complexity of normal form grammars abstract various types of grammars can be used to describe context free languages such are context free grammars and their normal form restrictions rewriting of a context free grammar to an equivalent grammar in required normal form can cause a change of parameters of the grammar such as the number of rules the number of nonterminals etc greibach normal form grammars and position restricted grammars will be investigated from the point of view of descriptional complexity of context free languages

design of robust static output feedback for large scale systems the design of static output feedback is of fundamental importance in control theory in this note we propose a new approach to this problem based on linear matrix inequalities a distinguishing feature of the method is its ability to handle large scale problems with additive nonlinearities the resulting control is robust with respect to uncertainties and can incorporate several types of information structure constraints the effectiveness of the proposed strategy is demonstrated by application to a practical large scale system

a characterization of decentralized fixed modes in terms of transmission zeros a simple development is given to show that a linear time invariant plant has a decentralized fixed mode at if and only if is a transmission zero of certain subsystems of the plant

cancellation in context free languages enrichment by reduction the following problem is shown to be decidable given a context free grammar g and a string w x does there exist a string u l g such that w is obtained from u by deleting all substrings ui that are elements of the symmetric dyck set d 1 the intersection of any two context free languages can be obtained from only one context free language by cancellation either with the smaller semi dyck set d 1 d 1 or with d 1 itself also the following is shown here for the first time if the set eq xnx n n n d 1 is used for this cancellation then each recursively enumerable set can be obtained from linear context free languages previous work has shown that cancellation of substrings from the semi dyck language d 1 or from any of the former languages d 1 or eq allows one to obtain the following from the context free languages any terminal petri net language 14 16 the intersections of any context free with a terminal petri net language and the nested iterated substitution thereof 15 we generalize this characterization by showing that linear context free languages suffice for generating terminal petri net languages in proving this we obtain a new closure property of the family of petri net languages which is not shared by the context free sets

controllability observability of expanded composite systems abstract the relation between original and expanded systems within the inclusion principle from the point of view of controllability observability of both subsystems and composite systems is studied it is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable observable two practically important large classes of complementary matrices are identified to offer results computationally attractive first the existence of complementary matrices ensuring controllability observability of decoupled subsystems is proved then using this result the same property is proved for the composite expanded system

an optimal monte carlo algorithm for multivariate feynman kac path integrals we study a monte carlo algorithm for approximating multivariate feynman kac path integrals parameterized by initial value and potential d variate functions this problem suffers from the curse of dimensionality in the worst case deterministic setting that is why we study the randomized setting in which the functions are sampled at randomized points and the algorithm uses a finite number of such samples we achieve optimality of the randomized algorithm due to variance reduction obtained by smolyak s algorithm for approximating tensor product functions the optimal convergence depends on the smoothness of initial value and potential functions when the initial value and potential functions are r times continuously differentiable we obtain the optimal convergence of order m 1 2 r d for m function samples thus if r d is negligible we do not gain much over the commonly used classical monte carlo algorithm whose convergence is of order m 1 2 hence the classical monte carlo algorithm turns out to be almost

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

contractibility of dynamic lti controllers using complementary matrices a generalized structure of complementary matrices involved in the input state output inclusion principle for linear time invariant systems including contractibility conditions for static state feedback controllers is well known in this note it is shown how to further extend this structure when considering contractibility of dynamic controllers necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion contraction transformation matrices explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion contraction transformation matrices moreover these conditions are further specialized for a particular class of transformation matrices

on greibach normal form construction abstract we present an algorithm which given an arbitrary e free and chain free context free grammar produces an equivalent context free grammar in greibach normal form gnf this algorithm is a generalization of an algorithm recently presented by ehrenfeucht and rozenberg using this algorithm the well known gnf construction of rosenkrantz can be obtained furthermore it is possible to rewrite a given context free grammar by a gnf grammar which has at most twice as much nonterminals as the original grammar this result is shown to be optimal with respect to the number of nonterminals

