In this paper we present the algebraic-λ-cube, an extension of Barendregt's λ-cube with first- and higher-order algebraic rewriting. We show that strong normalization is a modular property of all the systems in the algebraic-λ-cube, provided that the first-order rewrite rules are non-duplicating and the higher-order rules satisfy the general schema of Jouannaud and Okada. We also prove that local confluence is a modular property of all the systems in the algebraic-λ-cube, provided that the higher-order rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence.

Sound modelling is an important part of the analysis–synthesisprocess since it combines sound processing and algorithmic synthesis within the same formalism. Its aim is to make sound simulators by synthesis methodsbased on signal modelsor physical models, the parameters of which are directly extracted from the analysis of natural sounds. In this article thesuccessive steps for making such systems are described. These are numericalsynthesis and sound generation methods, analysis of natural sounds,particularly time–frequency and time–scale (wavelet) representations, extraction of pertinent parameters, and the determinationof the correspondence between these parameters and those corresponding tothe synthesis models. Additive synthesis, nonlinear synthesis, and waveguide synthesis are discussed.

In this paper, a systematic algorithm, the Parallel Scheme, is proposed to solve the multiple-goal problem of redundant manipulators. It can adaptively adjust all the weighting factors of the corresponding goals according to their individual needs. Therefore, conflicts due to redundancy competition are resolved. To upgrade the redundancy-release capability of the original Parallel Scheme, the Improved Parallel Scheme is also developed by using the exponential function to adjust the weightings. The Improved Parallel Scheme is shown to improve both the redundancy-release capability and the weighting-adjustment capability while retaining all the merits of the original Parallel Scheme.

In this paper, the realization of biped walking on even floor, sloping surfaces, and stairs is studied. The motion trajectories for the biped's body and its two feet are modeled by piecewise cubic polynomials. The main features of the biped robot include two variable-length legs and a moving weight which can be positioned side-to-side for balance. The contribution of this paper is gait synthesis and is experimental verification.

An assembly sequence is considered to be optimal when the sequence satisfies assembly constraints and yields the minimum assembly cost. While, a line balancing solution is considered to be optimal when the solution has the minimum idle time of the line, i.e. the minimum number of workstations for a given cycle time. Although optimal assembly sequences are generated without considering line balancing, they may not guarantee the minimum number of workstations. In such case, additional cost should be required to accommodate the increased number of workstations. Therefore, it is essential to consider line balancing in the generation of cost-effective assembly sequences. To generate such line-balanced assembly sequences for robotic assembly, this paper treats a single-model and deterministic (SMD) assembly line balancing (ALB) problem, and proposes a new method using a simulated annealing. In this method, an energy function is derived in consideration of the satisfaction of assembly constraints, and the minimization of assembly cost and the idle time. Then, the energy function is iteratively minimized and occasionally perturbed by a simulated annealing. When no further change in energy occurs, a solution of assembly sequence with consideration of line balancing is finally obtained. To show the effectiveness of the proposed scheme, case studies are presented for industrial products such as an electrical relay and an automobile alternator.

The time–frequency representation (TFR) is the initial stage of analysis in sound/music analysis–resynthesis (A–R) systems. Given a time-domain waveform, the TFR makes temporal and spectral detail available to the remainder of the analysis, so that the component features may be extracted. The resulting ‘feature set’ must represent the sound as completely as the original time-domain signal, if the A–R system is to be capable of effective transformation and good synthesis sound quality. Therefore the system as a whole is reliant upon the TFR to make the sound components detectable, separable and measurable. Yet the standard TFR to-date is the short-time Fourier transform (STFT), of which the shortcomings, in terms of resolution, are well recognised. The purpose of this paper is to demonstrate the importance of the TFR to system function and system design. Poor feature extraction is shown to result from the use of inappropriate TFRs, whose underlying assumptions and expectations do not match those of the system. Existing models are used as case studies, with examples of performance for different sound types. A philosophy for A–R system design that includes TFR design is presented and a methodology for implementing it is proposed.

