brief paper a dual optimization procedure for linear quadratic robust control problems this paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system the model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional this problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found although the direct solution of this problem will be discussed briefly the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available

logic test pattern generation using linear codes logic testing of today s integrated circuits is a task of increasing difficulty as the number of circuits or transistors packed onto a single chip grows higher and higher exhaustive pattern testing with adequate partitioning of logic has been explored regarding its potential in solving the problems in test pattern generation and fault coverage in this paper we propose a new method of simultaneously generating exhaustive test patterns for all possible input subsets each corresponding to an output up tq a specified size the method is based on the structure of linear polynomial codes and can be easily implemented by modifying existing shift registers in an lssd or scan path design to embody additional feedback connections this is particularly attractive since the implementation is compatible with the approach of self testing using pseudorandom patterns thus a very reasonable strategy is to combine limited exhaustive pattern testing with pseudorandom pattern testing ini cases where complete exhaustive testing is not practical

the triple autocorrelation of an m sequence is a lempel costas array the triple autocorrelation of a sequence is shown to be a lempel costas array iff the sequence is maximal assuming correlation is appropriately defined and the alphabet of the sequence is of prime size a method that allows the construction of thumbtack autocorrelation sequences of arbitrary alphabet size is subsequently proposed

linear dependencies in linear feedback shift registers linear feedback shift registers have been proposed to generate test patterns for the self test of logic networks the probability of linear dependence among k bit positions of a subset of k bits in a maximum length shift register sequence is an outstanding problem in this correspondence we derive a formula for the calculation of the probability

stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management we consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a european call option within a continuous time framework the dynamic management of a portfolio of assets is effected through continuous or point control activation costs and phase delay the performance index is derived from the unique weak variational solution to the ultraparabolic hamilton jacobi equation the value function is the optimal realization of the performance index relative to all feasible portfolios an approximation procedure based upon a temporal box scheme finite element method is analyzed numerical examples are presented in order to demonstrate the viability of the approach

characterization of m sequences of lengths 2 2k 1 and 2 k 1 with three valued cross correlation considered is the distribution of the cross correlation between in sequences of length 22k 1 where m 2k and m sequences of shorter length 2k 1 new pairs of m sequences with three valued cross correlation are found and the complete correlation distribution is determined finally we conjecture that there are no more cases with a three valued cross correlation apart from the ones proven here

vector sets for exhaustive testing of logic circuits l d universal sets are useful for exhaustively testing logic circuits with a large number of functional components designed so that every functional component depends on at most d inputs randomized and deterministic constructions of l d universal test sets are presented and lower and upper bounds on the optimal sizes of such sets are proven it is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an np complete problem

novel test pattern generators for pseudoexhaustive testing pseudoexhaustive testing of a combinational circuit involves applying all possible input patterns to all its individual output cones the testing ensures detection of all detectable multiple stuck at faults in the circuit and all detectable combinational faults within individual cones test pattern generators based on coding theory principles are not tailored to a specific circuit as they do not utilize any structural information they usually generate test sets that are several orders of magnitude larger than the minimum size pseudoexhaustive test set required for a specific circuit in this paper we describe hardware efficient test pattern generators that employ knowledge of the circuit output cone structures for generating minimal test sets using our techniques we have designed generators that generate minimum size test sets for the iscas benchmark circuits

an adaptive extrapolation discontinuous galerkin method for the valuation of asian options we consider the approximation of the optimal stopping problem associated with ultradiffusion processes in the context of mathematical finance and the valuation of asian options in particular the value function is characterized as the solution of an ultraparabolic variational inequality employing the penalty method and a regularization of the state space we develop higher order adaptive approximation schemes which utilize the extrapolation discontinuous galerkin method in temporal space numerical examples are provided in order to demonstrate the approach

exhaustive test pattern generation using cyclic codes the generation of exhaustive test patterns for vlsi circuits using linear feedback shift registers is described in terms of cyclic codes punctured cyclic codes are used to generate exhaustive test patterns of any length a techniques for the generation of punctured cyclic codes is presented a technique is also presented to reduce the size of test sets obtained from punctured cyclic codes

vector space theoretic analysis of additive cellular automata and its application for pseudoexhaustive test pattern generation a novel scheme for utilizing the regular structure of three neighborhood additive cellular automata cas for pseudoexhaustive test pattern generation is introduced the vector space generated by a ca can be decomposed into several cyclic subspaces a cycle corresponding to an m dimensional cyclic subspace has been shown to pseudoexhaustively test an n input circuit n or m such a cycle is shown to supply a m 1 bit exhaustive pattern including the all zeros m 1 tuple schemes have been reported specifying how one or more subsets of m 1 cell positions of an n cell ca can be identified to generate exhaustive patterns in an m dimensional cyclic subspace