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

a statistical method of estimation and simulation for systems of stochastic differential equations summary this paper proposes a new statistical method of estimation and simulation for systems of stochastic differential equations by using this method we can easily derive a discretised process from a system of stochastic differential equations the discretised process is tractable enough to simulate the system and to construct the likelihood which is used to estimate the coefficients of the stochastic differential equations from discrete observation

convergence rate of weak local linearization schemes for stochastic differential equations with additive noise there exists a diversity of weak local linearization ll schemes for the integration of stochastic differential equations with additive noise which differ in the algorithms employed for the numerical implementation of the weak local linear discretizations despite convergence results for these discretizations have been already developed the convergence of the weak ll schemes has not been considered up to date in this work a general result concerning the convergence rate of the weak ll schemes is presented as well as specificities for a number of particular schemes as an application the convergence of weak ll schemes for equations driven by poisson processes is presented in addition

output feedback negative imaginary synthesis under structural constraints the negative imaginary property is a property that many practical systems exhibit this paper is concerned with the negative imaginary synthesis problem for linear time invariant systems by output feedback control sufficient conditions are developed for the design of static output feedback controllers dynamic output feedback controllers and observer based feedback controllers based on the design conditions a numerical algorithm is suggested to find the desired controllers structural constraints can be imposed on the controllers to reflect the practical system constraints also the separation principle is shown to be valid for the observer based design finally three numerical examples are presented to illustrate the efficiency of the developed theory

unbiased multi step estimators for the monte carlo evaluation of certain functional integrals abstract a general class of unbiased monte carlo estimators for functional integrals is introduced this class contains previously known unbiased estimators as well as some classical biased estimators improved with special correction terms the new algorithm is applicable under weaker conditions on the functional integral numerical results of simulation studies are presented the variance reduction problem in the infinite dimensional space is considered

on nonnegative unbiased estimators we study the existence of algorithms generating almost surely non negative unbiased estimators of some quantities of practical interest our work is motivated by recent exact approximation methods to compute integrals with respect to any target distribution up to any arbitrary precision these techniques can be implemented as long as non negative unbiased estimators of the target density evaluations are available in particular we show that given a non constant function f from r to r and real valued unbiased estimators xn of r there is no algorithm yielding almost surely non negative unbiased estimators of f even if xn is itself a s non negative then there is no algorithm yielding a s non negative unbiased estimators of f if f is not increasing however if the support of xn is a known interval of r then such algorithms exist as long as the function f satisfies some polynomial bound away from zero the results are discussed in the light of several typical situations corresponding to different functions f

a weak local linearization scheme for stochastic differential equations with multiplicative noise abstract in this paper a weak local linearization scheme for stochastic differential equations sdes with multiplicative noise is introduced first for a time discretization the solution of the sde is locally approximated by the solution of the piecewise linear sde that results from the local linearization strategy the weak numerical scheme is then defined as a sequence of random vectors whose first moments coincide with those of the piecewise linear sde on the time discretization the scheme is explicit preserves the first two moments of the solution of sdes with linear drift and diffusion coefficients in state and time and inherits the mean square stability or instability that such solution may have the rate of convergence is derived and numerical simulations are presented for illustrating the performance of the scheme

random weight particle filtering of continuous time processes it is possible to implement importance sampling and particle filter algorithms where the importance sampling weight is random such random weight algorithms have been shown to be efficient for inference for a class of diffusion models as they enable inference without any time discretization approximation of the underlying diffusion model one difficulty of implementing such random weight algorithms is the requirement to have weights that are positive with probability 1 we show how wald s identity for martingales can be used to ensure positive weights we apply this idea to analysis of diffusion models from high frequency data for a class of diffusion models we show how to implement a particle filter which uses all the information in the data but whose computational cost is independent of the frequency of the data we use the wald identity to implement a random weight particle filter for these models which avoids time discretization error

sufficient conditions for finite time stability and stabilization of nonlinear quadratic systems in this paper we deal with the finite time stability problem for quadratic systems such class of systems plays an important role in the modeling of a wide class of nonlinear processes electrical robotic biological etc the main results of the paper consist of two sufficient conditions for finite time stability analysis and finite time stabilization via static state feedback both conditions are given in terms of the feasibility of a convex optimization problem involving linear matrix inequalities a numerical example illustrates the applicability of the proposed technique

