homotopy approach for solving constrained optimization problems a homotopy approach for solving constrained parameter optimization problems is examined the first order necessary conditions with the complementarity conditions represented using a technique due to mangasarian 1967 are solved the equations are augmented to avoid singularities which occur when the active constraint changes the chow yorke 1978 algorithm is used to track the homotopy path leading to the solution to the desired problem at the terminal point a simple example which illustrates the technique and an application to a fuel optimal orbital transfer problem are presented

a complete equational axiomatization for mpa with string iteration we study equational axiomatizations of bisimulation equivalence for the language obtained by extending milner s basic ccs with string iteration string iteration is a variation on the original binary version of the kleene star operation p q obtained by restricting the first argument to be a non empty sequence of atomic actions we show that for every positive integer k bisimulation equivalence over the set of processes in this language with loops of length at most k is finitely axiomatizable provided that the set of actions is finite we also offer an infinite equational theory that completely axiomatizes bisimulation equivalence over the whole language we prove that this result cannot be improved upon by showing that no finite equational axiomatization of bisimulation equivalence over basic ccs with string iteration can exist unless the set of actions is empty

exploring collision free path planning by using homotopy continuation methods autonomous and semi autonomous robots play significant roles in space and terrestrial exploration even more in unfavorable and dangerous environments although recent advances allow robots to evolve in many such environments one of the most important problems remains the establishment of collision free trajectories in static or partially temporal static environments this paper presents a different approach to address this problem proposing a methodology based on homotopy continuation methods hcm capable of generating collision free trajectories in two and three dimensions the basic idea behind the proposal relies on the construction of a nonlinear equation representing the map of the environment making it possible to apply hcm methods to obtain collision free paths a series of simulations are presented to show the effectiveness of the method avoiding circular semi rectangular spherical shaped and semi parallelepipeds obstacles

homotopy methods for solving the optimal projection equations for the h2 reduced order model problem the optimal projection approach to solving the h2 reduced order model problem produces two coupled highly nonlinear matrix equations with rank conditions as constraints due to the resemblance of these equations to standard matrix lyapunov equations they are called modified lyapunov equations the algorithms proposed herein utilize probability one homotopy theory as the main tool it is shown that there is a family of systems the homotopy that make a continuous transformation from some initial system to the final system with a carefully chosen initial problem a theorem guarantees that all the systems along the homotopy path will be asymptotically stable controllable and observable one method which solves the equations in their original form requires a decomposition of the projection matrix using the drazin inverse of a matrix it is shown that the appropriate inverse is a differentiable function an effective algorithm for computing the derivative of the projection matrix that involves solving a set of sylvester equations is given another class of methods considers the equations in a modified form using a decomposition of the pseudogramians based on a contragredient transformation some freedom is left in making an exact match between the number of equations and the number of unknowns thus effectively generating a family of methods

polynomial solution of the standard multivariable spl hscr sub 2 optimal control problem in this work the authors solve the standard multivariable spl hscr sup 2 optimal control problem using polynomial matrix techniques

probability one homotopies in computational science probability one homotopy algorithms are a class of methods for solving nonlinear systems of equations that under mild assumptions are globally convergent for a wide range of problems in science and engineering convergence theory robust numerical algorithms and production quality mathematical software exist for general nonlinear systems of equations and special cases such as brouwer fixed point problems polynomial systems and nonlinear constrained optimization using a sample of challenging scientific problems as motivation some pertinent homotopy theory and algorithms are presented the problems considered are analog circuit simulation for nonlinear systems reconfigurable space trusses for polynomial systems and fuel optimal orbital rendezvous for nonlinear constrained optimization the mathematical software packages hompack90 and polsys plp are also briefly described

the singular h 2 control problem in this paper we discuss the standard h2 control problem for linear finite dimensional time invariant systems without any assumptions on the system parameters we give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained

probability one homotopy algorithms for solving the coupled lyapunov equations arising in reduced order h2 h modeling estimation and control optimal reduced order modeling estimation and control with respect to combined h 2 h criteria give rise to coupled lyapunov and riccati equations to develop reliable numerical algorithms for these problems this paper focuses on the coupled lyapunov equations which appear as a subset of the synthesis equations in particular this paper systematically examines the requirements of probability one homotopy algorithms to guarantee global convergence homotopy algorithms for nonlinear systems of equations construct a continuous family of systems and solve the given system by tracking the continuous curve of solutions to the family the main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the coupled lyapunov equations and variations based upon canonical forms these results are essential to the probability one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms

free rotation of a circular ring with an unbalanced mass large space structures are much more flexible than their terrestrial counterparts rotation of large space structures may be desirable for stability thermal or artificial gravity reasons previous literature includes the large deformations due to the free rotation of a slender rod and a ring about a diameter an important model of a space station is a ring rotating about its axis of symmetry if the ring is balanced it will be stable and remain circular the present note considers the case when the ring is unbalanced by a mass attached to a point on the ring

