paracategories ii adjunctions fibrations and examples from probabilistic automata theory in this sequel to hermida and mateus paracategories i internal paracategories and saturated partial algebras theoret comput sci in press we explore some of the global aspects of the category of paracategories we establish its co completeness and cartesian closure from the closed structure we derive the relevant notion of transformation for paracategories we set up the relevant notion of adjunction between paracategories and apply it to define co completeness and cartesian closure exemplified by the paracategory of bivariant functors and dinatural transformations we introduce partial multicategories to account for partial tensor products we also consider fibrations for paracategories and their indexed paracategory version finally we instantiate all these concepts in the context of probabilistic automata

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

metrics for labelled markov processes the notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions thus a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent this instability is due to the quantitative nature of probabilistic processes in a situation where the process behavior has a quantitative aspect there should be a more robust approach to process equivalence this paper studies a metric between labelled markov processes this metric has the property that processes are at zero distance if and only if they are bisimilar the metric is inspired by earlier work on logics for characterizing bisimulation and is related in spirit to the hutchinson metric

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

bisimulation for probabilistic transition systems a coalgebraic approach the notion of bisimulation as proposed by larsen and skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of aczel and mendier in terms of a set functor this coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving borel probability measures under reasonable conditions generalized probabilistic bisimilarity can be characterized categorically application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation

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

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

language based performance prediction for distributed and mobile systems we present a framework for performance prediction of distributed and mobile systems we rely on process calculi and their structural operational semantics the dynamic behaviour is described through transition systems whose transitions are labelled by encodings of their proofs that we then map into stochastic processes we enhance related works by allowing general continuous distributions resorting to a notion of enabling between transitions we also discuss how the number of resources available affects the overall model finally we introduce a notion of bisimulation that takes stochastic information into account and prove it to be a congruence when only exponential distributions are of interest our equivalence induces a lumpable partition on the underlying markov process

measuring the confinement of probabilistic systems in this paper we lay the semantic basis for a quantitative security analysis of probabilistic systems by introducing notions of approximate confinement based on various process equivalences we recast the operational semantics classically expressed via probabilistic transition systems pts in terms of linear operators and we present a technique for defining approximate semantics as probabilistic abstract interpretations of the pts semantics an operator norm is then used to quantify this approximation this provides a quantitative measure e of the indistinguishability of two processes and therefore of their confinement in this security setting a statistical interpretation is then given of the quantity e which relates it to the number of tests needed to breach the security of the system

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

quantitative kleene coalgebras we present a systematic way to generate 1 languages of generalised regular expressions and 2 sound and complete axiomatizations thereof for a wide variety of quantitative systems our quantitative systems include weighted versions of automata and transition systems in which transitions are assigned a value in a monoid that represents cost duration probability etc such systems are represented as coalgebras and 1 and 2 above are derived in a modular fashion from the underlying functor type of these coalgebras in previous work we applied a similar approach to a class of systems without weights that generalizes both the results of kleene on rational languages and dfa s and milner on regular behaviours and finite lts s and includes many other systems such as mealy and moore machines in the present paper we extend this framework to deal with quantitative systems as a consequence our results now include languages and axiomatizations both existing and new ones for many different kinds of probabilistic systems

observing branching structure through probabilistic contexts probabilistic automata pas constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior such as distributed algorithms and network protocols the behavior of pas is commonly defined using schedulers also called adversaries or strategies which resolve all nondeterministic choices based on past history from the resulting purely probabilistic structures trace distributions can be extracted whose intent is to capture the observable behavior of a pa however when pas are composed via an asynchronous parallel composition operator a global scheduler may establish strong correlations between the behavior of system components and for example resolve nondeterministic choices in one pa based on the outcome of probabilistic choices in the other it is well known that as a result of this the linear time trace distribution precongruence is not compositional for pas in his 1995 ph d thesis segala has shown that the branching time probabilistic simulation preorder is compositional for pas in this paper we establish that the simulation preorder is in fact the coarsest refinement of the trace distribution preorder that is compositional we prove our characterization result by providing 1 a context of a given pa cal a called the tester which may announce the state of cal a to the outside world and 2 a specific global scheduler called the observer which ensures that the state information that is announced is actually correct now when another pa cal b is composed with the tester it may generate the same external behavior as the observer only when it is able to simulate cal a in the sense that whenever cal a goes to some state s cal b can go to a corresponding state u from which it may generate the same external behavior our result shows that probabilistic contexts together with global schedulers are able to exhibit the branching structure of pas