design of test sequences for vlsi self testing using lfsr consider a shift register sr of length n and a collection of designated subsets of 0 1 n 1 the problem is how to add feedback to the sr such that the resulting linear feedback shift register lfsr exercises almost exhaustively each of the designated subsets and is of small period several previously known results for maximum length lfsr are extended to more general lfsr and in particular a previously known algorithm is simplified and extended applications to the problems of vlsi self testing are discussed and illustrated

pseudorandom arrays for built in tests parallel pseudorandom sequences for use in built in test are discussed the two dimensional nature of these sequences makes it natural to consider the resulting binary arrays some of the desired properties of such arrays are discussed as well as some of the problems generators for such arrays are described a conventional lfsr with parallel output is shown to be a poor choice for such a generator several compact generators are described which are shown to be compromises between complexity and varying degrees of implementation of the desired properties in the resulting sequences one of the compact generators produces sequences which have the desired properties for built in tests

implicit explicit runge kutta methods for financial derivatives pricing models abstract implicit explicit runge kutta methods are investigated for application to financial derivatives pricing models in the partial differential equations approach the methods are showed to be an alternative to other existing procedures for the numerical valuation of american type contracts we follow the method of lines in order to have a numerical method that can be used with a variety of state variable discretizations including finite elements finite differences and finite volume methods some numerical experiments are presented

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

the multiple linear quadratic gaussian problem in this paper we define and solve the multiple linear quadratic gaussian lqg problem for discrete time systems using salukvadze s ideal point method which treats dynamic but deterministic multicriteria optimization problems the solution consists in designing a scalar regulator where the weighting matrices are replaced by the sums of their counterparts in the individual criteria the resulting control is optimal in the sense that it minimizes the difference between the cost of the implemented policy from the cost that would occur if we optimized each criterion separately and added the outcomes all the nice properties of the scalar lqg regulator are enjoyed by the multicriteria regulator as well extension to the continuous time case is straightforward yielding identical results

numerical analysis of american option pricing in a jump diffusion model we discuss pricing formulae for american options in merton s jump diffusion model with the help of variational inequalities we derive some regularity properties of price functions using the finite difference method a discretization scheme is presented and a convergence theorem for the first order derivatives is proved numerical methods and results are also discussed

on the use of boundary conditions for variational formulations arising in financial mathematics the general intractability of derivative security valuation models to present techniques both analytic and numerical arguably remains one of the preeminant problem of mathematical finance it is the focus of this paper to examine the applicability of a promising recent development namely radial basis functions rbf to the problem of option valuation a black scholes framework is considered for american and european options written on a one and two risky assets the performance of rbf and finite differencing algorithms are examined with respect to artificial boundary conditions computational domain domain decomposition and mesh scaling

exhaustive test pattern generation with constant weight vectors we develop in this paper a simple way of generating a test set which simultaneously provides exhaustive pattern testing with respect to all input subsets of a logic circuit up to a certain size it is shown that such a test set may be formed with vectors of a particular set of weights main theorems and examples are established and illustrated in the binary case for 2 value logic circuits and then generalized to nonbinary cases for multivalue logic circuits such test sets are simple in structure and become optimal in size in certain cases it is also shown that such a test set can be effectively implemented via a scan path type shifter

recursive pseudoexhaustive test pattern generation a recursive technique for generating exhaustive patterns is presented the method is optimal i e in one experiment it covers exhaustively every block of k adjacent inputs in the first 2 sup k vectors implementation methods based on characteristic functions of test vectors are provided they include a parallel pattern generator employing an exclusive or array and two serial generators that can be easily adopted in a scan based built in self test environment

a theory of state covariance assignment for discrete systems in many regulation control problems it is desired to design the controller so that various system states have acceptable root mean squared values this is a multiple objective problem one way to satisfy these objectives is to assign a specified state covariance to the system this paper introduces and solves the following problem 1 characterize the entire set of state covariances which may be assigned to a linear discrete time system by state feedback and 2 find the set of all state feedback gains which will assign an admissible state covariance to the system extensions are also presented for state estimate feedback

