a fast covariance type algorithm for sequential least squares filtering and prediction fast implementation of sequential least squares ls algorithms is of great importance in various applications of signal processing estimation system identification and control the purpose of this note is the introduction of an efficient sequential ls algorithm for multichannel unwindowed signals covariance case the new scheme in the single channel case requires 10 m madpr multiplications and divisions per recursion m being the number of estimated parameters this offers a saving of 5 m madpr compared to other existing algorithms

a general orthogonalization technique with applications to time series analysis and signal processing a new orthogonalization technique is presented for computing the qr factorization of a general n x p matrix of full rank p n 2 p the method is based on the use of projections to solve increasingly larger subproblems recursively and has an o np2 operation count for general matrices the technique is readily adaptable to solving linear least squares problems if the initial matrix has a circulant structure the algorithm simplifies significantly and gives the so called lattice algorithm for solving linear prediction problems from this point of view it is seen that the lattice algorithm is really an efficient way of solving specially structured least squares problems by orthogonalization as opposed to solving the normal equations by fast toeplitz algorithms

the algebra of timed processes atp the algebra of timed processes atp uses a notion of discrete global time and suggests a conceptual framework for introducing time by extending untimed languages the action vocabularly of atp contains a special element representing the progress of time the algebra has apart from standard operators of process algebras such as prefixing by an action alternative choice and parallel composition a primitive unit delay operator for two arguments processes p and q this operator gives a process which behaves as p before the execution of a time event and behaves as q afterwards it is shown that several d unit delay constructs such as timeouts and watchdogs can be expressed in terms of the unit delay operator and standard process algebra operators a sound and complete axiomatization for bisimulation semantics is studied and two examples illustrating the adequacy of the language for the description of timed systems are given finally we provide a comparison with existing timed process algebras

least squares adaptive lattice and transversal filters a unified geometric theory a unified theory is presented to characterize least squares adaptive filters in either lattice or transversal filter form for nonstationary processes the derivations are based upon a geometric formulation of least squares estimation and on the concept of displacement rank a few basic geometric relations are shown to underlie the various algorithms insights into the fundamental concepts that unify lattice and transversal filter approaches to least squares adaptive filters are also given the general results are illustrated by applications to the so called pre windowed and growing memory covariance formulations of the deterministic least squares problem

the block processing ftf adaptive algorithm a new block type adaptive filtering algorithm is presented this new block adaptive filter differs from the frequency domain block adaptive filters of ferrara 1980 and of clark mitra and parker 1980 in that the new method applies a deterministic time domain least squares criteria within each of the data blocks information is carried from block to block via a weighted initial condition this new block fast transversal filters bftf algorithm is a numerically stable algorithm and can also be used to perform efficient least squares system identification on any one data block in which case it shows a moderate computational advantage over the previous most efficient single data block algorithms of morf et al 1977 of marple 1981 and of kalouptsidis manolakis and carayannis 1984 1985 mechanisms for tracking and varying block length from block to block are also presented and evaluated finally we indicate how the new algorithm could be pipelined for maximum throughput with delay proportional to the number of parameters after computation of the sample correlation lags

on askey scheme and d orthogonality i a characterization theorem this is the first in a series of papers dealing with generalized hypergeometric d orthogonal polynomials extending the polynomial families in the askey scheme in this paper we give a characterization theorem to introduce new examples of generalized hypergeometricd orthogonal polynomials to be studied in the forthcoming works for d 1 we obtain an unification of some known characterization theorems in the orthogonal polynomials theory

d orthogonality of little q laguerre type polynomials abstract in this paper we solve a characterization problem in the context of the d orthogonality that allows us on one hand to provide a q analog for the d orthogonal polynomials of laguerre type introduced by the first author and douak and on the other hand to derive new l q classical d orthogonal polynomials generalizing the little q laguerre polynomials various properties of the resulting basic hypergeometric polynomials are singled out for d 1 we obtain a characterization theorem involving as far as we know new l q classical orthogonal polynomials for which we give the recurrence relation and the difference equation

