w) > cor(w′) then aw(n)−aw′(n) > (|Ω|−1)(aw(n−1)−aw′(n−1)) for n [ges ] N, and the value of N is given. This result confirms a conjecture by Eriksson [2], which was previously proved to be true by Cakir, Chryssaphinou and Månsson [1] when |Ω| [ges ] 3.