rounding error and perturbation bounds for the cholesky and ldl t factorizations abstract componentwise rounding error and perturbation bounds for the cholesky and ldl t factorizations are derived the precision of the computed cholesky and ldl t factorizations is given

exact pathwise simulation of multi dimensional ornstein uhlenbeck processes abstract the exact pathwise simulation of multidimensional ornstein uhlenbeck processes is considered we propose two procedures that allow the exact pathwise simulation of this type of processes and simultaneously the generation of the underlying wiener trajectories from the same source of randomness this is particularly important when both processes are system components in larger stochastic models for which the study of pathwise dynamics is required

brief paper control of continuous time lti systems by means of structurally constrained controllers this paper deals with the characterization of the fixed modes of multi channel systems with respect to linear time invariant lti structurally constrained controllers fixed modes can be found numerically for any lti system with respect to any given control structure using a random number generator the existing analytical methods however are not capable of characterizing the fixed modes in the most general case of non strictly proper systems with non block diagonal i e overlapping control structure efficiently the notion of a decentralized overlapping fixed mode dofm is introduced in this paper to address the above problem in the most general case to this end the knowledge of the overlapping control structure is translated into a bipartite graph whose vertices correspond to the input and output vectors of various control channels an efficient technique is applied to the obtained graph to identify the dofms of the system it is to be noted that a system is stabilizable via an appropriate lti decentralized overlapping controller if and only if it does not have any unstable dofm moreover it is shown how those modes which are not dofms can be placed freely in the complex plane using a proper lti decentralized overlapping controller the efficacy of this work is demonstrated through an example

accurate evaluation of stochastic wiener integrals with applications to scattering in random media and to nonlinear filtering in 1973 a j chorin math comp 27 1973 pp 1 15 reported quadrature formulas for the approximation of a class of wiener path integrals by n fold ordinary integrals with an error similar formulas are presented here for certain stochastic wiener function space integrals in which n fold integral approximations result in errors o n 2 or o n 3 2 stochastic wiener integrals arise in the physics of wave propagation in random media and in signal estimation problems in communication theory the present formulas provide simple accurate computational tools for these applications among others this point is illustrated by several examples in the paper

technical communique structurally constrained h2 and h control a rank constrained lmi approach this paper describes an iterative linear matrix inequality lmi approach to the design of a structurally constrained output feedback controller the structured synthesis is formulated as a novel rank constrained lmi optimization problem where the controller parameters are explicitly described so as to impose structural constraints on the parameter matrices an iterative penalty function method based on heuristics is used to solve the rank constrained lmi problem a numerical experiment illustrates the practicality of the proposed method

an easy proof of greibach normal form we present an algorithm which given an arbitrary a free context free grammar produces an equivalent context free grammar in 2 greibach normal form the upper bound on the size of the resulting grammar in terms of the size of the initially given grammar is given our algorithm consists of an elementary construction while the upper bound on the size of the resulting grammar is not bigger than the bounds known for other algorithms for converting context free grammars into equivalent context free grammars in greibach normal form

brief paper a note on control of a class of discrete time stochastic systems with distributed delays and nonlinear disturbances this paper is concerned with the state feedback control problem for a class of discrete time stochastic systems involving sector nonlinearities and mixed time delays the mixed time delays comprise both discrete and distributed delays and the sector nonlinearities appear in the system states and all delayed states the distributed time delays in the discrete time domain are first defined and then a special matrix inequality is developed to handle the distributed time delays within an algebraic framework an effective linear matrix inequality lmi approach is proposed to design the state feedback controllers such that for all admissible nonlinearities and time delays the overall closed loop system is asymptotically stable in the mean square sense sufficient conditions are established for the nonlinear stochastic time delay systems to be asymptotically stable in the mean square sense and then the explicit expression of the desired controller gains is derived a numerical example is provided to show the usefulness and effectiveness of the proposed design method

approximation of wiener integrals we present a new proof of chorin s quadrature formula for weiner integrals numerical experiments show that the rate of convergence may not be quadratic if the functional is not twice differentiable copyright 1987 academic press inc