instrumental variable methods for arma spectral estimation the modified yule walker technique of arma spectral estimation is shown to be a special case of the instrumental variable method of system identification several recursive instrumental variable algorithms are proposed for adaptive spectral estimation including a new algorithm for the overdetermined case an efficient lattice algorithm is presented for solving the modified yule walker equations given the sample correlation coefficients the performance of some of the algorithms is illustrated by simulation results

a tutorial on empa a theory of concurrent processes with nondeterminism priorities probabilities and time we give an overview of empa a process algebra for modeling and analyzing concurrent systems where nondeterminism priorities probabilities and time are present aiming at a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory

improvement of the fast recursive least squares algorithms via normalization a comparative study this paper deals with the derivation and the properties of fast optimal least squares algorithms and particularly with their normalization it is shown how the well known fast kalman algorithm written in the most general form can be normalized through a purely algebraic point of view leading to the normalized least squares transversal filter derived by cioffi kailath and lev ari from the geometric approach an improved form of the algorithm is presented the different algorithms have been compared from a practical point of view as regards their convergence initialization procedures complexity and numerical properties normalized transversal algorithms are shown to be interesting because of their nice structured form simplicity of conception and improved good numerical behavior

hyperbolic householder transformations a class of transformation matrices analogous to the householder matrices is developed with a nonorthogonal property designed to permit the efficient deletion of data from least squares problems these matrices which we term hyperbolic householder are shown to effect deletion or simultaneous addition and deletion of data with much less sensitivity to rounding errors than for techniques based on normal equations when the addition deletion sets are large this numerical robustness is obtained at the expense of only a modest increase in computations and when only a relatively small fraction of the data set is modified there is a decrease in required computations two applications to signal processing problems are considered first these transformations are used to obtain a square root algorithm for windowed recursive least squares filtering second the transformations are employed to implement the rejection of spurious data from the weight vector estimator in an adaptive array

on d symmetric classical d orthogonal polynomials abstract the d symmetric classical d orthogonal polynomials are an extension of the standard symmetric classical polynomials according to the hahn property in this work we give some characteristic properties for these polynomials related to generating functions and recurrence differential equations as applications we characterize the d symmetric classical d orthogonal polynomials of boas buck type we construct a d 1 order linear differential equation with polynomial coefficients satisfied by each polynomial of a d symmetric classical d orthogonal set and we show that the d symmetric classical d orthogonal property is preserved by the derivative operator some of the obtained properties appear to be new even for the case d 1

spherical trigonometry yule s parcor identity and frls fully normalized lattice yule s parcor identity is recognized as the cosine law of spherical trigonometry the six parcors propagated by the fully normalized frls lattice filter are the cosines of the six elements of a spherical triangle and this lattice algorithm is one solution to a spherical triangle problem that arises naturally in navigation and astronomy exploiting this new geometric interpretation yields unnoticed and potentially useful recursions among frls quantities

d orthogonality of hermite type polynomials abstract in this paper we state a characterization theorem for d orthogonal polynomials of hermite type as application we solve two characterization problems related to gould hopper polynomials and charlier type polynomials various properties of the resulting generalized hypergeometric polynomials are singled out in particularly we derive the d dimensional functional vectors ensuring the d orthogonality of these polynomials the obtained weight functions are reduced to the well known weight functions of charlier and hermite polynomials for d 1 we also explicitly express the d dimensional functional vector associated with polynomials of laguerre type which are related to the obtained hermite type polynomials

