States and the free orthogonality monoid

Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let (, ) denote the free orthogonality monoid over (X, #). Let C₀(, ) be the subset of C(, ), consisting of all closures of bounded orthogonal sets. We show that C₀(, ) is a suborthomodular lattice of C(, ) and we provide a necessary and sufficient condition for C₀(, ) to carry a full set of dispersion free states.The work of the second author on this paper was supported by National Science Foundation Grant GP-9005.     

A New Implementation of Automath

This paper presents aut, a modern Automath checker. It is a straightforward re-implementation of the Zandleven Automath checker from the seventies. It was implemented about five years ago, in the programming language C. It accepts both the AUT-68 and AUT-QE dialects of Automath. This program was written to restore a damaged version of Jutting's translation of Landau's Grundlagen. Some notable features: It is fast. On a 1 GHz machine it will check the full Jutting formalization (736 K of nonwhitespace Automath source) in 0.6 seconds. Its implementation of -terms does not use named variables or de Bruijn indices (the two common approaches) but instead uses a graph representation. In this representation variables are represented by pointers to a binder. The program can compile an Automath text into one big Automath single line-style -term. It outputs such a term using de Bruijn indices. (These -terms cannot be checked by modern systems like Coq or Agda, because the -typed -calculi of de Bruijn are different from the -typed -calculi of modern type theory.)The source of aut is freely available on the Web at the address .     

Automated Proof Construction in Type Theory Using Resolution

We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. A clausification procedure in type theory, equipped with a correctness proof, all encoded using higher-order primitive recursion. A novel representation of clauses in minimal logic such that the -representation of resolution steps is linear in the size of the premisses. A translation of resolution proofs into lambda terms, yielding a verification procedure for those proofs. Availability of the power of resolution theorem provers in interactive proof construction systems based on type theory.     

A Full Bayesian Approach to Curve and Surface Reconstruction

When interpolating incomplete data, one can choose a parametric model, or opt for a more general approach and use a non-parametric model which allows a very large class of interpolants. A popular non-parametric model for interpolating various types of data is based on regularization, which looks for an interpolant that is both close to the data and also smooth in some sense. Formally, this interpolant is obtained by minimizing an error functional which is the weighted sum of a fidelity term and a smoothness term.The classical approach to regularization is: select optimal weights (also called hyperparameters) that should be assigned to these two terms, and minimize the resulting error functional.However, using only the optimal weights does not guarantee that the chosen function will be optimal in some sense, such as the maximum likelihood criterion, or the minimal square error criterion. For that, we have to consider all possible weights.The approach suggested here is to use the full probability distribution on the space of admissible functions, as opposed to the probability induced by using a single combination of weights. The reason is as follows: the weight actually determines the probability space in which we are working. For a given weight , the probability of a function f is proportional to exp(– f² _uu du) (for the case of a function with one variable). For each different , there is a different solution to the restoration problem; denote it by f. Now, if we had known , it would not be necessary to use all the weights; however, all we are given are some noisy measurements of f, and we do not know the correct . Therefore, the mathematically correct solution is to calculate, for every , the probability that f was sampled from a space whose probability is determined by , and average the different f's weighted by these probabilities. The same argument holds for the noise variance, which is also unknown.Three basic problems are addressed is this work: Computing the MAP estimate, that is, the function f maximizing Pr(f/D) when the data D is given. This problem is reduced to a one-dimensional optimization problem. Computing the MSE estimate. This function is defined at each point x as f(x)Pr(f/D) f. This problem is reduced to computing a one-dimensional integral.In the general setting, the MAP estimate is not equal to the MSE estimate. Computing the pointwise uncertainty associated with the MSE solution. This problem is reduced to computing three one-dimensional integrals.     