the weighted syndrome sums approach to vlsi testing with the advent of vlsi testing has become one of the most costly complicated and time consuming problems the method of syndrome testing is applicable toward vlsi testing since it does not require test generation and fault simulation it can also be considered as a vehicle for self testing in order to employ syndrome testing in vlsi we electronically partition the chip into macros in test mode the macros are then syndrome tested in sequence

adaptive finite element methods for parabolic problems i a linear model problem this paper is the first part in a series of papers on adaptive finite element methods for parabolic problems in this paper an adaptive algorithm is presented and analyzed for choosing the space a

built in test for circuits with scan based on reseeding of multiple polynomial linear feedback shift registers we propose a new scheme for built in test bit that uses multiple polynomial linear feedback shift registers mp lfsr s the same mp lfsr that generates random patterns to cover easy to test faults is loaded with seeds to generate deterministic vectors for difficult to test faults the seeds are obtained by solving systems of linear equations involving the seed variables for the positions where the test cubes have specified values we demonstrate that mp lfsr s produce sequences with significantly reduced probability of linear dependence compared to single polynomial lfsr s we present a general method to determine the probability of encoding as a function of the number of specified bits in the test cube the length of the lfsr and the number of polynomials theoretical analysis and experiments show that the probability of encoding a test cube with s specified bits in an s stage lfsr with 16 polynomials is 1 10 sup 6 we then present the new bit scheme that allows for an efficient encoding of the entire test set here the seeds are grouped according to the polynomial they use and an implicit polynomial identification reduces the number of extra bits per seed to one bit the paper also shows methods of processing the entire test set consisting of test cubes with varied number of specified bits experimental results show the tradeoffs between test data storage and test application time while maintaining complete fault coverage

the use of linear sums in exhaustive testing the increasing role of exhaustive testing techniques in vlsi has prompted a number of investigations into methods for achieving locally exhaustive testing of the components of a large digital circuit using a comparatively small number of test signals this paper examines the possibility of introducing linear sums of the test signals into this testing process it is shown that with the addition of a relatively small amount of additional circuitry significant reductions in the number of required test signals and tests can often be achieved in particular it is shown that for any specific combinational circuit the number of required test signals can be made to be independent of the number of inputs and to depend only logarithmically on the number of outputs the role of these linear sums in the generation of universal test sets is also discussed

pseudoexhaustive test pattern generator with enhanced fault coverage a method of pseudoexhaustive test pattern generation is proposed that is suitable above all for circuits using random access scan two linear feedback shift registers are used to generate scan addresses and test patterns to be scanned into these addresses it is shown that the method gives better results than random testing

monotone multigrid methods for elliptic variational inequalities i we derive fast solvers for discrete elliptic variational inequalities of the first kind obstacle problems as resulting from the approximation of related continuous problems by piecewise linear finite elements using basic ideas of successive subspace correction we modify well known relaxation methods by extending the set of search directions extended underrelaxations are called monotone multigrid methods if they are quasioptimal in a certain sense by construction all monotone multigrid methods are globally convergent we take a closer look at two natural variants the standard monotone multigrid method and a truncated version for the considered model problems the asymptotic convergence rates resulting from the standard approach suffer from insufficient coarse grid transport while the truncated monotone multigrid method provides the same efficiency as in the unconstrained case

parametric lq control the parametric linear quadratic plq control problem is considered for discrete time stochastic systems the control problem consists of a non linear optimization problem in the parameters of a linear regulator results on global convergence and on rate of convergence are given for the linear descent mapping method for solving the optimal regulator parameter values furthermore a non linear mapping method based on the solution of a generalized discrete riccati equation is given the plq control problem is a useful extension of the optimal output feedback problem with applications to the design of low order regulators decentralized control and adaptive control

adaptive multilevel methods for obstacle problems the authors consider the discretization of obstacle problems for second order elliptic differential operators by piecewise linear finite elements assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies the linear problems are solved iteratively by preconditioned conjugate gradient iterations the proposed preconditioners are treated theoretically as abstract additive schwarz methods and are implemented as truncated hierarchical basis preconditioners to allow for local mesh refinement semilocal and local a posteriors error estimates are derived providing lower and upper estimates for the discretization error the theoretical results are illustrated by numerical computations

