Verifying programs in the calculus of inductive constructions

This paper deals with a particular approach to the verification of functional programs. A specification of a program can be represented by a logical formula [Con86, NPS90]. In a constructive framework, developing a program then corresponds to proving this formula. Given a specification and a program, we focus on reconstructing a proof of the specification whose algorithmic contents corresponds to the given program. The best we can hope is to generate proof obligations on atomic parts of the program corresponding to logical properties to be verified. First, this paper studies a weak extraction of a program from a proof that keeps track of intermediate specifications. From such a program, we prove the determinism of retrieving proof obligations. Then, heuristic methods are proposed for retrieving the proof from a natural program containing only partial annotations. Finally, the implementation of this method as a tactic of theCoq proof assistant is presented.This research was partly supported by ESPRIT Basic Research Action Types for Proofs and Programs and by Programme de Recherche Coordonnes and CNRS Groupement de Recherche Programmation.     

The risk-sensitive index and theH 2 andH ∞, norms for nonlinear systems

In this paper we study two measures of the size of systems, namely, the so-calledH ₂ and H norms. These measures are important tools for determining the influence of disturbances on performance. We show that the risk-sensitive index on an infinite time horizon contains detailed information concerning these measures, via small noise and small risk limits.The authors wish to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program. The first author was partially supported by AFOSR F49620-92-J-0081, ARO DAAL03-92-G-0115, and NSF DMS-9300048.     

Provably good approximation algorithms for optimal kinodynamic planning: Robots with decoupled dynamics bounds

We consider the following problem: given a robot system, find a minimal-time trajectory that goes from a start state to a goal state while avoiding obstacles by a speed-dependent safety margin and respecting dynamics bounds. In [1] we developed a provably good approximation algorithm for the minimum-time trajectory problem for a robot system with decoupled dynamics bounds (e.g., a point robot in ³). This algorithm differs from previous work in three ways. It is possible (1) to bound the goodness of the approximation by an error term; (2) to bound the computational complexity of our algorithm polynomially; and (3) to express the complexity as a polynomial function of the error term. Hence, given the geometric obstacles, dynamics bounds, and the error term, the algorithm returns a solution that is-close to optimal and requires only a polynomial (in (1/)) amount of time.We extend the results of [1] in two ways. First, we modify it to halve the exponent in the polynomial bounds from 6d to 3d, so that the new algorithm isO(c ^d N 1/)^3d ), whereN is the geometric complexity of the obstacles andc is a robot-dependent constant. Second, the new algorithm finds a trajectory that matches the optimal in time with an factor sacrificed in the obstacle-avoidance safety margin. Similar results hold for polyhedral Cartesian manipulators in polyhedral environments.The new results indicate that an implementation of the algorithm could be reasonable, and a preliminary implementation has been done for the planar case.This paper describes research done at the Computer Science Robotics Laboratory at Cornell University. Support for our robotics research there is provided in part by the National Science Foundation under Grant Nos. IRI-8802390 and IRI-9000532, by a Presidential Young Investigator award, and in part by the Mathematical Sciences Institute, Intel Corporation, and AT&T Bell Laboratories.     

Provably good approximation algorithms for optimal kinodynamic planning for Cartesian robots and open-chain manipulators

Inoptimal kinodynamic planning, given a robot system, we must find a minimal-time trajectory that goes from a start state to a goal state while avoiding obstacles by a speed-dependent safety margin and respecting dynamics bounds. With Canny and Reif [1], we approached this problem from an-approximation standpoint and introduced a provably good approximation algorithm for optimal kinodynamic planning for a robot obeying particle dynamics. If a solution exists, this algorithm returns a trajectory-close to optimal in time polynomial in both (1/) and the geometric complexity.We extend [1] and [2] tod-link three-dimensional robots with full rigid-body dynamics amidst obstacles. Specifically, we describe polynomial-time approximation algorithms for Cartesian robots obeyingL ₂ dynamic bounds and for open-kinematic-chain manipulators with revolute and prismatic joints. The latter class includes many industrial manipulators. The correctness and complexity of these algorithms rely on new trajectory tracking lemmas for robots with coupled dynamics bounds.This paper describes research done at the Computer Science Robotics Laboratory at Cornell University. Support for our robotics research there is provided in part by the National Science Foundation under Grant Nos. IRI-8802390 and IRI-9000532, by a Presidential Young Investigator award, and in part by the Mathematical Sciences Institute, Intel Corporation, and AT&T Bell Laboratories.     