a hierarchy of probabilistic system types we arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy our expressiveness criterion is the existence of a system translation from the less expressive type into the more expressive type that preserves and reflects probabilistic bisimilarity we model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature the theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy all these translations arise in a standard way from natural transformations between the two behaviour functors involved such a translation generally preserves coalgebraic bisimilarity we exploit a new result that under mild assumptions on the behaviour functors a system translation induced by a natural transformation with injective components also reflects bisimilarity

process algebra for performance evaluation this paper surveys the theoretical developments in the field of stochastic process algebras process algebras where action occurrences may be subject to a delay that is determined by a random variable a huge class of resource sharing systems like large scale computers client server architectures networks can accurately be described using such stochastic specification formalisms the main emphasis of this paper is the treatment of operational semantics notions of equivalence and sound and complete axiomatisations of these equivalences for different types of markovian process algebras where delays are governed by exponential distributions starting from a simple actionless algebra for describing time homogeneous continuous time markov chains we consider the integration of actions and random delays both as a single entity like in known markovian process algebras like tipp pepa and empa and as separate entities like in the timed process algebras timed csp and tccs in total we consider four related calculi and investigate their relationship to existing markovian process algebras we also briefly indicate how one can profit from the separation of time and actions when incorporating more general non markovian distributions

modular construction of complete coalgebraic logics we present a modular approach to defining logics for a wide variety of state based systems the systems are modelled as coalgebras and we use modal logics to specify their observable properties we show that the syntax semantics and proof systems associated with such logics can all be derived in a modular fashion moreover we show that the logics thus obtained inherit soundness completeness and expressiveness properties from their building blocks we apply these techniques to derive sound complete and expressive logics for a wide variety of probabilistic systems for which no complete axiomatisation has been obtained so far

testing probabilistic equivalence through reinforcement learning checking if a given system implementation respects its specification is often done by proving that the two are equivalent the equivalence is chosen in particular for its computability and of course for its meaning that is for its adequacy with what is observable from the two systems implementation and specification trace equivalence is easily testable decidable from interaction but often considered too weak in contrast bisimulation is accepted as the canonical equivalence for interaction but it is not testable richer than an equivalence is a form of distance it is zero between equivalent systems and it provides an estimation of their difference if the systems are not equivalent our main contribution is to define such a distance in a context where 1 the two systems to be compared have a stochastic behavior 2 the model of one of them e g the implementation is unknown hence our only knowledge is obtained by interacting with it 3 consequently the target equivalence observed when distance is zero must be testable to overcome the problem that the model is unknown we use a reinforcement learning approach that provides powerful stochastic algorithms that only need to interact with the model our second main contribution is a new family of testable equivalences called k moment the weakest of them 1 moment equivalence is trace equivalence as k grows k moment equivalences become finer all remaining as well as their limit weaker than bisimulation we propose a framework to define and test a bigger class of testable equivalences test observation equivalences toes and we show how they can be made coarser or not by tuning some parameters

analysis of a multiple recapture census by computing conditional probabilities in a multiple recapture census of a closed population using fixed sample sizes the total number of different animals captured during the census is a sufficient statistic for the population sized conditional on the population size the exact probability distribution of this sufficient statistic may be calculated and an algorithm for doing this is given standard techniques are applied to describe methods for using the conditional probabilities to form median and interval estimates of the population size the methods are illustrated with examples

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

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

identification of mimo systems using radial basis function networks with hybrid learning algorithm when a radial basis function network rbfn is used for identification of a nonlinear multi input multi output mimo system the number of hidden layer nodes the initial parameters of the kernel and the initial weights of the network must be determined first for this purpose a systematic way that integrates the support vector regression svr and the least squares regression lsr is proposed to construct the initial structure of the rbfn the first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the svr method then the weights of the rbfn are determined by solving a simple minimization problem based on the concept of lsr after initialization an annealing robust learning algorithm arla is then applied to train the rbfn with the proposed initialization approach one can find that the designed rbfn has few hidden layer nodes while maintaining good performance to show the feasibility and superiority of the annealing robust radial basis function networks arrbfns for identification of mimo systems several illustrative examples are included