an operational semantics for a calculus for wireless systems in wireless systems the communication mechanism combines features of broadcast synchrony and asynchrony we develop an operational semantics for a calculus of wireless systems we present different reduction semantics and a labelled transition semantics and prove correspondence results between them finally we apply cws to the modelling of the alternating bit protocol and prove a simple correctness result as an example of the kind of properties that can be formalized in this framework a major goal of the semantics is to describe the forms of interference among the activities of processes that are peculiar of wireless systems such interference occurs when a location is simultaneously reached by two transmissions the reduction semantics differ on how information about the active transmissions is managed we use the calculus to describe and analyse a few properties of a version of the alternating bit protocol

on steplength algorithms for a class of continuation methods the continuation methods considered here are algorithms for the computational analysis of the regular parts of the solution field of equations of the form fx b f d subset r n 1 to r n for given b in r n while these methods are similar in structure to those used for ode solvers their errors are independent of the history of the process and are solely determined by the termination criterion of the corrector at the current step this suggests the use of a posteriors estimates of the convergence radii of the corrector it is proved here that such estimates cannot be obtained from the sequence of corrector iterates alone but that they require some global information about f however it is shown that a finite sequence of corrector iterates does allow for the computation of effective estimates of the convergence quality of certain types of correctors this is used for the design of various step algorithms for continuation processes two of them are based on a newton corrector while the third o

algorithms for optimal control with invariant zeros on the extended imaginary axis abstract we transform an control problem with invariant zeros on the extended imaginary axis into a regular problem then using the nevanlinna pick theorem we find necessary and sufficient existence conditions for the original control problem an algorithm and examples with invariant zeros on the extended imaginary axis are given by the same approach we also solve the singular 2 control problem

preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation the dc operating point of a circuit may be computed by tracking the zero curve of an associated artificial parameter homotopy homotopy algorithms exist that are globally convergent with probability one for the dc operating point problem these algorithms require computing the one dimensional kernel of the jacobian matrix of the homotopy mapping at each step along the zero curve and hence the solution of a linear system of equations at each step these linear systems are typically large highly sparse non symmetric and indefinite several iterative methods which are applicable to such problems including craig s method gmres k bicgstab qmr kacz and lsqr are applied to a suite of test problems derived from simulations of actual bipolar circuits preconditioning techniques considered include incomplete lu factorization ilu sparse submatrix ilu and ilu allowing restricted fill in bands or blocks timings and convergence statistics are given for each iterative method and preconditioner

least change secant update methods for undetermined systems least change secant updates for nonsquare matrices have been addressed recently in 6 here the use of these updates in iterative procedures for the numerical solution of underde retrained systems is considered the model method is the normal flow algorithm used in homotopy or continuation methods for determining points on an implicitly defined curve a kantorovich type local convergence analysis is given which supports the use of least change secant updates in this al gorithm this analysis also provides a kantorovich type local convergence analysis for least change secant update methods in the usual case of an equal number of equations and unknowns this in turn gives a local convergence analysis for augmented jacobian algorithms which use least change secant updates in conclusion the results of some numerical experiments are given

sampled data and discrete time h_2 optimal control this paper deals with the sampled data h 2 optimal control problem given a linear time invariant continuous time system the problem of minimizing the h 2 performance over all sampled data controllers with a fixed sampling period can be reduced to a pure discrete time h 2 optimal control problem this discrete time h 2 problem is always singular motivated by this in this paper we give a treatment of the discrete time h 2 optimal control problem in its full generality the results we obtain are then applied to the singular discrete time h 2 problem arising from the sampled data h 2 problem in particular we give conditions for the existence of optimal sampled data controllers we also show that the h 2 performance of a continuous time controller can always be recovered asymptotically by choosing the sampling period sufficiently small finally we show that the optimal sampled data h 2 performance converges to the continuous time optimal h 2 performance as the sampling period converges to zero

about fair asynchrony abstract this paper examines the joint influence of fairness and asynchrony on the semantic modelling of a c c s like language fairness is the guarantee for every agent engaged in a computation to communicate with the other asynchronous agents if such communications are infinitely often possible programs are compared according to an implementation preorder which reflects the inclusion of observable properties whenever for every context c and for every program r no computation of r experimenting upon c p allows to recognize p versus q p is considered less than q a fully abstract model of the preorder is constructed in a domain of infinitary language preferred here to classical algebraic domains the restriction to bounded parallelism is analysed in that simplified framework the model turns effective and moreover decidable

a coprime factorisation and its application in ℋ2 control given a plant transfer matrix as a fraction of two polynomial matrices we present a doubly coprime factorisation identity over the proper stable rational matrices of the plant transfer matrix and