Finite Computation of the ℓ1 Estimator from Huber’s M-Estimator in Linear Regression

We review and extend previous work on the approximation of the linear ₁ estimator by the Huber M-estimator based on the algorithms proposed by Clark and Osborne [7], and Madsen and Nielsen [12]. Although the Madsen-Nielsen algorithm is a promising one, it is guaranteed to terminate finitely under certain assumptions. We describe a variant of the Madsen-Nielsen algorithm to compute the ₁ estimator from the Huber M-estimator in a finite number of steps without any restrictive steps nor assumptions. Summary computational results are given.     

Maximum queue size and hashing with lazy deletion

We answer questions about the distribution of the maximum size of queues and data structures as a function of time. The concept of maximum occurs in many issues of resource allocation. We consider several models of growth, including general birth-and-death processes, the M/G/ model, and a non-Markovian process (data structure) for processing plane-sweep information in computational geometry, called hashing with lazy deletion (HwLD). It has been shown that HwLD is optimal in terms of expected time and dynamic space; our results show that it is also optimal in terms of expectedpreallocated space, up to a constant factor.We take two independent and complementary approaches: first, in Section 2, we use a variety of algebraic and analytical techniques to derive exact formulas for the distribution of the maximum queue size in stationary birth-and-death processes and in a nonstationary model related to file histories. The formulas allow numerical evaluation and some asymptotics. In our second approach, in Section 3, we consider the M/G/ model (which includes M/M/ as a special case) and use techniques from the analysis of algorithms to get optimal big-oh bounds on the expected maximum queue size and on the expected maximum amount of storage used by HwLD in excess of the optimal amount. The techniques appear extendible to other models, such as M/M/1.Research was also done while the author was at Princeton University, supported in part by a Procter Fellowship.Research was also done while the author was on sabbatical at INRIA in Rocquencourt, France, and at Ecole Normale Supérieure in Paris, France. Support was provided in part by National Science Foundation Research Grant DCR-84-03613, by an NSF Presidential Young Investigator Award with matching funds from an IBM Faculty Development Award and an AT&T research grant, by a Guggenheim Fellowship, and by the Office of Naval Research and the Defense Advanced Research Projects Agency under Contract N00014-83-K-0146 and ARPA Order 6320, Amendment 1.     

High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes

In this paper we construct several numerical approximations for first order Hamilton–Jacobi equations on triangular meshes. We show that, thanks to a filtering procedure, the high order versions are non-oscillatory in the sense of satisfying the maximum principle. The methods are based on the first order Lax–Friedrichs scheme [2] which is improved here adjusting the dissipation term. The resulting first order scheme is -monotonic (we explain the expression in the paper) and converges to the viscosity solution as for the L -norm. The first high order method is directly inspired by the ENO philosophy in the sense where we use the monotonic Lax–Friedrichs Hamiltonian to reconstruct our numerical solutions. The second high order method combines a spatial high order discretization with the classical high order Runge–Kutta algorithm for the time discretization. Numerical experiments are performed for general Hamiltonians and L ¹, L ² and L -errors with convergence rates calculated in one and two space dimensions show the k-th order rate when piecewise polynomial of degree k functions are used, measured in L ¹-norm.     