Software Quality Evaluation Based on Expert Judgement

A method using expert judgement for the evaluation of software quality is presented. The underlying principle of the approach is the encoding of experts' tacit knowledge into probabilistic measures associated with the achievement level of software quality attributes. An aggregated quality measure is obtained based on preference statements related to the quality attributes. The technical objectives of the paper are to develop of a generic and operationally feasible measurement technique to transform the tacit knowledge of a software expert to a probability distribution depicting his/her uncertainty of the level of achievement related to a quality attribute; to develop rules for the construction of a consensus probability measure based on expert-specific probability measures; to derive a framework for specifying software quality strategy and for evaluating the acceptance of a software produced in a software development process;The above technical developments are used to support group decision-making regarding the launch or implementation decision of a software version; the allocation of resources during the software development process.     

A model implementation for protective domains

A combination hardware/software mechanism is presented which supports very general capabilities for the protection of and controlled access to sharable information structures. It is defined through symbolic algorithms in terms of the dedicated model hardware. The model centers on two key concepts, that of thetenant, who is a storage holding entity, and that of thedomain, which is an information accessing entity. The domain, defined as a capsular collection of mutually accessible information structures having a single common external protective interface, is an integral part of the hardware logic. It is contended that the definition of a mechanism to enforce access authorizations must include an underlying philosophy specifying the conditions under which such access authorizations may be granted. Such a philosophy is suggested. It is based on theprinciple of ownership according to which any area of storage is at all times held by a single tenant who has the exclusive right to grant/revoke access privileges to his proprietary information structures, i.e., information residing in proprietary storage.This is an extensively revised version of a paper presented under the title A Computer System Model for Controlled Sharing of Information at ONLINE72, September 1972, Brunel University, Uxbridge, Middlesex, England. Republished by permission of ONLINE72.Work reported in this paper is of a theoretical nature and may not be construed to imply any product commitment by the Digital Equipment Corporation, Maynard, Massachusetts.     

Enhancing the performance of an agent-based manufacturing system through learning and forecasting

Agent-based technology has been identified as an important approach for developing next generation manufacturing systems. One of the key techniques needed for implementing such advanced systems will be learning. This paper first discusses learning issues in agent-based manufacturing systems and reviews related approaches, then describes how to enhance the performance of an agent-based manufacturing system through learning from history (based on distributed case-based learning and reasoning) and learning from the future (through system forecasting simulation). Learning from history is used to enhance coordination capabilities by minimizing communication and processing overheads. Learning from the future is used to adjust promissory schedules through forecasting simulation, by taking into account the shop floor interactions, production and transportation time. Detailed learning and reasoning mechanisms are described and partial experimental results are presented.     

Logic Based Abstractions of Real-Time Systems

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called , n-equivalence, where is a set of actions and n is a natural number. It is proved that two transition systems are , n-equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in , and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set of actions and a natural number n, produces a reduced transition system , n-equivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving , n-equivalence.     

Sound and Complete Qualitative Simulation Needs “Quantitative” Filtering

The AI methodology of qualitative reasoning furnishes useful tools to scientists and engineers who need to deal with incomplete system knowledge during design, analysis, or diagnosis tasks. Qualitative simulators have a theoretical soundness guarantee; they cannot overlook any concrete equation implied by their input. On the other hand, the basic qualitative simulation algorithms have been shown to suffer from the incompleteness problem; they may allow non-solutions of the input equation to appear in their output. The question of whether a simulator with purely qualitative input which never predicts spurious behaviors can ever be achieved by adding new filters to the existing algorithm has remained unanswered. In this paper, we show that, if such a sound and complete simulator exists, it will have to be able to handle numerical distinctions with such a high precision that it must contain a component that would better be called a quantitative, rather than qualitative reasoner. This is due to the ability of the pure qualitative format to allow the exact representation of the members of a rich set of numbers.     

Redesign of a Systems Engineering Language: Formalisation of χ

This paper describes the redesign of a systems engineering language called . This is an engineering language designed to specify and analyse industrial systems. The main objective of this redesign was to enable mathematical reasoning about specifications. We discuss the original language, the requirements and design decisions, and the resulting syntax and semantics of the new version of , called . In particular, we elaborate on semantical aspects of s time model.     

