the model matching problem for periodic discrete time systems in this paper the model matching problem via state feedback is studied for discrete time periodic systems it is shown that under some zero matching conditions it is possible to assign a target input output periodic system by means of a periodic state feedback control law furthermore this entails that a periodic system can be converted into a closed loop time invariant system via state feedback

testing preorders for probabilistic processes can be characterized by simulations the domestic dog may be exceptionally well suited for behavioral genetic studies owing to its population history and the striking behavior differences among breeds to explore to what extent and ho

on the assignment of invariant factors by time varying feedback strategies abstract in this paper the realization of arbitrary invariant factors or cyclic components of the closed loop system matrix is discussed it is shown that the use of time varying feedback strategies enables one to realize arbitrary invariant factors in contrast with time invariant feedback control

the norm 1 property of a quantum observable a normalized positive operator measure x e x has the norm 1 property if e x 1 whenever e x o this property reflects the fact that the measurement outcome probabilities for the values of such observables can be made arbitrarily close to one with suitable state preparations some general implications of the norm 1 property are investigated as case studies localization observables phase observables and phase space observables are considered

computation of minimal periodic realizations of transfer function matrices we present a numerical approach to compute a minimal periodic state space realization of a transfer function matrix corresponding to a lifted state space representation the proposed method determines a realization with time varying state dimensions by using exclusively orthogonal transformations the new method is numerically reliable computationally efficient and thus well suited for robust software implementations

a note on robust pole assignment for periodic systems in this note a robust pole assignment algorithm is proposed for linear periodic discrete time systems with time varying dimensions of the state and or input spaces the algorithm deduces a periodic state feedback law by the minimization of the condition numbers of the eigenvector matrices of the closed loop system numerical examples are provided to show the performances of the algorithm

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

computing the zeros of periodic descriptor systems in this paper we give a numerically reliable algorithm to compute the zeros of a periodic descriptor system the algorithm is a variant of the staircase algorithm applied to the system pencil of an equivalent lifted time invariant state space system and extracts a low order pencil which contains the zeros both finite and infinite as well as the kronecker structure of the periodic descriptor system the proposed algorithm is efficient in terms of complexity by exploiting the structure of the pencil and is exclusively based on orthogonal transformations which ensures some form of numerical stability

properties of blocked linear systems this paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete time linear time invariant systems the main idea is to explore the relationship between the blocked and the unblocked systems existing results are reviewed and a number of important new results are derived focus is given particularly on the zero properties of the blocked system as no such study has been found in the literature

brief paper assigning closed loop invariant polynomials over polytopes for linear periodic systems this paper provides a parameterization of all output feedback periodic controllers providing closed loop invariant polynomials varying over some assigned polytopes for linear discrete time periodic plants using the notion of time invariant system associated to a periodic system the parameterization is provided in terms of the general solution of a suitably defined matrix diophantine equation

axiomatizations for probabilistic finite state behaviors we study a process calculus which combines both nondeterministic and probabilistic behavior in the style of segala and lynch s probabilistic automata we consider various strong and weak behavioral equivalences and we provide complete axiomatizations for finite state processes restricted to guarded recursion in case of the weak equivalences we conjecture that in the general case of unguarded recursion the natural weak equivalences are undecidable this is the first work to our knowledge that provides a complete axiomatization for weak equivalences in the presence of recursion and both nondeterministic and probabilistic choice

brief minimal representations of mimo time varying systems and realization of cyclostationary models this paper describes a family of minimally parameterized state space models for completely n step observable multi input multi output time varying systems and their algebraical links with equivalent input output models these results are then used to develop an algorithm for the realization of generic input output sequences generated by a periodic system a complete numerical example is also developed to illustrate all steps of the algorithm described in the paper

computation of transfer function matrices of periodic systems we present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state space representations as constant systems the proposed pole zero method determines each entry of the transfer function matrix in a minimal zeros poles gain representation a basic computation is the minimal realization of special single input single output periodic systems for which both balancing related as well as orthogonal periodic kalman forms based algorithms can be employed the main computational ingredient to compute poles is the extended periodic real schur form of a periodic matrix this form also underlies the solution of periodic lyapunov equations when computing minimal realizations via balancing related techniques to compute zeros and gains numerically stable fast algorithms are proposed which are specially tailored to particular single input single output periodic systems the new method relies exclusively on reliable numerical computations and is well suited f