Reasoning about programs in continuation-passing style

Plotkin's _v -calculus for call-by-value programs is weaker than the -calculus for the same programs in continuation-passing style (CPS). To identify the call-by-value axioms that correspond to on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interesting in their own right. Using the new CPS transformation, we determine the precise language of CPS terms closed under -transformations, as well as the call-by-value axioms that correspond to the so-called administrative -reductions on CPS terms. Using the inverse mapping, we map the remaining and equalities on CPS terms to axioms on call-by-value terms. On the pure (constant free) set of -terms, the resulting set of axioms is equivalent to Moggi's computational -calculus. If the call-by-value language includes the control operatorsabort andcall-with-current-continuation, the axioms are equivalent to an extension of Felleisenet al.'s _v -C-calculus and to the equational subtheory of Talcott's logic IOCC.This article is a revised and extended version of the conference paper with the same title [42]. The technical report of the same title contains additional material.The authors were supported in part by NSF grant CCR 89-17022 and by Texas ATP grant 91-003604014.     

Efficient low-contention asynchronous consensus with the value-oblivious adversary scheduler

We consider asynchronous consensus in the shared-memory setting. We present the first efficient low-contention consensus algorithm for the weak-adversary-scheduler model. The algorithm achieves consensus in total work and (hot-spot) contention, both expected and with high probability. The algorithm assumes the value-oblivious scheduler, which is defined in the paper. Previous efficient consensus algorithms for weak adversaries suffer from memory contention.Yonatan Aumann: This work was partially completed while theauthor was at Harvard University, supported in part by ONRcontract ONR-N00014-91-J-1981.Michael A. Bender: This work was supported inpart by HRL Laboratories, Sandia National Laboratories, and NSF GrantsACI-032497, CCR-0208670, and EIA-0112849. This work was partiallycompleted while the author was at Harvard University, supported inpart by NSF grants CCR-9700365, CCR-9504436, and CCR-9313775.An early version of this paper was presented in the 23rd International Colloquium on Automata, Languages, and Programming (ICALP 96) [8].     

Continuous-time time-varying entropy

In this paper we present a definition for the entropy for time-varying continuous-time systems. This entropy differs significantly from the entropy for discrete-time systems, which is defined as the memoryless component of the spectral factor of an operator related to the system. Properties of this entropy are discussed, the relationships with ₂ and , as well as the relationship with the discrete-time entropy.The work of P. A. Iglesias was supported in part by the National Science Foundation, under Contract ECS-9309387.     

On the Complexity of 2-Monotone Restarting Automata

The -automaton is the weakest form of the nondeterministic version of the restarting automaton that was introduced by Jančar et al. to model the so-called analysis by reduction. Here it is shown that the class ℒ(R) of languages that are accepted by -automata is incomparable under set inclusion to the class of Church-Rosser languages and to the class of growing context-sensitive languages. In fact this already holds for the class of languages that are accepted by 2-monotone -automata. In addition, we prove that already the latter class contains -complete languages, showing that already the 2-monotone -automaton has a surprisingly large expressive power. The results of this paper have been announced at DLT 2004 in Auckland, New Zealand. This work was mainly carried out while T. Jurdziński was visiting the University of Kassel, supported by a grant from the Deutsche Forschungsgemeinschaft (DFG). F. Mráz and M. Plátek were partially supported by the Grant Agency of the Czech Republic under Grant-No. 201/04/2102 and by the program ‘Information Society’ under project 1ET100300517. F. Mráz was also supported by the Grant Agency of Charles University in Prague under Grant-No. 358/2006/A-INF/MFF.     

Tracking the Best Disjunction

Littlestone developed a simple deterministic on-line learning algorithm for learning k-literal disjunctions. This algorithm (called ) keeps one weight for each of then variables and does multiplicative updates to its weights. We develop a randomized version of and prove bounds for an adaptation of the algorithm for the case when the disjunction may change over time. In this case a possible target disjunction schedule is a sequence of disjunctions (one per trial) and the shift size is the total number of literals that are added/removed from the disjunctions as one progresses through the sequence.We develop an algorithm that predicts nearly as well as the best disjunction schedule for an arbitrary sequence of examples. This algorithm that allows us to track the predictions of the best disjunction is hardly more complex than the original version. However, the amortized analysis needed for obtaining worst-case mistake bounds requires new techniques. In some cases our lower bounds show that the upper bounds of our algorithm have the right constant in front of the leading term in the mistake bound and almost the right constant in front of the second leading term. Computer experiments support our theoretical findings.     