Most motion controls of mobile robots are based on the classical scheme of planning-navigation-piloting. The navigation function, the main part of which consists in obstacle avoidance, has to react with the shortest response time. The real-time constraint hardly limits the complexity of sensor data processing. The described navigator is built around fuzzy logic controllers. Besides the well-known possibility of taking into account human know-how, the approach provides several contributions: a low sensitivity to erroneous or inaccurate measures and, if the inputs of the controllers are normalised, an effective portability on various platform. To show these advantages, the same fuzzy navigator has been implemented on two mobile robots. Their mechanical structures are close, except for size and the sensing system.

Among the many flavours of balanced binary trees, Braun trees (Braun and Rem, 1983) are perhaps the most circumscribed. For any given node of a Braun tree, the left subtree is either exactly the same size as the right subtree, or one element larger. Braun trees always have minimum height, and the shape of each Braun tree is completely determined by its size. In return for this rigor, algorithms that manipulate Braun trees are often exceptionally simple and elegant, and need not maintain any explicit balance information.

Braun trees have been used to implement both flexible arrays (Braun and Rem, 1983; Hoogerwoord, 1992; Paulson, 1996) and priority queues (Paulson, 1996; Bird, 1996). Most operations involving a single element (e.g. adding, removing, inspecting or updating an element) take O(log n) time, since the trees are balanced. We consider three algorithmically interesting operations that manipulate entire trees. First, we give an O(log2 n) algorithm for calculating the size of a tree. Second, we show how to create a tree containing n copies of some element x in O(log n) time. Finally, we describe an order-preserving algorithm for converting a list to a tree in O(n) time. This last operation is not nearly as straightforward as it sounds!

Neural networks were used to find the inverse kinematics of a two-link planar and three-link manipulator arms. The neural networks utilised were multi-layered perceptions with a back-propagation training algorithm. Because of the redundancy in the manipulators studied, this work used lookup tables for the different configurations of the manipulator arm.

Analysis–resynthesis (A–R) systems gain their flexibility forcreative transformation of sound by representing sound as a set of musicallyuseful features. The analysis process extracts these features from the timedomain signal by means of a time–frequency representation (TFR). TheTFR provides an intermediate representation of sound that must make thefeatures accessible and measurable to the rest of the analysis. Until veryrecently, the short-time Fourier transform (STFT) has been the obviouschoice for time–frequency representation, despite its limitations interms of resolution. Recent and ongoing developments are providing severalalternative schemes that allow for a more considered choice of TFR. Thispaper reviews these contemporary approaches in comparison with the moreclassical ones and with reference to their applicability, merits andshortcomings for application to sound analysis. (Where they have beensuccessfully applied, details are provided.) The techniquesreviewed include linear, bilinear and higher-order spectra, nonparametricand parametric methods and some sound-model-specific TFRs.

A robot has to be safe and reliable. An unreliable robot may become the cause of unsafe conditions, high maintenance costs, inconvenience, etc.

Over the years, in general safety and reliability areas various assessment methods have been developed, e.g. failure mode and effects analysis, fault tree analysis, and Markovian analysis. In view of these, this paper presents an overview of the most suitable robot safety and reliability assessment techniques.

This paper introduces trust analysis for higher-order languages. Trust analysis encourages the programmer to make explicit the trustworthiness of data, and in return it can guarantee that no mistakes with respect to trust will be made at run-time. We present a confluent λ-calculus with explicit trust operations, and we equip it with a trust-type system which has the subject reduction property. Trust information is presented as annotations of the underlying Curry types, and type inference is computable in O(n3) time.