pricing options in jump diffusion models an extrapolation approach we propose a new computational method for the valuation of options in jump diffusion models the option value function for european and barrier options satisfies a partial integrodifferential equation pide this pide is commonly integrated in time by implicit explicit imex time discretization schemes where the differential diffusion term is treated implicitly while the integral jump term is treated explicitly in particular the popular imex euler scheme is first order accurate in time second order accuracy in time can be achieved by using the imex midpoint scheme in contrast to the above approaches we propose a new high order time discretization scheme for the pide based on the extrapolation approach to the solution of odes that also treats the diffusion term implicitly and the jump term explicitly the scheme is simple to implement can be added to any pide solver based on the imex euler scheme and is remarkably fast and accurate we demonstrate our approach on the examples of merton s and kou s jump diffusion models the diffusion extended variance gamma model as well as the two dimensional duffie pan singleton model with correlated and contemporaneous jumps in the stock price and its volatility by way of example pricing a one year double barrier option in kou s jump diffusion model our scheme attains accuracy of 10 5 in 72 time steps in 0 05 seconds in contrast it takes the first order imex euler scheme more than 1 3 million time steps in 873 seconds and the second order imex midpoint scheme 768 time steps in 0 49 seconds to attain the same accuracy our scheme is also well suited for bermudan options combining simplicity of implementation and remarkable gains in computational efficiency we expect this method to be very attractive to financial engineering modelers

a geometric approach to stabilization by output feedback in this paper we present a geometric approach to the stabilizability of linear systems by output feedback the geometric approach is completely analysed for both discrete time and continuous time single input single output systems two examples are worked out in detail to illustrate the theoretical development we also show how our approach can be extended to dyadic systems the simplicity of the geometric approach in the special case when the number of inputs or outputs is one less than the order of the system is illustrated with the help of examples present address bell laboratories south plainfield new jersey 07080 u s a

multiple seed tpg structures linear feedback shift registers lfsrs are popular mechanisms for built in test pattern generation tpg they are normally used with a primitive characteristic polynomial because in that case only one initialization state seed is required we show that if the characteristic polynomial is nonprimitive irreducible the required seeds can still be efficiently generated we establish a formula that shows how the seeds of any nonprimitive irreducible polynomial relate to each other this leads to an efficient hardware implementation with small hardware overhead irrespective of the number of seeds and enhances the choices available for the design of appropriate tpg structures in the case of pseudoexhaustive tpg that were previously limited to primitive characteristic polynomials only

penalty methods for the numerical solution of american multi asset option problems we derive and analyze a penalty method for solving american multi asset option problems a small non linear penalty term is added to the black scholes equation this approach gives a fixed solution domain removing the free and moving boundary imposed by the early exercise feature of the contract explicit implicit and semi implicit finite difference schemes are derived and in the case of independent assets we prove that the approximate option prices satisfy some basic properties of the american option problem several numerical experiments are carried out in order to investigate the performance of the schemes we give examples indicating that our results are sharp finally the experiments indicate that in the case of correlated underlying assets the same properties are valid as in the independent case

paper optimal output feedback design of systems with ill conditioned dynamics singular perturbation concepts are exploited to develop a procedure for designing a constant gain output feedback control system it is assumed that the original system is ill conditioned in the sense that the plant contains widely separated dynamics and that an accurate description for the high frequency behavior may not be available the design procedure attempts to stabilize the system by minimizing a quadratic cost function made up of the control and states associated with a reduced order low frequency model for the plant and a measure of stability for the neglected fast dynamics the resulting design procedure does not require knowledge of the fast dynamics

on the approximation of optimal stopping problems with application to financial mathematics the determination of the value function associated with a given reward and stochastic process represents an important class of stochastic control problem in particular the expectations of such processes may be represented as solutions of variational inequalities of evolutionary type typically characterized by their high number of degrees of freedom unbounded domains and lack of natural boundary conditions in this paper we introduce two methodologies for computing the value function of optimal stopping associated with general stochastic processes our results are implemented utilizing finite elements and are validated using problems taken from financial mathematics

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

spectral fault signatures for single stuck at faults in combinational networks a method is described for the derivation of fault signatures for the detection of stuck at faults in single output combinational networks these signatures consist of a set of values derived from the network any single stuck at fault causes at least one value to change the fault signatures developed are a generalization of syndrome testing the technique is developed in the rademacher walsh spectral domain but is easily implemented using conters and basic gates

results of the enumeration of costas arrays of order 27 this correspondence presents the results of the enumeration of costas arrays of order 27 all arrays found except for one are accounted for by the golomb and welch construction methods

on multiple criteria stationary linear quadratic control multiple control criteria and design specifications are in general present in control systems design in this study all pareto optimal solutions are characterized for a large class of multiple criteria stationary linear quadratic control problems in terms of associated scalar criterion linear quadratic control problem solutions based on a supporting hyperplane argument and thus the results are fully constructive this argument which was used to establish these results is believed to be new