positive n periodic descriptor control systems this paper establishes the relationship between the positive n periodic descriptor system in discrete time and its associated invariant systems reachability and controllability properties of these kinds of systems are analyzed transmission of structural properties from the n periodic system to their associated invariant systems is studied finally some comments on the stability property are made

branching bisimulation congruence for probabilistic systems a notion of branching bisimilarity for the alternating model of probabilistic systems compatible with parallel composition is defined for a congruence result an internal transition immediately followed by a non trivial probability distribution is not considered inert a weaker definition of branching bisimilarity for the same model has been given earlier here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version to support the use of the present equivalence as a reduction technique we also show that probabilistic ctl formulae are preserved by our equivalence and we provide a polynomial time algorithm deciding branching bisimilarity

fault detection and isolation of linear discrete time periodic systems using the geometric approach this technical note solves the problem to detect and isolate faults in linear periodic discrete time systems a residual generator is designed through a suitable unknown input observer with the requirement that each residual should be sensitive only to one fault and simultaneously insensitive to the other faults that can affect the system and with the additional requirement of detectability that is the transition matrix of its relative error system has all eigenvalues smaller than in modulus for a given positive p 1 the solution is based on geometric tools and it makes use of the outer observable subspace notion

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

ccs expressions finite state processes and three problems of equivalence abstract we examine the computational complexity of testing finite state processes for equivalence in milner s calculus of communicating systems ccs the equivalence problems in ccs are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata nfa are equivalent i e accept the same language three notions of equivalence proposed for ccs are investigated namely observational equivalence strong observational equivalence and failure equivalence we show that observational equivalence can be tested in polynomial time as defined in ccs observational equivalence is the limit of a sequence of successively finer equivalence relations k where 1 is nondeterministic finite automaton equivalence we prove that for each fixed k deciding k is pspace complete we show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning a new combinatorial problem of independent interest finally we demonstrate that testing for failure equivalence is pspace complete even for a very restricted type of process

deformations for linear periodic discrete time systems the adjoint normal form following the technique proposed by arnold for matrices time invariant autonomous systems and extended by tannenbaum to time invariant linear control systems with inputs and outputs a normal form for linear periodic discrete time systems depending on physical parameters is proposed the considered actions are deformations i e linear periodic transformations depending on the parameters being identity at the nominal values of them

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

branching bisimulation for probabilistic systems characteristics and decidability we address the concept of abstraction in the setting of probabilistic reactive systems and study its formal underpinnings for the strictly alternating model of hansson in particular we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations viz coloured trace equivalence and branching bisimilarity using maximal probabilities we show that both alternatives coincide with branching bisimilarity the alternative characterisations have their own merits and focus on different aspects of branching bisimilarity coloured trace equivalence can be understood without knowledge of probability theory and is independent of the notion of a scheduler branching bisimilarity rephrased in terms of maximal probabilities gives rise to an algorithm of polynomial complexity for deciding the equivalence together they give a better understanding of branching bisimilarity furthermore we show that the notions of branching bisimilarity in the alternating model of hansson and in the nonalternating model of segala differ branching bisimilarity in the latter setting turns out to discriminate between systems that are intuitively branching bisimilar

on the zeros of blocked time invariant systems abstract this paper studies the zero properties of blocked linear systems resulting from blocking of linear time invariant systems the main idea is to establish a relation between the zero properties of blocked systems and the zero properties of their corresponding unblocked systems in particular it is shown that the blocked system has a zero if and only if the associated unblocked system has a zero furthermore the zero properties of blocked systems under a generic setting i e a setting which parameter matrices a b c d assume generic values are examined it is demonstrated that nonsquare blocked systems i e blocked systems with number of outputs unequal to the number of inputs generically have no zeros however square blocked systems i e blocked systems with equal number of inputs and outputs generically have only finite zeros and these finite zeros have geometric multiplicity one