absolute versus relative time in process algebras abstract timed process algebras are useful tools for the specification and verification of real time systems we study the relationships between two of these algebras c i pa closed interval process algebra and tccs temporal ccs which deal with temporal aspects of concurrent systems by following very different interpretations durational actions versus durationless actions absolute time versus relative time timed functional behavior versus time and functional behavior local clocks versus global clocks we show that these different choices are not irreconcilable by presenting simple mappings from c i pa to tccs which preserve the behavioral equivalences over the two timed calculi these results hold whenever basic actions are interpreted as either eager or lazy whenever the starting time of action execution is observed rather than their completion time a study on the size of the labelled transition systems describing the transitional semantics of cipa processes and those describing the transitional semantics of their translated versions is also presented

a polynomial approach to the generalized levinson algorithm based on the toeplitz distance a polynomial approach to the generalized levinson algorithm based on the toeplitz distance concept is given it turns out that most properties of the standard levinson algorithm admit natural generalizations including the three term recurrence relations the christoffel darboux formula and the reflection coefficients schur szego parameters obtainable from the data via an extension of the schur algorithm the theory of sum lossless transfer functions is shown to play the same illuminating role in the problem as the theory of szego orthogonal polynomials in the standard levinson algorithm

multiple orthogonal polynomials for classical weights a new set of special functions which has a wide range of applications from number theory to integrability of nonlinear dynamical systems is described we study multiple orthogonal polynomials with respect to p 1 weights satisfying pearson s equation in particular we give a classification of multiple orthogonal polynomials with respect to classical weights which is based on properties of the corresponding rodrigues operators we show that the multiple orthogonal polynomials in our classification satisfy a linear differential equation of order p 1 we also obtain explicit formulas and recurrence relations for these polynomials

d orthogonal polynomials and su 2 two families of d orthogonal polynomials related to su 2 are identified and studied the algebraic setting allows for their full characterization explicit expressions recurrence relations difference equations generating functions etc in the limit where su 2 contracts to the heisenberg weyl algebra h1 the polynomials tend to the standard meixner polynomials and d charlier polynomials respectively

some discrete multiple orthogonal polynomials in this paper we extend the theory of discrete orthogonal polynomials on a linear lattice to polynomials satisfying orthogonality conditions with respect to r positive discrete measures first we recall the known results of the classical orthogonal polynomials of charlier meixner kravchuk and hahn t s chihara an introduction to orthogonal polynomials gordon and breach new york 1978 r koekoek and r f swarttouw reports of the faculty of technical mathematics and informatics no 98 17 delft 1998 a f nikiforov et al classical orthogonal polynomials of a discrete variable springer berlin 1991 these polynomials have a lowering and raising operator which give rise to a rodrigues formula a second order difference equation and an explicit expression from which the coefficients of the three term recurrence relation can be obtained then we consider r positive discrete measures and define two types of multiple orthogonal polynomials the continuous case jacobi laguerre hermite etc was studied by van assche and coussement j comput appl math 127 2001 317 347 and aptekarev et al multiple orthogonal polynomials for classical weights manuscript the families of multiple orthogonal polynomials of type ii that we will study have a raising operator and hence a rodrigues formula this will give us an explicit formula for the polynomials finally there also exists a recurrence relation of order r 1 for these multiple orthogonal polynomials of type ii we compute the coefficients of the recurrence relation explicitly when r 2

multiple orthogonal polynomials results on multiple orthogonal polynomials will be surveyed multiple orthogonal polynomials are intimately related to hermite pade approximants and often they are also called hermite pade polynomials special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials referred to as angelesco and nikishin systems among the applications the number theory special functions and spectral analysis of nonsymmetric band operators will be highlighted in the analytic theory results and methods for the study of multiple orthogonal polynomials asymptotics will be reviewed new results on strong asymptotics of multiple orthogonal polynomials for nikishin system will be presented