Choosing reference classes and building provisional models

A well-known problem in default logic is the ability of naive reasoners to explain bothg and ¬g from a set of observations. This problem is treated in at least two different ways within that camp.One approach is examination of the various explanations and choosing among them on the basis of various explanation comparators. A typical comparator is choosing the explanation that depends on the most specific observation, similar to the notion of narrowest reference class.Others examine default extensions of the observations and choose whatever is true in any extension, or what is true in all extensions or what is true in preferred extensions. Default extensions are sometimes thought of as acceptable models of the world that are discarded as more knowledge becomes available.We argue that the notions of specificity and extension lack clear semantics. Furthermore, we show that the problems these ideas were supposed to solve can be handled easily within a probabilistic framework.     

Barely Random Algorithms for Multiprocessor Scheduling

We consider randomized algorithms for on-line scheduling on identical machines. For two machines, a randomized algorithm achieving a competitive ratio of was found by Bartal et al. (1995). Seiden has presented a randomized algorithm which achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295, and 1.81681, for m=3,4,5,6,7, respectively (Seiden, 2000). A barely random algorithm is one which is a distribution over a constant number of deterministic strategies. The algorithms of Bartal et al. and Seiden are not barely random–in fact, these algorithms potentially make a random choice for each job scheduled. We present the first barely random on-line scheduling algorithms. In addition, our algorithms use less space and time than the previous algorithms, asymptotically.     

Circuit-Switched Broadcasting in Multi-Port Multi-Dimensional Torus Networks

The one-to-all broadcast is the most primary collective communication pattern in a multicomputer network. This paper studies this problem in a circuit-switched torus with -port capability, where a node can simultaneously send and receive messages at one time. This is a generalization of the one-port and all-port models. We show how to efficiently perform broadcast in tori of any dimension, any size, square or nonsquare, using near optimal numbers of steps. The main techniques used are: (i) a span-by-dimension approach, which makes our solution scalable to torus dimensions, and (ii) a squeeze-then-expand approach, which makes possible solving the difficult cases where tori are non-square. Existing results, as compared to ours, can only solve very restricted sizes or dimensions of tori, or use more numbers of steps.     

A variotherm mold for micro metal injection molding

In this paper, a variotherm mold was designed and fabricated for the production of 316L stainless steel microstructures by micro metal injection molding (MIM). The variotherm mold incorporated a rapid heating/cooling system, vacuum unit, hot sprue and cavity pressure transducer. The design of the variotherm mold and the process cycle of MIM using the variotherm mold were described. Experiments were conducted to evaluate the molded microstructures produced using variotherm mold and conventional mold. The experiments showed that microstructures of higher aspect ratio such as 60 m × height 191 m and 40 m × height 174 m microstructures could be injection molded with complete filling and demolded successfully using the variotherm mold. Molded microstructures with dimensions of 60 m × height 191 m were successfully debound and sintered without visual defects.     

Path Integration on a Quantum Computer

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^-k with k>1. For the Wiener measure occurring in many applications we have k=2. We want to compute an -approximation to path integrals whose integrands are at least Lipschitz. We prove: Path integration on a quantum computer is tractable. Path integration on a quantum computer can be solved roughly ^-1 times faster than on a classical computer using randomization, and exponentially faster than on a classical computer with a worst case assurance. The number of quantum queries needed to solve path integration is roughly the square root of the number of function values needed on a classical computer using randomization. More precisely, the number of quantum queries is at most 4.46 ^-1. Furthermore, a lower bound is obtained for the minimal number of quantum queries which shows that this bound cannot be significantly improved. The number of qubits is polynomial in ^-1. Furthermore, for the Wiener measure the degree is 2 for Lipschitz functions, and the degree is 1 for smoother integrands. PACS: 03.67.Lx; 31.15Kb; 31.15.-p; 02.70.-c     