a polynomial time algorithm for the equivalence of probabilistic automata two probabilistic automata are equivalent if for any string x the two automata accept x with equal probability this paper presents an o n 1 n 2 4 algorithm for determining whether two probabilistic automata u 1 and u 2 are equivalent where n 1 and n 2 are the number of states in u 1 and u 2 respectively this improves the best previous result which showed that the problem was in conp the existence of this algorithm implies that the covering and equivalence problems for uninitiated probabilistic automata are also polynomial time solvable the algorithm used to determine the equivalence of probabilistic automata can also solve the path equivalence problem for nondeterministic finite automata without lambda transitions and the equivalence problem for unambiguous finite automata in polynomial time this paper studies the approximate equivalence or delta equivalence problem for probabilistic automata an algorithm for the approximate equivalence problem for positive p

a general sos theory for the specification of probabilistic transition systems this article focuses on the formalization of the structured operational semantics approach for languages with primitives that introduce probabilistic and non deterministic behavior we define a general theoretic framework and present the rule format that guarantees that bisimulation equivalence in the probabilistic setting is a congruence for any operator defined in this format we show that the bisimulation is fully abstract w r t the format and possibilistic trace equivalence in the sense that bisimulation is the coarsest congruence included in trace equivalence for any operator definable within the format in other words bisimulation is the smallest congruence relation guaranteed by the format we also provide a conservative extension theorem and show that languages that include primitives for exponentially distributed time behavior such as imc and markov automata based language fit naturally within our framework

survey invariant representations of discrete time periodic systems the correspondence between periodic and time invariant systems can take a variety of forms the purpose of this survey paper is to present a complete and clear picture on time invariant representations for discrete time periodic systems the core of the treatment evolves around the concept of periodic transfer function

discrete time generative reactive probabilistic processes with different advancing speeds we present a process algebra expressing probabilistic external internal choices multi way synchronizations and processes with different advancing speeds in the context of discrete time i e where time is not continuous but is represented by a sequence of discrete steps as in discrete time markov chains dtmcs to this end we introduce a variant of csp that employs a probabilistic asynchronous parallel operator whose synchronization mechanism is based on a mixture of the classical generative and reactive models of probability in particular differently from existing discrete time process algebras where parallel processes are executed in synchronous locksteps the parallel operator that we adopt allows processes with different probabilistic advancing speeds mean number of actions executed per time unit to be modeled moreover our generative reactive synchronization mechanism makes it possible to always derive dtmcs in the case of fully specified systems we then present a sound and complete axiomatization of probabilistic bisimulation over finite processes of our calculus that is a smooth extension of the axiom system for a standard process algebra thus solving the open problem of cleanly axiomatizing action restriction in the generative model as a further result we show that when evaluating steady state based performance measures which are expressible by attaching rewards to actions our approach provides an exact solution even if the advancing speeds are considered not to be probabilistic without incurring the state space explosion problem that arises with standard synchronous approaches we finally present a case study on multi path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications

balancing related methods for minimal realization of periodic systems we propose balancing related numerically reliable methods to compute minimal realizations of linear periodic systems with time varying dimensions the first method belongs to the family of square root methods with guaranteed enhanced computational accuracy and can be used to compute balanced minimal order realizations an alternative balancing free square root method has the advantage of a potentially better numerical accuracy in case of poorly scaled original systems the key numerical computation in both methods is the solution of nonnegative periodic lyapunov equations directly for the cholesky factors of the solutions for this purpose a numerically reliable computational algorithm is proposed to solve nonnegative periodic lyapunov equations with time varying dimensions

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

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

optimal and robust controllers for periodic and multirate systems the problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete time periodic systems the solution consists of solving an equivalent time invariant standard l sup 1 optimization problem subject to an additional constraint this constraint assures the causality of the resulting periodic controller by the duality theory the problem is shown to be equivalent to a linear programming problem which is no harder than the standard l sup 1 problem also it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems finally the results are applied to the problem of robust stabilization of periodic and multirate systems

output stabilization via pole placement of discrete time linear periodic systems the output stabilization problem for discrete time linear periodic systems is solved both the state feedback control law and the state predictor are based on a suitable time invariant state sampled reformulation associated with a periodic system preliminary concepts of periodic system theory are briefly recalled in particular the structural properties of a linear discrete time periodic system are properly related to those of a time invariant system associated with it by resorting to such a time invariant reformulation the output stabilization problem via pole placement is solved the stabilizing controller is constituted by a control law and an asymptotic state predictor both of which are shown to be periodic