on the tradeoff between compositionality and exactness in weak bisimilarity for integrated time markovian process calculi integrated time markovian process calculi rely on actions whose durations are quantied by exponentially distributed random variables the markovian bisimulation equivalences dened so far for these calculi treat exponentially timed internal actions like all the other actions because each such action has a nonzero duration and hence can be observed if it is executed between a pair of exponentially timed noninternal actions however no dierence may be noted at stationary state between a sequence of exponentially timed internal actions and a single exponentially timed internal action if their expected durations and execution probabilities coincide a fact exploited in hillston s weak isomorphism we show that milner s approach can be adapted on the basis of this fact so to derive a weak bisimulation equivalence for integrated time markovian process calculi up to a tradeo between compositionality and exactness inherent to the markovian setting the resulting weak markovian bisimulation equivalence induces a pseudo aggregation that is exact at stationary state for all the considered processes but turns out to be a congruence only over sequential processes to achieve compositionality over concurrent processes we need to enhance the abstraction capability of the equivalence in the presence of interleaved computations however the corresponding pseudo aggregation turns out to be exact at stationary state only for a subset of concurrent processes in addition to this tradeo we present for the rst equivalence a sound and complete axiomatization over sequential processes which is instrumental to characterize pseudo aggregations and a polynomial time equivalence checking algorithm which can be exploited for the compositional minimization of concurrent processes

on the identification of systems from data measurements using arma lattice models methods for the autoregressive moving average arma modeling of digital systems using a two channel autoregressive ar lattice are presented one method has the advantage that one half of the lattice parameters are zero when the system s excitation signal is white noise

pure time updates for least squares lattice algorithms this note presents some new time update formulas for certain types of lattice algorithms used in autoregressive modeling of stationary time series the new formulas enable the computation of the autoregressive coefficients in a number of operations per time step proportional to the model order

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

efficient recursive in order least squares fir filtering and prediction this paper is concerned with the efficient determination of the optimum in the least squares sense fir filter on the basis of data samples of the input and desired response signals by procedures recursive in the filter order this situation typically arises when no a priori statistics are available and the system order is not known the general multiinput multioutput multichannel case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2s 15m multiplications mps per order m s being the number of samples in the special case of linear prediction it calls for about s 12m mps hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of marple 1 and morf et al 2 respectively additionally the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter

recursive least squares ladder estimation algorithms recursive least squares ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability compared to gradient based algorithms we present some recently developed square root normalized exact least squares ladder form algorithms that have fewer storage requirements and lower computational requirements than the unnormalized ones a hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented the normalized forms are expected to have even better numerical properties than the unnormalized versions other normalized forms such as joint process estimators e g adaptive line enhancer and arma pole zero models will also be presented applications of these algorithms to fast or zero startup equalizers adaptive noise and echo cancellers non gaussian event detectors and inverse models for control problems are also mentioned

square root covariance ladder algorithms square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting a simplified derivation of the general update formulas for such ladder forms is presented and is used to develop the growing memory and sliding memory covariance ladder algorithms new ladder form realizations for the identified models are presented leading to convenient methods for computing the model parameters from estimated reflection coefficients a complete solution to the problem of possible singularity in the ladder update equations is also presented

some generalized hypergeometric d orthogonal polynomial sets in this paper we characterize the d orthogonal polynomial sets given by their explicit expressions in a specific basis as application we consider the generalized hypergeometric case to characterize d orthogonal polynomial sets of laguerre type meixner type meixner pollaczek type krawtchouk type continuous dual hahn type and dual hahn type for d 1 we obtain a unification of some characterization theorems in the orthogonal polynomials theory

a process algebra for timed systems a standard process algebra is extended by a new action which is meant to denote idling until the next clock cycle a semantic theory based on testing is developed for the new language this is characterised in terms of barbs a variety of ready traces and also characterised as the initial theory generated by a set of equations