explicit evaluation of a path integral with memory kernel an explicit expression is presented for the path integral of an harmonic oscillator interacting with itself in the past the time dependence of the memory kernel is assumed to be exponential the relation with the feynman trial action for the variational calculation of the polaron ground state energy is discussed

a numerical method for the computation of the lyapunov exponents of nonlinear ordinary differential equations in this paper an alternative method to compute the lyapunov exponents of dynamical systems described by ordinary differential equations odes is introduced the lyapunov exponents are computed in terms of the solutions of two piecewise linear odes that approximate respectively the solutions of the original ode and its associated variational equation this approach is strongly connected with the local linearization ll method for odes and its major advantage is that these piecewise linear odes might be exactly integrated in a non simultaneous way the performance of the method is illustrated with a numerical example

sequential monte carlo methods for diffusion processes in this paper we show how to use sequential monte carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w r t the initial condition of the process in some cases via the exact simulation of the diffusion there is no time discretization error otherwise the methods use euler discretization we illustrate our approach on both high and low dimensional problems from optimal control and establish that our approach substantially outperforms standard monte carlo methods typically adopted in the literature the methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging

dynamic properties of the local linearization method for initial value problems some dynamic properties of the local linearization ll scheme for the numerical integration of initial value problems in ordinary differential equations odes are investigated specifically the general conditions under which this scheme preserves the stationary points and periodic orbits of the odes and the local stability at these steady states are studied these dynamic properties are also examined by means of numerical experiments and the results are compared with those achieved by other numerical schemes in addition a brief review of the computational implementations of the ll scheme is also presented

language equivalence of probabilistic pushdown automata we study the language equivalence problem for probabilistic pushdown automata ppda and their subclasses we show that the problem is interreducible with the multiplicity equivalence problem for context free grammars the decidability of which has been open for several decades interreducibility also holds for ppda with one control state in contrast for the case of a one letter input alphabet we show that ppda language equivalence and hence multiplicity equivalence of context free grammars is in pspace and at least as hard as the polynomial identity testing problem

brief paper stability and stabilization of aperiodic sampled data control systems using robust linear matrix inequalities stability analysis of an aperiodic sampled data control system is considered for application to networked and embedded control the stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals although this condition is numerically intractable a tractable sufficient condition can be constructed with the mean value theorem special attention is paid to tightness of the sufficient condition for less conservative stability analysis a region dividing technique for the reduction of conservatism and generalization to stabilization are also discussed an example demonstrates the efficacy of the approach

on structural controllability theorem the structural controllability theorem was given first by lin for the single input case by the graph theoretic approach and several authors extended this to the multiinput case by the matrix algebra in this correspondence a graph theoretic interpretation of the condition that the structured matrix a b has generically full rank is derived from well known theorem in the graph theory and this leads to a quite simple proof of the structural controllability theorem

technical communique static output feedback control under information structure constraints an important challenge in the static output feedback control context is to provide an isolated gain matrix possessing a zero nonzero structure mainly in problems presenting information structure constraints although some previous works have contributed some relevant results to this issue a fully satisfactory solution has not yet been achieved up to now in this note by using a linear matrix inequality approach and based on previous results given in the literature we present an efficient methodology which permits us to obtain an isolated static output feedback gain matrix having simultaneously a zero nonzero structure imposed a priori

approximation of lyapunov exponents of nonlinear stochastic differential equations we consider nonlinear stochastic differential systems defined either on a compact orientable manifold or on mathbb r d under our hypotheses their lyapunov exponents are deterministic we propose an efficient algorithm of numerical computation of these exponents and we give a theoretical estimate for the approximation error the method is based upon the discretization of the linearized stochastic flows of diffeomorphisms generated by the differential systems results of numerical experiments are also presented

weak local linear discretizations for stochastic differential equations convergence and numerical schemes weak local linear wll discretizations are playing an increasing role in the construction of effective numerical integrators and inference methods for stochastic differential equations sdes with additive noise however due to limitations in the existing numerical implementations of wll discretizations the resulting integrators and inference methods have either been restricted to particular classes of autonomous sdes or showed low computational efficiency another limitation is the absence of a systematic theoretical study of the rate of convergence of the wll discretizations and numerical integratos this task is the main purpose of the present paper a second goal is introducing a new wll scheme that overcomes the numerical limitations mentioned above additionally a comparative analysis between the new wll scheme and some conventional weak integrators is also presented