Measurement and defect modeling for a legacy software system

This paper analyzes the quality of a large-scale legacy software system using selected metrics. Quality measurements include defect information collected during product development and in-field operation. Other software metrics include measurements on various product and process attributes, including design, size, change, and complexity. Preliminary analyses revealed the high degree of skew in our data and a weak correlation between defects and software metrics. Tree-based models were then used to uncover relationships between defects and software metrics, and to identify high-defect modules together with their associated measurement characteristics. As results presented in tree forms are natural to the decision process and are easy to understand, tree-based modeling is shown to be suitable for change solicitation and useful in guiding remedial actions for quality improvement.The following are trademarks or service marks in the United States and/or other countries: IBM is a trademark of International Business Machines Corporation. REFINE and Software Refinery are trademarks of Reasoning Systems Inc. SAS is a trademark of the SAS Institute Inc. S-PLUS is a trademark of the Statistical Sciences, Inc.     

From Conditional Events to Conditional Measures: A New Axiomatic Approach

Our starting point is a definition of conditional event EH which differs from many seemingly similar ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same third value u (undetermined) to all conditional events, but make it depend on EH, it turns out that this function t(EH) can be taken as a general conditional uncertainty measure, and we get (through a suitable – in a sense, compulsory – choice of the relevant operations among conditional events) the natural axioms for many different (besides probability) conditional measures.     

On-line Learning and the Metrical Task System Problem

The problem of combining expert advice, studied extensively in the Computational Learning Theory literature, and the Metrical Task System (MTS) problem, studied extensively in the area of On-line Algorithms, contain a number of interesting similarities. In this paper we explore the relationship between these problems and show how algorithms designed for each can be used to achieve good bounds and new approaches for solving the other. Specific contributions of this paper include: An analysis of how two recent algorithms for the MTS problem can be applied to the problem of tracking the best expert in the decision-theoretic setting, providing good bounds and an approach of a much different flavor from the well-known multiplicative-update algorithms. An analysis showing how the standard randomized Weighted Majority (or Hedge) algorithm can be used for the problem of combining on-line algorithms on-line, giving much stronger guarantees than the results of Azar, Y., Broder, A., & Manasse, M. (1993). Proc ACM-SIAM Symposium on Discrete Algorithms (pp. 432–440) when the algorithms being combined occupy a state space of bounded diameter. A generalization of the above, showing how (a simplified version of) Herbster and Warmuth's weight-sharing algorithm can be applied to give a finely competitive bound for the uniform-space Metrical Task System problem. We also give a new, simpler algorithm for tracking experts, which unfortunately does not carry over to the MTS problem.Finally, we present an experimental comparison of how these algorithms perform on a process migration problem, a problem that combines aspects of both the experts-tracking and MTS formalisms.     

End-to-end communications management using TMN “X” interfaces

The ongoing integration of LANs and WANs to support global communications and businesses and the emergence of integrated broadband communication services has created an increased demand for cooperation between customers, network and service providers to achieve end-to-end service management. Such a cooperation between autonomous authorities, each defining their own administrative management domains, requires the application of an open standardized framework to facilitate and regulate interworking. Such a framework is given by the ITU-T recommendations on TMN, where the so-called X interface is of particular importance for inter-domain management. In this paper, we explain the role of the TMN X interface within an inter-domain TMN architecture supporting end-to-end communications management. We identify the important issues that need to be addressed for the definition and realization of TMN X interfaces and report about our practical experiences with the implementation of TMN X interfaces in the PREPARE project.     

Unitary immersions of nonlinear systems

In this paper, we define what we call a unitary immersion of a nonlinear system. We observe that, for classical Hamiltonian systems, this notion contains, in some sense, the concept of quantization. We restrict our attention to degree-zero unitary immersions, where all observation functions must be represented by operators of the type multiplication by a function. We show that the problem of classifying such degree-zero unitary immersions of a given nonlinear system is not obvious. In some cases, we solve this problem.Chargé de Recherche au CNRS.Maître de Conférences.