the realization problem for linear periodic systems abstract the realization problem for discrete time linear periodic systems is considered deep insight on the various complicated aspects of minimal quasi minimal and uniform realization is provided based on the knowledge of the structural properties of discrete time periodic systems the results hinge on the lifting isomorphism between such systems and time invariant ones

an algebraic riccati equation for the discrete time periodic prediction problem abstract in this paper the periodic problem is reformulated as a prediction problem relative to a suitable time invariant system this enables one to establish a one to one correspondence between the solutions of the discrete time periodic riccati equation dpre and the solutions of a suitable discrete time and time invariant riccati equation in particular the constant solutions of this last equation are the periodic generators of the original periodic riccati equation this enables one to easily derive existence uniqueness and convergence results for the drpe from known results relative to the time invariant case

computational issues for linear periodic systems paradigms algorithms open problems linear periodic systems originate in various control fields involving periodic phenomena in the beginnings of algorithmic developments for periodic systems computational detours have been often employed to reduce the computational problems for periodic systems to those for standard systems well known techniques are the employment of lifted representations in discrete time or the use of periodic generators in continuous time new computational paradigms evolved later whose main ingredients are numerically reliable and efficient algorithms for manipulating matrix products without forming explicitly them reduction of large scale structured matrix pencils without building the underlying pencils computing with discrete time periodic system models with time varying state dimensions or solving periodic matrix differential equations using multiple shooting techniques the paper will give a succinct overview of all these new developments and will point out some of still existing open computational problems

brief a periodically time varying minimal partial realization algorithm based on twisting the 1975 paper of meyer and burrus gave necessary conditions on the coefficients of a periodically time varying difference equation to generate a prespecified set of impulse responses the main contribution of the present paper consists of an algorithm that constructs the coefficients of such a periodically time varying realization of minimal lag thus the algorithm solves the minimal partial realization problem for the periodically time varying scalar case we use a general technique twisting for associating a time invariant system with a periodically time varying system in such a way that the time step is preserved the technique plays an essential role in the ideas underlying the algorithm

observation equivalence as a testing equivalence a notion of testing is developed for transition systems with divergence the forms of testing include traces refusals copying and global testing both denotational and operational formulations of testing are given the equivalence based on this notion of testing is shown to coincide with observation equivalence

robust tracking and regulation of linear periodic discrete time systems in this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete time systems and for general classes of disturbance functions and reference signals consisting in free responses of periodic processes the necessary and sufficient conditions for the existence of a solution which involve the periodic notion of invariant zero are found a constructive design procedure of the periodic compensator is given it is based on the internal model principle

zeros of discrete time linear periodic systems in this note the concept of zero for linear discrete time siso periodic systems is discussed the definition is based on a time invariant mimo equivalent representation an input output characterization of the zeros is provided which extends a well known property for time invariant systems

testing preorders for probabilistic processes we present a testing preorder for probabilistic processes based on a quantification of the probability with which processes pass tests the theory enjoys close connections with the classical testing theory of de nicola and hennessy in that whenever a process passes a test with probability 1 respectively some nonzero probability in our setting then the process must respectively may pass the test in the classical theory we also develop an alternative characterization of the probabilistic testing preorders that takes the form of a mapping from probabilistic traces to the interval 0 1 where a probabilistic trace is an alternating sequence of actions and probability distributions over actions finally we give proof techniques derived from the alternative characterizations for establishing preorder relationships between probabilistic processes the utility of these techniques is demonstrated by means of some simple examples

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

comparative branching time semantics for markov chains this paper presents various semantics in the branching time spectrum of discrete time and continuous time markov chains dtmcs and ctmcs strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterized in terms of the temporal logics probabilistic computation tree logic pctl and continuous stochastic logic csl apart from presenting various existing branching time relations in a uniform manner this paper presents the following new results i strong simulation for ctmcs ii weak simulation for ctmcs and dtmcs iii logical characterizations thereof including weak bisimulation for dtmcs iv a relation between weak bisimulation and weak simulation equivalence and v various connections between equivalences and pre orders in the continuous and discrete time setting the results are summarized in a branching time spectrum for dtmcs and ctmcs elucidating their semantics as well as their relationship