simulation of stochastic differential equations through the local linearization method a comparative study a new local linearization ll scheme for the numerical integration of nonautonomous multidimensional stochastic differential equations sdes with additive noise is introduced the numerical scheme is based on the local linearization of the sde s drift coefficient by means of a truncated ito taylor expansion a comparative study with the other ll schemes is presented which shows some advantanges of the new scheme over other ones

robust overlapping guaranteed cost control of uncertain state delay discrete time systems this note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state delayed discrete time systems with norm bounded uncertainties using the concept of guaranteed cost control expansion contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved including conditions on the equality of guaranteed performance bounds the controllers are designed in the expanded space using a linear matrix inequality lmi delay independent procedure specifically adapted to this class of problems the designed controllers are then contracted and implemented into the original system the results are specialized for the overlapping decentralized control design the method enables an effective construction of block tridiagonal controllers a numerical illustrative example is supplied

robust variance reduction for random walk methods random walk methods are effective for solving linear partial differential equations in many dimensions especially those involving complex geometries they are based on an equivalence given by a feynman kac formula between an expectation of a functional of a stochastic process and the solution at a point of a partial differential equation the drawback is that the error is proportional only to the square root of the reciprocal of the number of trials efficiency depends critically on variance reduction a general strategy for doing this in the case of stochastic differential equations is proposed by milstein the idea is to introduce a bias in the drift term and to exactly compensate for this by unequal weighting of the trials there is an optimal bias defined in terms of the solution of the partial differential equation which reduces the variance to zero in practice an approximation is used this idea has been tested under the name biased brownian dynamics on the problem of calculating rate constants for diffusion limited reactions the approach is successful in some cases but is less successful in more difficult cases due to the occasional occurrence of a well above average weight proposed and tested here is a weight control algorithm which greatly enhances the effectiveness of biased brownian dynamics

decision problems for word hyperbolic semigroups abstract this paper studies decision problems for semigroups that are word hyperbolic in the sense of duncan and gilman a fundamental investigation reveals that the natural definition of a word hyperbolic structure has to be strengthened slightly in order to define a unique semigroup up to isomorphism this does not alter the class of word hyperbolic semigroups the isomorphism problem is proven to be undecidable for word hyperbolic semigroups in contrast to the situation for word hyperbolic groups it is proved that it is undecidable whether a word hyperbolic semigroup is automatic asynchronously automatic biautomatic or asynchronously biautomatic these properties do not hold in general for word hyperbolic semigroups it is proved that the uniform word problem for word hyperbolic semigroups is solvable in polynomial time improving on the previous exponential time algorithm algorithms are presented for deciding whether a word hyperbolic semigroup is a monoid a group a completely simple semigroup a clifford semigroup or a free semigroup

explicit evaluation of certain gaussian functional integrals arising in problems of statistical physics an explicit formula is presented for a conditional wiener integral the integrand of which is an exponential of a general quadratic functional of the path the functional integrals arising in non markovian gaussian approximations to various problems of statistical physics e g theory of the large polaron theory of disordered systems are easily recovered as special cases

local linearization method for numerical integration of delay differential equations in this paper a new approach for the numerical computation of delay differential equations ddes is introduced the essential idea consists of obtaining numerical integrators that use a code expressly developed for linear ddes in contrast with the conventional approach of using a code for ordinary differential equations specifically two numerical schemes of this new class of integrators are proposed and their numerical viability analyzed it includes the estimation of the convergence rate the evaluation of the computational cost of the schemes and a simulation study it is proved that these one step explicit integrators converge uniformly with order two to the solution of nonlinear ddes and are able to integrate stiff equations in a satisfactory way with low computational cost