Integration of parametric and “ad hoc” second order polymorphism in a calculus with subtyping

In this paper we define an extension ofF [CUG92] to which we add functions that dispatch on different terms according to the type they receive as argument. In other words, we enrich the explicit parametric polymorphism ofF by an explicit ad hoc polymorphism (according the classification of [Str67]). We prove that the calculus we obtain, calledF ^& , enjoys the properties of Church-Rosser and Subject Reduction and that its proof system is coherent. We also define a significant subcalculus for which the subtyping is decidable. This extension has not only a logical interest but it is strongly motivated by the foundation of a broadly used programming style: object-oriented programming. The connections betweenF ^& and object-oriented languages are widely stressed, and the modelling byF ^& of some features of the object-oriented style is described, continuing the work of [CGL96].Part of this work has appeared under the title F ^& : integrating parametric and ad hoc second order polymorphism in the 4th International Workshop on Database Programming Languages. New York City, August 1993.The author was supported by grant n. 203.01.56 of the Consiglio Nazionale delle Ricerche-Comitato Nazionale delle Scienze Matematiche to work at LIENS.     

Searching minimax game trees under memory space constraint

Games such as CHESS, GO and OTHELLO can be represented by minimax game trees. Among various search procedures to solve such game trees,- and SSS^* are perhaps most well known. Although it is proved that SSS^* explores only a subset of the nodes explored by-, - is commonly believed to be faster in real applications, since it requires very little memory space and hence its storage management cost is low. Contrary to this folklore, however, this paper reports, using the OTHELLO game as an example, that SSS^* is much faster than-. It is also demonstrated that SSS^* can be modified to make the required memory space controllable to some extent, while retaining the high efficiency of the original SSS^*.This research was partially supported by the Ministry of Education, Science and Culture of Japan, under a Scientific Grant-in-Aid.     

Virtual Private/Overlay Network Design With Traffic Concentration and Shared Protection

In this paper different algorithms are presented and evaluated for designing Virtual Private/Overlay Network (VPNs/VONs) over any network that supports resource partitioning e.g. ATM (Asynchronous Transfer Mode), MPLS (Multi Protocol Label Switching), or SDH/SONET (Synchronous Digital Hierarchy/Synchronous Optical Networking). All algorithms incorporate protection as well. The VPNs/VONs are formed by full mesh demand sets between VPN/VON endpoints. The service demands of VPNs/VONs are characterized by the bandwidth requirements of node-pairs (pipe-model).We investigated four design modes with three pro-active path based shared protection path algorithms and four heuristics to calculate the pairs of paths. The design mode determines the means of traffic concentration. The protection path algorithms use Dijkstras shortest path calculation with different edge weights. The demands are routed one-by-one, therefore the order in which they are processed matters.To eliminate this factor we used three heuristics (simulated allocation, simulated annealing, threshold accepting). We present numerical results obtained by simulation regarding the required total amount of capacity, the number of reserved edges, and the average length of paths.Péter Hegyi received MSc (2004) degree from the Budapest University of Technology and Economics, Hungary, where he is currently a PhD student at the Department of Telecommunications and Media Informatics. His research interests focus on design of intra- and inter-domain multilayer grooming networks and routing with protection. He has been involved in a few related projects (IKTA, ETIK, NOBEL).Markosz Maliosz is a researcher in the High Speed Networks Laboratory, Department of Telecommunication and Media Informatics at the Budapest University of Technology and Economics, where he received his MSc degree in Computer Science (1998). He has participated in projects concerning telecommunication services, network device control, Voice and Video over IP. His current research areas are Virtual Private Networking and traffic engineering in optical networks.Ákos Ladányi is a student at the Department of Telecommunications and Media Informatics at the Budapest University of Technology and Economics. His research interests focus on routing, network resilience, and combinatorial optimization.Tibor Cinkler has received MSc(94) and PhD(99) degrees from the Budapest University of Technology and Economics, Hungary, where he is currently Associate Professor at the Department of Telecommunications and Media Informatics. His research interests focus on routing, design, configuration, dimensioning and resilience of IP,MPLS, ATM, ngSDH and particularly of WR-DWDMbased multilayer networks. He is the author of over 60 refereed scientific publications and of 3 patents.     