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

normal covariant quantization maps we consider questions related to quantizing complex valued functions defined on a locally compact topological group in the case of bounded functions we generalize r werner s approach to prove the characterization of the associated normal covariant quantization maps

parametrized solution of the periodic dead beat control problem the dead beat control problem for linear periodic discrete time systems in presence of unmeasurable disturbances and external reference signals is considered using a polynomial method a parametrization of all causal output feedback controllers solving the problem is provided

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

the difference periodic ricati equation for the periodic prediction problem gives a comprehensive treatment of several important aspects of the discrete time periodic riccati equation dpre arising from the prediction problem for linear discrete time periodic systems the authors analyze the symmetric periodic positive semidefinite spps solution of the dpre under appropriate assumptions of stabilizability and detectability of the periodic system among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the spps solution and the stability of the resulting closed loop system some of these results can be seen as extensions of the corresponding results for the time invariant case however a number of them contain contributions to the time invariant case as well the paper also gives a numerical algorithm based on an iterative linearization procedure for computing the spps solution the algorithm is a periodic version of kleinman s algorithm for the time invariant case

minimal periodic realizations of transfer matrices periodic controllers designed based on the so called lifting technique are usually represented by transfer matrices real operations require that the controllers be implemented as periodic systems the problem of realizing an nn sub o nn sub i proper rational transfer matrix as an n sub i input n sub o output n periodic discrete time system is studied an algorithm for obtaining periodic realizations which have a minimal number of states is proposed the result can also be used to remove any redundant states that exist in a periodic system

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

a new class of shift varying operators their shift invariant equivalents and multirate digital systems a class of linear shift varying operators that generalize the notion of n periodicity is defined it is shown that shift invariant equivalents for these operators exist and that the equivalence is in a strong sense preserving both algebraic and analytic system properties it is shown that multirate sampled data systems although not generally periodic fall into this class kranc vector switch decomposition and block filter implementations for single input single output multirate systems are connected under the unifying framework of shift invariant equivalents and this framework provides a way to extend them both to multi input multi output systems

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

a complete axiomatisation for observational congruence of finite state behaviours abstract finite state automata with non determinism and silent transitions can be interpreted not as subsets of the free monoid as in classical automata theory but as congruence classes under a congruence relation based upon the notion of weak bisimulation or observational equivalence due to park and milner in this paper a complete axiomatisation for this congruence is presented it extends the previously known complete axiomatisation by hennessy and milner for the case when all computations are finite the extension consists of five simple rules for recursion

weak bisimulation is sound and complete for pctl abstract we investigate weak bisimulation of probabilistic systems in the presence of nondeterminism i e labelled concurrent markov chains lcmc with silent transitions we develop an approach based on allowing convex combinations of computations similar to segala and lynch s use of randomized schedulers the definition of weak bisimulation destroys the additivity property of the probability distributions yielding instead capacities the mathematics behind capacities naturally captures the intuition that when we deal with nondeterminism we must work with bounds on the possible probabilities rather than with their exact values our analysis leads to three new developments we identify a characterization of image finiteness for countable state systems and present a new definition of weak bisimulation for these lcmcs we prove that our definition coincides with that of philippou lee and sokolsky for finite state systems we show that bisimilar states have matching computations the notion of matching involves convex combinations of transitions we study a minor variant of the probabilistic logic pctl the variation arises from an extra path formula to address action labels we show that bisimulation is sound and complete for this variant of pctl this is an extended complete version of a paper that was presented at concur 2002

brief paper mpc of constrained discrete time linear periodic systems a framework for asynchronous control strong feasibility stability and optimality via periodic invariance state feedback model predictive control mpc of discrete time linear periodic systems with time dependent state and input dimensions is considered the states and inputs are subject to periodically time dependent hard convex polyhedral constraints first periodic controlled and positively invariant sets are characterized and a method to determine the maximum periodic controlled and positively invariant sets is derived the proposed periodic controlled invariant sets are then employed in the design of least restrictive strongly feasible reference tracking mpc problems the proposed periodic positively invariant sets are employed in combination with well known results on optimal unconstrained periodic linear quadratic regulation lqr to yield constrained periodic lqr control laws that are stabilizing and optimal one motivation for systems with time dependent dimensions is efficient control law synthesis for discrete time systems with asynchronous inputs for which a novel modeling framework resulting in low dimensional models is proposed the presented methods are applied to a multirate nano positioning system