a uniform framework for modeling nondeterministic probabilistic stochastic or mixed processes and their behavioral equivalences labeled transition systems are typically used as behavioral models of concurrent processes their labeled transitions define a one step state to state reachability relation this model can be generalized by modifying the transition relation to associate a state reachability distribution with any pair consisting of a source state and a transition label the state reachability distribution is a function mapping each possible target state to a value that expresses the degree of one step reachability of that state values are taken from a preordered set equipped with a minimum that denotes unreachability by selecting suitable preordered sets the resulting model called ultras from uniform labeled transition system can be specialized to capture well known models of fully nondeterministic processes lts fully probabilistic processes adtmc fully stochastic processes actmc and nondeterministic and probabilistic mdp or nondeterministic and stochastic ctmdp processes this uniform treatment of different behavioral models extends to behavioral equivalences they can be defined on ultras by relying on appropriate measure functions that express the degree of reachability of a set of states when performing multi step computations it is shown that the specializations of bisimulation trace and testing equivalences for the different classes of ultras coincide with the behavioral equivalences defined in the literature over traditional models except when nondeterminism and probability stochasticity coexist then new equivalences pop up

a robust recursive least squares algorithm a new algorithm is developed which guarantees the normalized bias in the weight vector due to persistent and bounded data perturbations to be bounded robustness analysis for this algorithm has been presented an approximate recursive implementation is also proposed it is termed as the robust recursive least squares rrls algorithm since it resembles the rls algorithm in its structure and is robust with respect to persistent bounded data perturbation simulation results are presented to illustrate the efficacy of the rrls algorithm

vector orthogonal relations vector qd algorithm vector pade approximants to a function f f 1 f d from to d have been defined uniquely without any auxiliary choice than the degrees of the numerator and the denominator the same for all the components f i as in the scalar case 1 5 the denominators are associated to polynomials p r s which are given by vector orthogonal properties r and which satisfy for each s recurrence relations of order d 1 i e with d 2 terms called relations d we study here consequences of r and d first we prove an algorithm similar to the generalized mna al gorithm then we define a vector qd algorithm which links two diagonals p r s r and p r s 1 r conversely if a family p r s r 0 verifying d is given it is possible to build p r s r 0 s 0 and d linear functionals c a a 1 d such that p r 0 p r and p r s verify the orthogonal relations r with respect to the c a

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

positive definite toeplitz embedding based on the cyclic extension of a data matrix embedding in a block toeplitz matrix is one of the techniques for efficient inversion of arbitrary covariance matrices arising in least squares estimation delosme and morf have shown how the concept of toeplitz distance leads to a positive definite embedding via a mixed form representation of the given matrix in this paper a new method is proposed for the positive definite block toeplitz embedding which has the particular feature of taking the signal itself as a starting point it consists of a suitable cyclic extension and embedding of the given signal in a multichannel stationary signal the main advantage of the method is that given the signal the embedding can be performed by inspection

inversion and factorization of non hermitian quasi toeplitz matrices abstract this paper considers formulas and fast algorithms for the inversion and factorization of non hermitian toeplitz and quasi toeplitz qt matrices matrices with a certain hidden toeplitz structure the results include the following generalizations 1 a schur algorithm that extends to non hermitian matrices a previous triangular factorization algorithm for hermitian qt matrices 2 a levinson algorithm that generalizes to non hermitian matrices a previous levinson algorithm that finds the triangularly factorized inverses of certain so called admissible qt matrices 3 the extension to qt matrices of the gohberg semencul gs inversion formula for non hermitian toeplitz matrices next the paper introduces a new fast algorithm called the extended qt factorization algorithm that overcomes the restriction to admissibility matrices of the above levinson algorithm the new algorithm is efficient and comprehensive it produces for a general qt matrix r n of size n 1 n 1 the triangularly factorized inverses and the gs type inverses of the matrix and all its submatrices as well as the triangular factorization of r n itself all in approximately 7 n 2 elementary operations for a non hermitian and 3 5 n 2 for a hermitian matrix the fast algorithms for non hermitian qt matrices are shown to be associated with two discrete transmission lines which reduce to the familiar single lattice in the hermitian case all the presented algorithms are illustrated and interpreted in terms of input sequences and flows of signals in the related transmission line realization