real time optimization algorithm for nonlinear receding horizon control abstract a real time optimization technique is discussed concerning state feedback control of general nonlinear systems an optimal state feedback law is determined so that a receding horizon performance index with a moving terminal time is minimized it is shown that the receding horizon control problem can be converted to an initial value problem for an ordinary differential equation that can be solved numerically without recourse to iterative methods the proposed solution technique is applied to a control experiment on a simplified space vehicle model the penalty function approach is employed in the performance index so that the space vehicle model attains the objective state avoiding an obstacle the model is controlled successfully at the sampling frequency of 30 hz in the hardware experiment

a parallel method of eigenvalue analysis using dynamic substructuring and homotopy continuation a parallel method to solve large eigenvalue problems using dynamic substructuring and homotopy continuation is presented unlike the conventional approaches in substructuring the non linear term is not neglected for improved accuracy therefore instead of solving the approximated condensed problems full exact condensed forms are treated homotopy continuation method is introduced to solve the non linear reduced eigenvalue problem in the process small number of substructure modes are used to reduce the original eigenvalue problem and additional degrees of freedom besides those at interfaces are selected the whole procedures are implemented to workstation cluster using pvm to show how the method works simple two dimensional numerical examples are solved it is demonstrated that the method yields highly accurate results and good parallel efficiency 1998 john wiley sons ltd

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

bisimulation and action refinement abstract for event structures with silent moves we consider several types of bisimulation that incorporate true concurrency to a varying degree and show how each can be lifted in a uniform way to a congruence with respect to action refinement we prove that we have constructed the coarsest congruences that respect interleaving pomset and history preserving bisimulation

structure of concurrency abstract noninterleaving models of concurrency assume that behavioural properties of systems can be adequately modelled in terms of causal partial orders we claim that the structure of concurrency is richer with causality being only one of the invariants generated by a set of closely related executions or observations the model we propose supports three levels of abstraction the observation level invariant level and system level and we will proceed from the bottom observation level to the top system level this is in contrast to the way other models for concurrency are introduced as they essentially support two levels of abstraction the system level and behavioural level which includes both observations and invariants with the direction of development going from the system to behavioural level in this paper we first discuss the notion of an observation of a concurrent behaviour in particular we investigate the role played by interval partial orders we then introduce a general framework for dealing with invariants generated by sets of closely related observations this leads to the formulation of the notion of a concurrent history whose structural properties are subsequently studied

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

a transformation to avoid solutions at infinity for polynomial systems in finding all solutions to polynomial systems the existence of solutions at infinity makes the problem more difficult particularly when a continuation method is being used as the solution technique systems with solutions at infinity do arise in applications for example in computer graphics and geometric modeling in this paper a simple transformation of the system is given which eliminates solutions at infinity

computation of critical boundaries on equilibrium manifolds the study of various equilibrium phenomena leads to nonlinear equations 1 f y u 0 where y in r n is a vector of behavior or state variables u in r p a vector of p geqq 2 parameters or controls and f d subset r n times r p to r n a sufficiently differentiable map the solution set of 1 in r n times r p is often called the equilibrium surface of the problem and in many applications it is of interest to determine the critical boundary that is the set of solutions of 1 where the derivative d y f x is singular for example in structural problems these points may represent buckling points after characterizing the various properties of the problem we present three different numerical methods which allow for a computational trace of paths in the critical boundary these methods represent extensions of the earlier developed locally parametrized continuation method for tracing regular paths on the equilibrium surface they permit for instance a direct computational deter

note on the homotopy perturbation method for multivariate vector value oscillatory integrals this paper considers a homotopy perturbation method for approximating multivariate vector value highly oscillatory integrals the asymptotic formulae of the integrals and the asymptotic order of the asymptotic method are presented numerical examples show the efficiency of the approximation method

asynchronous mappings and asynchronous cellular automata the aim of this paper is the study of asynchronous automata a special kind of automata which encode the independency relation between actions and which enable their concurrent execution these automata introduced by zielonka rairo inform theor appl 21 99 135 1987 constitute a natural extension of finite automata to the case of asynchronous parallelism their behaviour is described by trace languages subsets of partially commutative monoids the main result concerning this class of automata states that they accept exactly all recognizable trace languages in this paper we give new improved constructions of asynchronous automata in the final part of the paper we present a distributed system of messages with bounded time stamps based on asynchronous automata

numerical linear algebra aspects of globally convergent homotopy methods probability one homotopy algorithms are a class of methods for solving nonlinear systems of equations that are globally convergent with probability one these methods are theoretically powerful and if constructed and implemented properly are robust numerically stable accurate and practical the concomitant numerical linear algebra problems deal with rectangular matrices and good algorithms require a delicate balance not always achieved of accuracy robustness and efficiency in both space and time the author s experience with globally convergent homotopy algorithms is surveyed here and some of the linear algebra difficulties for dense and sparse problems are discussed