Querying high-dimensional data in single-dimensional space

In this paper, we propose a new tunable index scheme, called iMinMax( ), that maps points in high-dimensional spaces to single-dimensional values determined by their maximum or minimum values among all dimensions. By varying the tuning knob, , we can obtain different families of iMinMax structures that are optimized for different distributions of data sets. The transformed data can then be indexed using existing single-dimensional indexing structures such as the B ⁺ -trees. Queries in the high-dimensional space have to be transformed into queries in the single-dimensional space and evaluated there. We present efficient algorithms for evaluating window queries as range queries on the single-dimensional space. We conducted an extensive performance study to evaluate the effectiveness of the proposed schemes. Our results show that iMinMax( ) outperforms existing techniques, including the Pyramid scheme and VA-file, by a wide margin. We then describe how iMinMax could be used in approximate K-nearest neighbor (KNN) search, and we present a comparative study against the recently proposed iDistance, a specialized KNN indexing method.Received: 21 May 2000, Revised: 14 March 2002, Published online: 8 April 2004Edited by: M. Kitsuregawa.     

Fuzzy output feedback control of nonlinear systems under sampled measurements

This paper studies the problem of designing an fuzzy feedback control for a class of nonlinear systems described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are allowed to be unavailable. We develop a technique for designing an fuzzy feedback control that guarantees the gain from an exogenous input to a controlled output is less than or equal to a prescribed value. A design algorithm for constructing the fuzzy feedback controller is given.     

From Pre-Historic to Post-Modern Symbolic Model Checking

Symbolic model checking, which enables the automatic verification of large systems, proceeds by calculating expressions that represent state sets. Traditionally, symbolic model-checking tools are based on backward state traversal; their basic operation is the function pre, which, given a set of states, returns the set of all predecessor states. This is because specifiers usually employ formalisms with future-time modalities, which are naturally evaluated by iterating applications of pre. It has been shown experimentally that symbolic model checking can perform significantly better if it is based, instead, on forward state traversal; in this case, the basic operation is the function post, which, given a set of states, returns the set of all successor states. This is because forward state traversal can ensure that only parts of the state space that are reachable from an initial state and relevant for the satisfaction or violation of the specification are explored; that is, errors can be detected as soon as possible.In this paper, we investigate which specifications can be checked by symbolic forward state traversal. We formulate the problems of symbolic backward and forward model checking by means of two -calculi. The pre- calculus is based on the pre operation, and the post- calculus is based on the post operation. These two -calculi induce query logics, which augment fixpoint expressions with a boolean emptiness query. Using query logics, we are able to relate and compare the symbolic backward and forward approaches. In particular, we prove that all -regular (linear-time) specifications can be expressed as post- queries, and therefore checked using symbolic forward state traversal. On the other hand, we show that there are simple branching-time specifications that cannot be checked in this way.     

Complex-Weighted One-Unit ‘Rigid-Bodies’ Learning Rule for Independent Component Analysis

Over the recent years, noticeable theoretical efforts have been devoted to the understanding of the role of networks' parameter spaces in neural learning. One of the contributions in this field concerns the study of weight-flows on Stiefel manifold, which is the natural parameter-space's algebraic-structure in some unsupervised (information-theoretic) learning task. An algorithm belonging to the class of learning equations generating Stiefel-flows is based on the rigid-body theory, introduced by the present Author in 1996. The aim of this Letter is to present an investigation on the capability of a complex-weighted neuron, trained by a rigid-bodies learning theory, with application to blind source separation of complex-valued independent signals for telecommunication systems.