structurally constrained controller synthesis for general proper plants with application to vehicle platooning abstractthis paper considers the problem of synthesizing a static output feedback sof subject to arbitrary information structure constraints in particular the plants can be non strictly proper in such a case the existing methods are hardly applicable except few special cases a general approach that significantly differs from the existing methods is proposed that is able to deal with the most general case with the feature that both finite frequency and full frequency h infinity performance specifications can be addressed in a unified manner sufficient solvability conditions are derived in terms of a set of finite frequency positive real and strictly positive real conditions of linear matrix inequalities lmis form some frequency dependent matrices are introduced into the design with the merit of making the conditions less restrictive several numerical examples are given that demonstrate the efficacy of the proposed approach including applications to vehicle platooning

letter to the editor computing multiple integrals involving matrix exponentials in this paper a generalization of a formula proposed by van loan computing integrals involving the matrix exponential ieee trans automat control 23 1978 395 404 for the computation of multiple integrals of exponential matrices is introduced in this way the numerical evaluation of such integrals is reduced to the use of a conventional algorithm to compute matrix exponentials the formula is applied for evaluating some kinds of integrals that frequently emerge in a number classical mathematical subjects in the framework of differential equations numerical methods and control engineering applications

double greibach operator grammars every context free grammar can be transformed into one in double greibach operator form that satisfies both double greibach form and operator form examination of the expressive power of various well known subclasses of context free grammars in double greibach and or operator form yields an extended hierarchy of language classes basic decision properties such as equivalence can be stated in stronger forms via new classes of languages in this hierarchy

a canonical form for the inclusion principle of dynamic systems the inclusion principle provides a mathematical framework for comparing behavior of dynamic systems having different dimensions our main objective is to derive a canonical form for larger systems expansions that are obtained by expanding smaller systems contractions the form offers full freedom in selecting appropriate matrices for the expansion contraction process we will broaden the form to include feedback and propose an explicit characterization of contractible control laws subject to overlapping information structure constraints

griebach normal form transformation revisited we develop a new method for placing a given context free grammar into greibach normal form with only polynomial increase of its size starting with an arbitrarye free context free grammarg we transformginto an equivalent context free grammarhin extended greibach normal form i e in addition to rules fulfilling the greibach normal form properties the grammar can have chain rules the size ofhwill beo g 3 where g is the size ofg moreover in the case thatgis chain rule free hwill be already in greibach normal form ifhis not chain rule free then we use the standard method for chain rule elimination for the transformation ofhinto greibach normal form the size of the constructed grammar iso g 4

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

a new approach to control design with overlapping information structure constraints in this paper a new strategy is proposed for decentralized state feedback design with overlapping information structure constraints the method combines linear matrix inequalities and the inclusion principle in a way that eliminates controllability problems that are inherent to standard decentralized control design in the expanded space this approach can be extended to include an important class of uncertain nonlinearities and its validity is demonstrated through applications to strings of moving vehicles

unbiased monte carlo evaluation of certain functional integrals abstract a monte carlo algorithm for the evaluation of certain functional integrals is introduced this algorithm is not based on the approximation of the functional integral by a finite dimensional integral unbiased estimators for the functional integrals are constructed and corresponding variance reduction techniques are considered numerical results of simulation studies are presented

a new algorithm and worst case complexity for feynman kac path integration abstract we study algorithms for approximation of feynman kac path integrals in the worst case setting the algorithms use a finite number of samples of the initial condition and potential functions we present a new algorithm and an explicit bound on its cost to compute an e approximation to the feynman kac path integral we also establish bounds on the worst case complexity of feynman kac path integration the upper bound is equal to the cost of the new algorithm and is given in terms of the complexity of a certain function approximation problem the lower bound is given in terms of the complexity of a certain weighted integration problem for some classes of functions these two bounds coincide modulo a multiplicative factor in this case the new algorithm is almost optimal the new algorithm requires precomputation of some real coefficients that are combinations of multivariate integrals with special weights this precomputation is difficult and limits the application of the new algorithm we report the results of the precomputation for specific cases

categorial dependency grammars categorial dependency grammars cdgs are classical categorial grammars extended by oriented polarized valencies at the same time cdgs represent a class of completely lexicalized dependency grammars they express both projective and non projective dependencies cdgs generate non context free languages at that they are parsed in polynomial time under realistic conditions cdgs possess a normal form that is analogous to greibach normal form for cf grammars cdg languages are closed under almost all afl operations and are accepted by a special class of push down automata with independent counters