infinite streams and finite observations in the semantics of uniform concurrency two ways of assigning meaning to a language with uniform concurrency are presented and compared the language has uninterpreted elementary actions from which statements are composed using sequential composition nondeterministic choice parallel composition with communication and recursion the first semantics uses infinite streams in the sense which is a refinement of the linear time semantics of de bakker et al the second semantics uses the finite observations of hoare et al situated in between the divergence and readiness semantics of olderog hoare it is shown that the two models are isomorphic and that this isomorphism induces an equivalence result between the two semantics

on general ℋ2 control from frequency to time domain this article presents a general formula for discrete time 2 control it works with the regular and singular case of 2 control i e in the case of possibly non left invertible matrices g 12 and non right invertible matrices g 21 with possible unit circle invariant zeros in the generic case it can be simplified and adapted to work with the plant transfer matrix directly without invoking the matrices of the parameterisation of stabilising controllers a further result of this article is the presented necessary and sufficient conditions for state space 2 control under only stabilisability and detectability assumptions if the conditions are satisfied an observer based 2 controller is constructed the corresponding numerical algorithm consists of solving two discrete time algebraic riccati systems darss and two eigen problems

two decentralized algorithms for strong interaction fairness for systems with unbounded speed variability abstract we present two randomized algorithms one for message passing and the other for shared memory that with probability 1 schedule multiparty interactions in a strongly fair manner both algorithms improve upon a previous result by joung and smolka proposed in a shared memory model along with a straightforward conversion to the message passing paradigm in the following aspects first processes speeds as well as communication delays need not be bounded by any predetermined constant secondly our algorithms are completely decentralized and the shared memory solution makes use of only single writer variables finally both algorithms are symmetric in the sense that all processes execute the same code and no unique identifier is used to distinguish processes

stable families of behavioural equivalences abstract many of the behavioural equivalences studied in the literature see 1 2 3 4 are defined generically on any transition system in particular on their own quotient system it would seem reasonable to expect such an equivalence to be idempotent in this respect in other words to yield the identity the second time we capture this idea in the notion of a stable family of preorders on transition systems and investigate the stability of the equivalences in 1 2 3 4 in addition our approach involves general schemes of definition of equivalences on transition systems which lead to extensions of the hierarchy results of 1

the h2 control problem a general transfer function solution a general solution of the h2 control problem is presented for linear systems described by rational transfer matrices not necessarily proper or stable the control system is considered in the standard configuration which includes the synthesis model of the plant and the controller the h2 control problem consists of internally stabilizing the control system while minimizing the h2 norm of its transfer function the notion of internal stability is based on bounded input bounded output stability and means that subsystems defined by any pair of input and output signals within the control system all are bounded input bounded output stable in this manner the optimal control system is devoid of impulsive as well as non decaying exponential modes the solution proceeds in three steps first the set of all controllers that internally stabilize the control system is parameterized then the subset of the stabilizing controllers that achieve a finite value of the h2 norm of the control system transfer matrix is

lq control of descriptor systems a spectral factorisation approach a spectral factorisation algorithm of improper matrices and existence results under controllability conditions are presented based on these results an algorithm for linear quadratic lq control of rectangular descriptor systems without the detectability and infinite observability conditions is presented the matrix pencil associated with the euler lagrange differential equations can be singular can have finite generalised eigenvalues on the imaginary axis and infinite generalised eigenvalues of any multiplicity in the class of optimal state feedback controls we find a control that renders the closed loop system marginally stable and impulse free also we find conditions on x 0 that guarantee the optimality it is shown how the disturbance attenuation problem of descriptor systems can be re formulated as an optimal state feedback feedforward control problem for which the results of this article can be applied when applied to state space systems the algorithm of this article which is based on

deciding bisimulation equivalences for a class of non finite state programs traditionally many automatic program verification techniques have been applicable only to finite state programs in this paper we extend some of these techniques to a class of infinite state programs that in addition to having a finite state control component may read store and write but not perform any other computations on data such programs are data independent in the sense that their behavior does not depend on the actual data values supplied we consider the problems of deciding strong equivalence and observation equivalence defined by bisimulations as in ccs between such programs these equivalences have major applications in verification of communication protocols we present reductions of these problems to the problem of deciding strong equivalence and observation equivalence between finite state programs for which polynomial time algorithms exist the equivalence problems on data independent programs are shown to be np hard in the size of the programs

on the semantics of markov automata markov automata describe systems in terms of events which may be nondeterministic may occur probabilistically or may be subject to time delays we define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between such systems a generalisation of reduction barbed congruence the well known touchstone equivalence for a large variety of process description languages

non well founded sets modeled as ideal fixed points abstract motivated by ideas from the study of abstract data types we show how to interpret non well founded sets as fixed points of continuous transformations of an initial continuous algebra we conisder a preordered structure closely related to the set hf of well founded hereditarily finite sets by taking its ideal completion we obtain an initial continuous algebra in which we are able to solve all of the usual systems of equations that characterize hereditarily finite non well founded sets in this way we are able to obtain a structure which is isomorphic to hf 1 the non well founded analog of hf

a homotopy for solving polynomial systems this paper presents a continuation method for finding all solutions to polynomial systems it features a simpler homotopy than has been previously published