a fast arma transversal rls filter algorithm a fast pole zero arma transversal rls recursive least squares algorithm is derived using a geometric formulation and the concept of projection onto a vector subspace to derive a recursive solution the algorithm estimates a parameter vector that contains both numerator and denominator coefficients of an unknown system transfer function i e models an arma pole zero process the algorithm has a transversal filter structure but is distinguished from previous multichannel transversal algorithms wherein each input channel is constrained to have the same order here the pole and zero orders can be independently and arbitrarily specified the derivation of the algorithm uses permutation matrices similar to those in the arma fast kalman algorithm but achieves a significant reduction in computations when compared to that algorithm it is shown that when the pole and zero orders of the arma process are correctly specified the algorithm generates an extremely good estimate furthermore if the poles and zeros are overspecified it is shown that a spectral match is still achieved by mutual cancellation of superfluous poles and zeros

adaptive interpolation of discrete time signals that can be modeled as autoregressive processes this paper presents an adaptive algorithm for the restoration of lost sample values in discrete time signals that can locally be described by means of autoregressive processes the only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a sufficiently large neighborhood of known samples the estimates of the unknown samples are obtained by minimizing the sum of squares of the residual errors that involve estimates of the autoregressive parameters a statistical analysis shows that for a burst of lost samples the expected quadratic interpolation error per sample converges to the signal variance when the burst length tends to infinity the method is in fact the first step of an iterative algorithm in which in each iteration step the current estimates of the missing samples are used to compute the new estimates furthermore the feasibility of implementation in hardware for real time use is established the method has been tested on artificially generated auto regressive processes as well as on digitized music and speech signals

an order recursive algorithm for estimating pole zero models this paper deals with the pole zero estimation of a discrete time linear system from a measured input output record it is shown that the minimization of the squared equation error for a recursive n n 1 filter can be implemented by an order recursive algorithm using scalar products of records derived from the data the algorithm is based on the gram schmidt orthogonalization of an intertwined krylov sequence which consists of successively time shifted or circularly time shifted versions of the input and output records

on sigma lossless transfer functions and related questions abstract this paper is concerned with a systematic approach to the properties of lossless rational transfer functions in the discrete as well as in the continuous time case as a result a unifying framework is revealed where several known results fit naturally special attention is given to the embedding problem of the lyapunov equation in view of its direct application to generalized levinson algorithms

the relation of the d orthogonal polynomials to the appell polynomials abstract we are dealing with the concept of d dimensional orthogonal abbreviated d orthogonal polynomials that is to say polynomials verifying one standard recurrence relation of order d 1 among the d orthogonal polynomials one singles out the natural generalizations of certain classical orthogonal polynomials in particular we are concerned in the present paper with the solution of the following problem p find all polynomial sequences which are at the same time appell polynomials and d orthogonal the resulting polynomials are a natural extension of the hermite polynomials a sequence of these polynomials is obtained all the elements of its d 1 order recurrence are explicitly determined a generating function a d 1 order differential equation satisfied by each polynomial and a characterization of this sequence through a vectorial functional equation are also given among such polynomials one singles out the d symmetrical ones definition 1 7 which are the d orthogonal polynomials analogous to the hermite classical ones when d 1 ordinary orthogonality we meet again the classical orthogonal polynomials of hermite

branching time and abstraction in bisimulation semantics in comparative concurrency semantics one usually distinguishes between linear time and branching time semantic equivalences milner s notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence in this paper we investigate whether observation equivalence really does respect the branching structure of processes and find that in the presence of the unobservable action of ccs this is not the case therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes in the sense that it preserves computations together with the potentials in all intermediate states that are passed through even if silent moves are involved on closed ccs terms branching bisimulation congruence can be completely axiomatized by the single axion scheme a y z y a y z where a ranges over all actions and the usual loaws for strong congruence we also establish that for sequential processes observation equivalence is not preserved under refinement of actions whereas branching bisimulation is for a large class of processes it turns out that branching bisimulation and observation equivalence are the same as far as we know all protocols that have been verified in the setting of observation equivalence happen to fit in this class and hence are also valid in the stronger setting of branching bisimulation equivalence