a numerical analysis of variational valuation techniques for derivative securities in this paper we consider the partial differential equations approach for valuing european and american style options on multiple assets we use a method of lines finite element implementation available in the software package femlab in order to solve the variational inequality that characterizes the american style option as well as the partial differential equation that defines the european style option for two and three state variables a detailed study of the approximation error is provided including a theoretical estimate an asymptotic analysis the space time distribution and the dependence on the size of the truncation domain

cross correlation of p ary gmw sequences the cross correlation function of p ary p prime gmw sequences is investigated the well known m sequences are incorporated in these sequences gmw sequences also have the two level autocorrelation function but their linear span may be much larger than those of m sequences the calculation of the cross correlation function of gmw sequences is reduced to the cross correlation of the m sequences because many results on this kind of sequence are known in the literature only the cross correlation function of an m sequence with a gmw sequence has been known up to now

brief linear quadratic control revisited infinite horizon linear quadratic control is re examined and generalized to include a class of non stationary disturbances this revision is achieved by defining a generalized infinite horizon linear quadratic control problem using a flexible functional analytic signal description specifically an instantaneous linear quadratic output feedback problem is considered in this way it is shown that the solution to the generalized linear quadratic problem is equivalent to the solution of the corresponding standard linear quadratic problem with disturbance and noise covariance matrices having in the generalized problem a different more general meaning than in the standard problem in the generalized problem these covariance matrices are majorizing matrices that have a precise meaning even in the non stationary signal case this result justifies in a nice way the wide practice of interpreting the disturbance and noise covariance matrices in linear quadratic control as design variables

on linear dependencies in subspaces of lfsr generated sequences the probability of linear dependency in subsequences generated by linear feedback shift registers is examined it is shown that this probability for a short subsequence e g a sequence defined by the length of a scan chain can be much higher than that for an entire m sequence

a bicriteria stationary lq control problem abstract this note gives a simple derivation of the minimal loss vectors and the pareto optimal solutions to a certain bicriteria stationary lq control problem

the design of optimal output regulators for linear multivariable systems with constant disturbances a method recently developed for solving the output regulator problem is extended to linear systems with constant disturbances the design of static and low order dynamic regulators for linear systems based on the use of projective controls is reviewed first the proposed method determines through a unified procedure the order and the parameters of the compensator together with the feedback parameters this methodology is then applied to systems with external disturbances and various control structures incorporating integral action are investigated in the light of the proposed methodology

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

on the anderson moore method for solving the optimal output feedback problem a descent anderson moore method for solving the optimal constant output feedback gains for the stochastic discrete time optimal output feedback problem is discussed an efficient descent mapping algorithm is given in detail the algorithm involves a partial line search mapping implemented as a finite search process to determine a step length parameter so as to guarantee global convergence of the algorithm to a stationary point of the loss function under very mild assumptions furthermore the algorithm involves a scheme to bound the condition numbers of certain critical matrix inverses in the anderson moore method so that the algorithm can be applied to a wider class of control problems

efficient vlsi fault simulation let c be an acyclic boolean circuit with n gates and n inputs a circuit manufacture error may result in a stuck at s a fault in a circuit identical to c except a gate v only outputs a fixed boolean value the s a fault simulation problem for c is to determine all possible s a faults which can be detected i e faults circuit and c would give distinct outputs by a given test pattern input we consider the case where c is a tree i e has fan out 1 we give a practical algorithm for fault simulation which simultaneously determines all detectable s a faults for every gate in the circuit tree c our algorithm required only the evaluation of a circuit fs c which has 7n gates and has depth 3 d 1 when d is the depth of c thus the sequential time of our algorithm is 7n and the parallel time is 3 d 1 furthermore fs c requires only a small constant factor more vlsi area than does the original circuit c we also extend our results to get efficient methods for fault simulation of oblivious vlsi circuits with feedback lines

exhaustive generation of bit patterns with applications to vlsi self testing one has a shift register of length n and a collection of designated subsets of 0 1 n 1 the problem is to devise a method for feeding a string of bits into the shift register in such an order that for each designated subset s k1 kr if one keeps track of the bit patterns appearing at the corresponding positions k1 krof the shift register all 2r possible bit patterns will ultimately appear at those positions a simple and efficient solution to this problem derived from the connections between polynomials over finite fields and linear feedback shift registers is presented applications of this solution to the problem of vlsi self testing are discussed and illustrated