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

large deformations of rotating polygonal space structures the effects of rotation on space structures are very important nowadays because the structures are large and thus relatively flexible unacceptable stresses or deformations may occur due to centrifugal forces in a recent paper we considered the effects of rotation on an unbalanced circular ring the present note studies a related problem i e the free rotation of polygonal frames these shapes are basic in structural design

a globally convergent probability one homotopy for linear programs with linear complementarity constraints a solution of the standard formulation of a linear program with linear complementarity constraints lpcc does not satisfy a constraint qualification a family of relaxations of an lpcc associated with a probability one homotopy map proposed here is shown to have several desirable properties the homotopy map is nonlinear replacing all the constraints with nonlinear relaxations of ncp functions under mild existence and rank assumptions 1 the lpcc relaxations rlpcc lambda have a solution for 0 le lambda le1 2 rlpcc 1 is equivalent to lpcc 3 the kuhn tucker constraint qualification is satisfied at every local or global solution of rlpcc lambda for almost all 0 le lambda 1 4 a point is a local solution of rlpcc 1 and lpcc if and only if it is a kuhn tucker point for rlpcc 1 and 5 a homotopy algorithm can find a kuhn tucker point for rlpcc 1 since the homotopy map is a globally convergent probability one homotopy robust and efficient numerical algorithms exist to f

parallel adaptive gmres implementations for homotopy methods the success of probability one homotopy methods in solving large scale optimization problems and nonlinear systems of equations on parallel architectures may be significantly enhanced by the accurate parallel solution of large sparse nonsymmetric linear systems iterative solution techniques such as gmres k favor parallel implementations however their straightforward parallelization usually leads to a poor parallel performance because of global communication incurred by processors one variation of gmres k considered here is to adapt the restart value k for any given problem and use householder reflections in the orthogonalization phase coupled with graph based matrix partitioning to achieve high accuracy and reduce the communication overhead this particular gmres implementation is tailored to the uniquely stringent requirements imposed on a linear system solver by probability one homotopy algorithms occasionally unusually high accuracy ability to adapt to problems of widely varying difficulty and parallelism

theory of globally convergent probability one homotopies for nonlinear programming for many years globally convergent probability one homotopy methods have been remarkably successful on difficult realistic engineering optimization problems most of which were attacked by homotopy methods because other optimization algorithms failed or were ineffective convergence theory has been derived for a few particular problems and considerable fixed point theory exists but generally convergence theory for the homotopy maps used in practice for nonlinear constrained optimization has been lacking this paper derives some probability one homotopy convergence theorems for unconstrained and inequality constrained optimization for linear and nonlinear inequality constraints and with and without convexity some insight is provided into why the homotopies used in engineering practice are so successful and why this success is more than dumb luck by presenting the theory as variations on a prototype probability one homotopy convergence theorem the essence of such convergence theory is elucidated

additive models of probabilistic processes we propose a new model of probabilistic processes in this model a probability is assigned to the action of a prefix and a probability distribution is assigned to the components of a parallel composition in addition the probability of a transition of a probabilistic summation is evaluated as the sum of the probabilities of the same transition of summands multiplied by the probabilities associated to them in the summation the concepts of strong bisimulation degree and weak bisimulation degree are introduced these notions provide us with continuous spectra of strong bisimilarities weak bisimilarities and observation congruences which equate probabilistic processes with different degrees of belief various equational laws of probabilistic processes with respect to these equivalence relations are presented and substitutivities of these equivalence relations under various combinators are established

gsos and finite labelled transition systems recently there has been considerable interest in studying formats of plotkin style inference rules which ensure that the induced labelled transition system semantics have certain properties in this note i shall give a contribution to this line of research by giving a restricted version of bloom istrail and meyer s gsos format bloom et al 1988 bloom 1989 which induces finite labelled transition systems

a complete axiomatization of finite state acsr processes a real time process algebra called acsr has been developed to facilitate the specification and analysis of real time systems acsr supports synchronous timed actions and asynchronous instantaneous events timed actions are used to represent the usage of resources and to model the passage of time events are used to capture synchronization between processes to be able to specify real time systems accurately acsr supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization in addition to operators common to process algebra acsr includes the scope operator which can be used to model timeouts and interrupts equivalence between acsr terms is based on the notion of strong bisimulation this paper briefly describes the syntax and semantics of acsr and then presents a set of algebraic laws that can be used to prove equivalence of acsr processes the contribution of this paper is the soundness and completeness proofs of this set of laws the completeness proof is for finite state acsr processes which are defined to be processes without free variables under parallel operator or scope operator