Working on Analogique B in the late 1950s, Xenakis formulated the ‘hypothesis of a second order sonority’. This paper focuses on this concept, and shows its crucial meaning in the composition of a number of pieces, such as Concret PH, Analogique B and the very recent Gendy3 and S709. Theperspective taken is twofold: on one side, the problem of 2nd-order sonorities is seen as a problem in modelling perceptual attributes (or timbre) of sound in terms of ‘emergent properties of organised sound structure’. This is also related to the composer’s pioneering work with granular sound representations and nonstandard methods of sound synthesis. On the other, the issue is discussed in conjunction with Xenakis’ attempt at implementing thoroughly formalised ‘mechanisms’ or ‘systems’ based on the mathematics of stochastic processes. The paper shows that the issue touched on here is essential to the aesthetics of Xenakis’ electroacoustic music. It also questions whether the formalisation of stochastics is a suitable means to let 2nd-order sonorities emerge from the internal life of the sound matter. The limitations of Xenakis’ ‘mechanisms’ are described in terms of their cybernetics, and are situated in the context of artistic and scientific paradigm shifts concerning the relationship between order, disorder and chaos.

We constructed a high reliability parts-picking device with an active and multi-sensor visual system, that picks up a part from randomly stacked parts. The system determines the orders in which to pick up the parts. To determine the order, we introduce concepts of risks of collapsing a stack by picking, and the ease of manipulator operations. The system examines if the risks exist and estimates the ease. We show that the parts-picking system can achieve high reliability by determining the orders, using the effects of the examination and the estimation. We also give some experimental results.

A combinatory system (or equivalently the set of its basic combinators) is called combinatorially complete for a functional system, if any member of the latter can be defined by an entity of the former system. In this paper the decision problem of combinatory completeness for finite sets of proper combinators is studied for three subsystems of the pure lambda calculus. Precise characterizations of proper combinator bases for the linear and the affine λ-calculus are given, and the respective decision problems are shown to be decidable. Furthermore, it is determined which extensions with proper combinators of bases for the linear λ-calculus are combinatorially complete for the λI-calculus.

Algebraic CPOs naturally generalize to finitely accessible categories, and Scott domains (i.e., consistently complete algebraic CPOs) then correspond to what we call Scott-complete categories: finitely accessible, consistently (co-)complete categories. We prove that the category SCC of all Scott-complete categories and all continuous functors is cartesian closed and provides fixed points for a large collection of endofunctors. Thus, SCC can serve as a basis for semantics of computer languages.

We construct an approximating chain of simple valuations on the upper space of a compact metric space whose lub is a given probability measure on the metric space. We show that whenever a separable metric space is homeomorphic to a Gδ subset of an ω-continuous dcpo equipped with its Scott topology, the space of probability measures of the metric space equipped with the weak topology is homeomorphic with a subset of the maximal elements of the probabilistic power domain of the ω-continuous dcpo. Given an effective approximation of a probability measure by an increasing chain of normalised valuations on the upper space of a compact metric space, we show that the expected value of any Hölder continuous function on the space can be obtained up to any given accuracy. We present a novel application in computing integrals in dynamical systems. We obtain an algorithm to compute the expected value of any Hölder continuous function with respect to the unique invariant measure of the Feigenbaum map in the periodic doubling route to chaos.

We propose a uniform way of isolating a subcategory of predomains within the category of modest sets determined by a partial combinatory algebra (PCA). Given a divergence on a PCA (which determines a notion of partiality), we identify a candidate category of predomains, the well-complete objects. We show that, whenever a single strong completeness axiom holds, the category satisfies appropriate closure properties. We consider a range of examples of PCAs with associated divergences and show that in each case the axiom does hold. These examples encompass models allowing a ‘parallel’ style of computation (for example, by interleaving), as well as models that seemingly allow only ‘sequential’ computation, such as those based on term-models for the lambda-calculus. Thus, our approach provides a uniform approach to domain theory across a wide class of realizability models. We compare our treatment with previous approaches to domain theory in realizability models. It appears that no other approach applies across such a wide range of models.

Domain-theoretic categories are axiomatised by means of categorical non-order-theoretic requirements on a cartesian closed category equipped with a commutative monad. In this paper we prove an enrichment theorem showing that every axiomatic domain-theoretic category can be endowed with an intensional notion of approximation, the path relation, with respect to which the category Cpo-enriches.

Our analysis suggests more liberal notions of domains. In particular, we present a category where the path order is not ω-complete, but in which the constructions of domain theory (such as, for example, the existence of uniform fixed-point operators and the solution of domain equations) are available.