on the toeplitz embedding of an arbitrary matrix abstract it has been shown by delosme and morf that an arbitrary block matrix can be embedded into a block toeplitz matrix the dimension of this embedding depends on the complexity of the matrix structure compared to the block toeplitz structure due to the special form of the embedding matrix the algebra of matrix polynomials relative to block toeplitz matrices can be interpreted directly in terms of the original matrix and therefore can be extended to arbitrary matrices in fact these polynomials turn out to provide an appropriate framework for the recently proposed generalized levinson algorithm solving the general matrix inversion problem

normalized lattice algorithms for least squares fir system identification recently developed algorithms for least squares identification of autoregressive models are extended in this paper so as to facilitate least squares identification of finite impulse response models the algorithms belong to the class of square root normalized lattice algorithms hence they share the computational efficiency and good numerical behavior of the latter two versions are presented one for identifying time invariant models and the other for tracking time varying parameters new lattice form realizations of the identified fir models are given the general framework is then specialized to the important cases of prediction and smoothing

timed process calculi with deterministic or stochastic delays several deterministically stochastically timed process calculi have been proposed in the literature that apart from their synchronization mechanism mainly differ for the way in which actions and delays are represented in particular a distinction is made between integrated time calculi in which actions are durational and orthogonal time calculi in which actions are instantaneous and delays are expressed separately in a previous work on deterministic time the two approaches have been shown to be reconcilable through an encoding from the integrated time calculus cipa to the orthogonal time calculus tccs which preserves strong timed bisimilarity under certain conditions in this paper the picture is completed by first defining a reverse encoding from tccs to cipa which requires slight modifications to both calculi and is shown to preserve only weak timed bisimilarity under conditions tighter than those for the direct encoding stochastic time is then addressed by exhibiting an encoding from the integrated time calculus mtipp to the orthogonal time calculus iml together with a reverse encoding requiring slight modifications only to the former calculus with both encodings being shown to preserve strong markovian bisimilarity under suitable conditions all the four encodings rely on the assumption that action execution is urgent variants are finally discussed in which action execution is delayable in the sense that an enabled action can let time advance before starting its execution or only the execution of internal actions is urgent which is known as maximal progress

d orthogonality via generating functions in this paper starting from a suitable generating function of a polynomial set we show how to decide whether the considered polynomial set is d orthogonal and if it is so how to determine the corresponding d dimensional functional vector then we apply the obtained results to some known and new d orthogonal polynomial sets for the known ones we give new proofs for some already obtained results

some discrete d orthogonal polynomial sets in this paper we characterize all polynomial sets which are at the same time d orthogonal and appell the resulting polynomials reduce to charlier polynomials for d 1 1 various properties of the obtained polynomials are singled out generating function recurrence relation of order d 1 and a difference equation of order d 1 we also explicitly express the d dimensional functional for which the d orthogonality holds

performance measure sensitive congruences for markovian process algebras the modeling and analysis experience with process algebras has shown the necessity of extending them with priority probabilistic internal external choice and time while preserving compositionality the purpose of this paper is to make a further step by introducing a way to express performance measures in order to allow the modeler to capture the qos metrics of interest we show that the standard technique of expressing stationary and transient performance measures as weighted sums of state probabilities and transition frequencies can be imported in the process algebra framework technically speaking if we denote by n n the number of performance measures of interest in this paper we define a family of extended markovian process algebras with generative master reactive slaves synchronization mechanism called empagrn including probabilities priorities exponentially distributed durations and sequences of rewards of length n then we show that the markovian bisimulation equivalence mbn is a congruence for empagrn which preserves the specified performance measures and we give a sound and complete axiomatization for finite empagrn terms finally we present a case study conducted with the software tool two towers in which we contrast the average performance of a selection of distributed algorithms for mutual exclusion modeled with empagrn