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

numerical approximations for highly oscillatory bessel transforms and applications abstract this paper presents an efficient numerical method for approximating highly oscillatory bessel transforms based on analytic continuation we transform the integrals into the problems of integrating the forms on 0 with the integrand that does not oscillate and decays exponentially fast which can be efficiently computed by using gauss laguerre quadrature rule we then derive the error of the method depending on the frequency and the node number moreover we apply the scheme for studying the approximations of the solutions of two kinds of highly oscillatory integral equations preliminary numerical results show the efficiency and accuracy of numerical approximations

a context dependent equivalence between processes abstract in recent years several equivalences between nondeterministic and concurrent processes have been proposed in order to capture different notions of the extensional behaviour of a process usually the equivalences are congruences with respect to the process constructing operations in order to support hierarchic development of systems with the purpose of achieving more flexible hierarchic development methods we suggest parametrizing the equivalences with information about contexts we carry out the suggestion in full for the bisimulation equivalence which we parameterize with a special type of context information called environments as a main theorem we offer a useful characterization of the information ordering on environments also a modal characterization of the parameterized bisimulation equivalence is presented

solving nonlinear systems of equations with only one nonlinear variable abstract we describe a method for solving systems of n 1 nonlinear equations in n 1 unknowns y te r and z te r n of the form a y z b y 0 where the n 1 n matrix a y and vector b y are functions of y alone such equations arise in minimax approximation we reduce the problem to one equation in y only an efficient quadratically convergent numerical technique based on newton s method in one variable is used to solve this equation computational details and results are provided and two generalizations are discussed

numerical complexiton solutions for the complex kdv equation by the homotopy perturbation method in this paper the homotopy perturbation method is extended to investigate the numerical complexiton solutions of the complex kdv equation by constructing special forms of initial conditions three new types of realistic numerical solutions are obtained numerical positon solution expressed by the trigonometric functions numerical negaton solution expressed by the hyperbolic functions and particularly the numerical analytical complexiton solutions expressed by combinations of the two kinds of functions all these numerical solutions obtained can rapidly converge to the exact solutions obtained by lou et al illustrative numerical figures are exhibited the efficiency of the proposed method

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

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

a globally convergent parallel algorithm for zeros of polynomial systems certain classes of nonlinear systems of equations such as polynomial systems have properties that make them particularly amenable to solution on distributed computing systems some algorithms considered unfavorably on a single processor serial computer may be excellent on a distributed system this paper considers the solution of polynomial systems of equations via a globally convergent homotopy algorithm on a hypercube some computational results are reported

a homotopy method applied to elastica problems abstract the inverse problem in nonlinear incompressible elastica theory where the end positions and inclinations rather than the forces and moment are specified is considered based on the globally convergent chow yorke algorithm a new homotopy method which is simple accurate stable and efficient is developed for comparison numerical results of some other simple approaches e g newton s method based on shooting or finite differences standard embedding are presented the new homotopy method does not require a good initial estimate and is guaranteed to have no singular points the homotopy method is applied to the problem of a circular elastica ring subjected to n symmetrical point loads and numerical results are given for n 2 3 4

proof systems for satisfiability in hennessy milner logic with recursion abstract an extension of hennessy milner logic with recursion is presented a recursively specified formula will have two standard interpretations a minimal one and a maximal one minimal interpretations of formulas are useful for expressing liveness properties of processes whereas maximal interpretations are useful for expressing safety properties we present sound and complete proof systems for both interpretations for when a process satisfies a possibly recursive formula the rules of the proof systems consist of an introduction rule for each possible structure of a formula and are intended to extend the work of stirling and winskel moreover the proof systems may be presented directly in prolog to yield a decision procedure for verifying when a finite state process satisfies a specification given as a possibly recursive formula

unfolding and fixpoint semantics of concurrent constraint logic programs we present a new semantics for a language in the family of concurrent constraint logic languages the semantics can be based on a notion of clause unfolding since the language is closed under this transformation the unfolding semantics is obtained as limit of an infinite unfolding process unfolding is also used to define an immediate consequences operator and therefore a fixpoint semantics in the typical logic programming style the result of both the unfolding and the fixpoint semantics is a set of reactive behaviors which are trees abstractly representing all the possible computations of a program including deadlocks and finite failures the semantics can be made more abstract by defining a suitable notion of equivalence on reactive behaviors in our approach this can be done by reasoning on constraints only thus generalizing the typical behavior of constraint logic programming

compositionality of hennessy milner logic by structural operational semantics this paper presents a method for the decomposition of hml formulas it can be used to decide whether a process algebra term satisfies a hml formula by checking whether subterms satisfy certain formulas obtained by decomposing the original formula the method uses the structural operational semantics of the process algebra the main contribution of this paper is the extension of an earlier decomposition method for the de simone format from the ph d thesis of larsen in 1986 to more general formats

structural operational semantics for weak bisimulations in this study we present rule formats for four main notions of bisimulation with silent moves weak bisimulation is a congruence for any process algebra defined by wb cool rules we have similar results for rooted weak bisimulation milner s observational equivalence branching bisimulation and rooted branching bisimulation the theorems stating that say observational equivalence is an appropriate notion of equality for ccs are corollaries of the results of this paper we also give sufficient conditions under which equational axiom systems can be generated from operational rules indeed many equational axiom systems appearing in the literature are instances of this general theory