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

from singular to nonsingular filtering of periodic systems filling the gap with the spectral interactor matrix with reference to periodic discrete time systems the concept of the periodic spectral interactor matrix operator psimo is introduced such an interactor enables one to transform the singular system into a nonsingular one with identical spectral properties this concept is useful to characterize the family of periodic solutions of the singular periodic riccati equation arising from the singular filtering problem the psimo is also a synthetic tool to represent the invariant zeros structure at infinity delays of periodic systems in an operational fashion

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

relating strong behavioral equivalences for processes with nondeterminism and probabilities we present a comparison of behavioral equivalences for nondeterministic and probabilistic processes whose activities are all observable in particular we consider trace based testing and bisimulation based equivalences for each of them we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via schedulers the first approach compares two resolutions with respect to the probability distributions of all considered events the second approach requires that the probabilities of the set of events of a resolution be individually matched by the probabilities of the same events in possibly different resolutions the third approach only compares the extremal probabilities of each event stemming from the different resolutions the three approaches have very reasonable motivations and when applied to fully nondeterministic processes or fully probabilistic processes give rise to the classical well studied relations we shall see that for processes with nondeterminism and probability they instead give rise to a much wider variety of behavioral relations whose discriminating power is thoroughly investigated here in the case of deterministic schedulers

equivalence notions and model minimization in markov decision processes many stochastic planning problems can be represented using markov decision processes mdps a difficulty with using these mdp representations is that the common algorithms for solving them run in time polynomial in the size of the state space where this size is extremely large for most real world planning problems of interest recent ai research has addressed this problem by representing the mdp in a factored form factored mdps however are not amenable to traditional solution methods that call for an explicit enumeration of the state space one familiar way to solve mdp problems with very large state spaces is to form a reduced or aggregated mdp with the same properties as the original mdp by combining equivalent states in this paper we discuss applying this approach to solving factored mdp problems we avoid enumerating the state space by describing large blocks of equivalent states in factored form with the block descriptions being inferred directly from the original factored representation the resulting reduced mdp may have exponentially fewer states than the original factored mdp and can then be solved using traditional methods the reduced mdp found depends on the notion of equivalence between states used in the aggregation the notion of equivalence chosen will be fundamental in designing and analyzing algorithms for reducing mdps optimally these algorithms will be able to find the smallest possible reduced mdp for any given input mdp and notion of equivalence i e find the minimal model for the input mdp unfortunately the classic notion of state equivalence from non deterministic finite state machines generalized to mdps does not prove useful we present here a notion of equivalence that is based upon the notion of bisimulation from the literature on concurrent processes our generalization of bisimulation to stochastic processes yields a non trivial notion of state equivalence that guarantees the optimal policy for the reduced model immediately induces a corresponding optimal policy for the original model with this notion of state equivalence we design and analyze an algorithm that minimizes arbitrary factored mdps and compare this method analytically to previous algorithms for solving factored mdps we show that previous approaches implicitly derive equivalence relations that we define here

a period specific realization of linear continuous time systems it is a well known fact that a weighting pattern matrix has a periodic realization if and only if the matrix is separable and periodic this fact however does not cope with a reasonable question of period specific realization problem for a given weighting pattern matrix and a given positive real number find a periodic realization corresponding to the given matrix and with a period equal to the given number this paper answers the question by showing that the period specific realization problem has a solution if and only if the given weighting pattern matrix is separable and has a period equal to the given positive real number to this end two types of period specific realizations are constructed one is with a constant a matrix whose dimension is not necessarily minimal among all possible period specific realizations the other is with a non constant and periodically time varying a matrix whose dimension turned out minimal among all possible period specific realizations

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