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

asymptotic expansions of bessel anger and weber transformations in this paper we explore higher order numerical quadrature for the integrations of systems containing bessel anger and weber functions the method is constructed by finding the approximate solution of the differential equation and truncating the asymptotic series numerical examples based on theoretical results are presented to demonstrate the efficiency of the method

a fully abstract denotational semantics for the calculus of higher order communicating systems abstract in this paper we study the calculus of higher order communicating systems chocs thomsen proc of popl 89 acm 1989 pp 143 154 inform comput 116 1 1995 38 57 in a denotational setting we present a construction of a denotational semantics for chocs which resides in a domain constructed using the standard constructions of separated sum cartesian product the plotkin power domain constructor and recursively defined domains we show under mild restrictions that the denotational semantics and the operational semantics of chocs are fully abstract we have previously proved using bisimulation arguments that processes as first class objects are powerful enough to simulate recursion however the proof is very long and tedious to demonstrate the power of the denotational approach we use it to obtain a very simple proof of the simulation of recursion result

the expressive power of implicit specifications abstract in this paper we investigate the expressive power of implicit specifications of concurrent systems that is we consider specifications s specifying a system p not directly but rather in combination with a given environment formally we shall represent the environment as a ccs context of the form a l where a is a process expression and l and are the parallel restriction and renaming operators of ccs respectively we investigate the expressive power of the following three types of implicit specifications a p l b i where is strong bisimulation equivalence and b is a process expression a p l s ii where s is a modal specification and is refinement between modal specifications a generalization of bisimulation equivalence and a p l f iii where f is a formula of hennessy milner logic extended with a maximal recursion construct the paper offers the following two main results when a b and s are recursion free and f is a hennessy milner logic formula the expressive powers of all three types of implicit specifications are the same and equal that of hennessy milner logic when a and s are regular the expressive powers of implicit specifications of type ii and iii are the same and identical to that of hennessy milner logic extended with maximal recursion finally we recall from 21 that the expressive power of implicit specifications does not increase by modelling the environment as other contexts of ccs or other process calculi

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

generalized om bisimulation history preserving bisimilarity and maximality preserving bisimilarity take full account of the interplay between causality and branching and they are congruences w r t action refinement for suitable classes of petri nets but even for finite safe petri nets they are based on possibly infinite transition systems and it is not obvious how to decide them om bisimulation gives a characterization of history preserving bisimulation for safe nets without internal moves and it allows a decidability result in this paper we generalize om bisimulation and this decidability result to safe nets with internal moves and also treat the case of maximality preserving bisimulation

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

numerical study of porous channel flow in a rotating system by a homotopy method abstract problems in lubrication transpiration cooling dialysis gaseous diffusion processes subterranean rivers fed by porous bedrock and flow under the polar icecap are examples of porous channel flow in a rotating system using similarity equations the navier stokes equations reduce to a 10th order two point boundary value problem for certain parameter ranges this problem is very difficult and is not amenable to simple shooting techniques or classical locally convergent iterative methods a recently developed globally convergent homotopy algorithm is applied to the boundary value problem and numerical results are reported for a wide range of parameter values

non regular iterators in process algebra we consider three forms of non regular iteration in process algebra the push down operation de5ned by x y x x y x y y the nesting operation de5ned by x y x x y x y and the back and forth operation de5ned by xy x xy y y in the process algebraic framework acp with abstraction and one of orwe provide de5nitions of the following standard processes stack context free process bag and queue these de5nitions apply to all standard behavioural equivalences we only use x x whereis the silent step moreover these results yield the expressive power to express computable processes modulo rooted branching bisimulation equivalence and hence support the equational founding of process algebra standard processes can be represented as terms c 2001 elsevier science b v all rights reserved

bifurcations via singular value decompositions we study the relation between bifurcation theory and singular value decomposition in numerical analysis given a nonlinear equation we give a local analysis in a neighborhood of a solution via the liapunov schmidt method and the singular value decomposition the theorem is applicable to regular turning or bifurcation points a numerical method for global bifurcation problems based on the above analysis is presented

determinancy observation equivalence trace equivalence abstract if an experiment s is conducted on a parallel process p then in general different processes may result from the experiment due to the nondeterministic behaviour of p in the notation of milner 1980 p p for different p process p is called determinate if the resulting processes are all equivalent i e if p p and p p then p and p are equivalent this means that although p behaves nondeterministically this cannot be detected by an observer of p let denote observation equivalence used in ccs milner 1980 let f denote the much weaker failure equivalence used for csp hoare et al 1981 brookes 1983 and let t denote the still weaker trace equivalence we show that the three corresponding notions of determinancy are the same and that for determinate processes f and t are the same determinacy is preserved under and f but not under t

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

bisimulation of automata abstract we view ccs terms as defining nondeterministic automata an algebraic representation of automata is given and categories of automata and simulations between them are defined the crucial feature is the consideration of only the pure simulations which carry the pure actual determined states of the domain automation to the pure states of the codomain automaton the pure epimorphisms between the automata partition the category into bisimulation equivalence classes there is a unique canonical representative for each bisimulation equivalence class these results hold for weak bisimulation and hence for strong bisimulation essentially the same results are obtained with regard to rooted bisimulation equivalence classes of automata with start states

a semantic theory for value passing processes based on the late approach a general class of languages for value passing calculi based on the late semantic approach is defined and a concrete instantiation of the general syntax is given this is a modification of the standard ccs according to the late approach three kinds of semantics are given for this language first a plotkin style operational semantics by means of an applicative labelled transition system is introduced this is a modification of the standard labelled transition system that caters for value passing according to the late approach as an abstraction late bisimulation preorder is given then a general class of denotational models for the late semantics is defined a denotational model for the concrete language is given as an instantiation of the general class two equationally based proof systems are defined the first one which is value finitary i e only reasons about a finite number of values at each time is shown to be sound and complete with respect to this model the second proof system a value infinitary one is shown to be sound with respect to the model whereas the completeness is proven later the operational and the denotational semantics are compared and it is shown that the bisimulation preorder is finer than the preorder induced by the denotational model we also show that in general the bisimulation preorder is strictly included in the model induced preorder finally a value finitary version of the bisimulation preorder is defined and the full abstractness of the denotational model with respect to it is shown it is also shown that for ccsl the bisimulation preorder coincides with the preorder induced by the model from this we can conclude that if we allow for parameterized recursion in our language we may express processes which coincide in any algebraic domain but are distinguished by the bisimulation this shows that if we extend ccsl in this way we obtain a strictly more expressive language

semantics for finite delay abstract we produce a fully abstract model for a notion of process equivalence taking into account issues of fairness called by milner fair bisimilarity the model uses aczel s anti foundation axiom and it is constructed along the lines of the anti founded model for sccs given by aczel we revisit aczel s semantics for sccs where we prove a unique fixpoint theorem under the assumption of guarded recursion then we consider milner s extension of sccs to include a finite delay operator e working with fair bisimilarity we construct a fully abstract model which is also fully abstract for fortification we discuss the solution of recursive equations in the model the paper is concluded with an investigation of the algebraic theory of fair bisimilarity

on meije and sccs infinite sum operators vs non guarded definitions une des principales differences actuellement entre meije et sccs se trouve dans les limites que le calcul precedent etablit a l interieur de sa syntaxe sur la creation de choix de comportement inifini a chaque point du processus

towards categorical models for fairness fully abstract presheaf semantics of sccs with finite delay we present a presheaf model for the observation of infinite as well as finite computations we give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems which are a special case of the general transition systems of hennessy and stirling this can be viewed as a first step towards representing fairness in categorical models for concurrency the open map bisimulation is shown to coincide with extended bisimulation of hennessy and stirling which is essentially fair ctl bisimulation we give a denotational semantics of milner s sccs with finite delay in the presheaf model which differs from previous semantics by giving the meanings of recursion by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay finally we formulate milner s operational semantics of sccs with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation

compact structures in a class of nonlinearly dispersive equations with time fractional derivatives in this work variants of the kdv equation with time fractional derivatives which exhibits compactons solitons with compact support are investigated new solitary wave solutions with compact support are developed the homotopy perturbation method is employed to derive compact solutions for these variants the chosen initial solution or trial function plays a major role in changing the physical structure of the solution the proposed scheme can be used to construct compact and noncompact solutions for a wide class of nonlinear fractional evolution equations

general optimal attenuation of harmonic disturbance with unknown frequencies we present algorithms for optimal harmonic disturbance attenuation in standard discrete time control structure based on a parametrisation of marginally stabilising controllers the frobenius norm and the spectral norm of the closed loop transfer matrix at the disturbance frequencies are minimised if there is only one frequency of the disturbance the controller has an observer based form which we obtain by solving a static output feedback sof stabilisation control problem although the sof stabilisation problem is hard the generical case of nonsquare matrix g 22 is solved by linear algebra methods numerical simulation results are presented as a corollary we transform the control problem with unit circle invariant zeros into a control problem without such zeros the elimination of the unit circle invariant zeros is based on the fact that matrix y zi a bf 1 is stable where y f with y 0 is a solution of a discrete time algebraic riccati system