bisimulations for fuzzy transition systems there has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems however the comparison at this level is too coarse recently a finer behavioral measure i e bisimulation has been introduced to fuzzy finite automata however the results obtained are applicable only to finite state systems in this paper we consider bisimulation for general fuzzy systems which may be infinite state or infinite event by modeling them as fuzzy transition systems ftss to help understand and check bisimulation we characterize it in three ways by enumerating whole transitions comparing individual transitions and using a monotonic function in addition we address composition operations subsystems quotients and homomorphisms of ftss and discuss their properties connected with bisimulation the results presented here are useful to compare the behavior of general fuzzy systems in particular this makes it possible to relate an infinite fuzzy system to a finite one which is easier to analyze with the same behavior

non expansive e bisimulations for probabilistic processes e bisimulation equivalence has been proposed in the literature as a technique to study the concept of behavioral distance between probabilistic processes in this paper we first consider the generative model of probabilistic processes and introduce two stronger equivalence notions action e bisimulation and global e bisimulation for each of these three equivalence notions we propose an sos transition rule format ensuring the property of non expansiveness non expansiveness means that if the behavioral distance between s i and t i is e i then the behavioral distance between f s 1 s n and f t 1 t n is no more that e 1 e n as expected the stronger the e bisimulation considered the weaker the constraints of the transition rule format then we switch to the reactive model of probabilistic processes and we propose a rule format for e bisimulation and action e bisimulation arguing that global e bisimulation is not needed in such a context

distributed probabilistic input output automata expressiveness un decidability and algorithms abstract probabilistic model checking computes the probability values of a given property quantifying over all possible schedulers it turns out that maximum and minimum probabilities calculated in such a way are over estimations on models of distributed systems in which components are loosely coupled and share little information with each other and hence arbitrary schedulers may result too powerful therefore we introduced definitions that characterise which are the schedulers that properly capture the idea of distributed behaviour in probabilistic and nondeterministic systems modelled as a set of interacting components in this paper we provide an overview of the work we have done in the last years which includes 1 the definitions of distributed and strongly distributed schedulers providing motivation and intuition 2 expressiveness results comparing them to restricted versions such as deterministic variants or finite memory variants 3 undecidability results in particular the model checking problem is not decidable in general when restricting to distributed schedulers 4 a counterexample guided refinement technique that using standard probabilistic model checking allows to increase precision in the actual bounds in the distributed setting and 5 a revision of the partial order reduction technique for probabilistic model checking we conclude the paper with an extensive review of related work dealing with similar approaches to ours

optimal supervisory control of probabilistic discrete event systems probabilistic discrete event systems pdes are modeled as generators of probabilistic languages and the supervisors employed are a probabilistic generalization of deterministic supervisors used in standard supervisory control theory in the case when there exists no probabilistic supervisor such that the behavior of a plant under control exactly matches the probabilistic language given as the requirements specification we want to find a probabilistic control such that the behavior of the plant under control is as close as possible to the desired behavior first as a measure of this proximity a pseudometric on states of generators is defined two algorithms for the calculation of the distance between states in this pseudometric are described then an algorithm to synthesize a probabilistic supervisor that minimizes the distance between generators representing the achievable and required behavior of the plant is presented

value passing ccs with noisy channels value passing ccs a full version of milner s ccs is a process algebra in which actions consist of sending and receiving values through noiseless communication channels the full calculus is a succinct yet expressive language for the specification and verification of reactive systems taking into account the reality of channel noise in reactive systems in this paper we introduce an extension of value passing ccs called value passing ccs with noisy channels vccs n in which noise is described by a probability distribution over the values after presenting the reduction operational semantics and labelled operational semantics of vccs n we develop the theory of behavioural equivalence by introducing barbed equivalence barbed congruence bisimilarity and full bisimilarity in particular we show that barbed equivalence and barbed congruence coincide with bisimilarity and full bisimilarity respectively based upon the labelled operational semantics of vccs n we establish a probabilistic modal logic for expressing system properties and show its connection with the notion of bisimilarity finally we use vccs n to model a communication protocol for ensuring the reliable transmission of data across an error prone channel

a modular approach to defining and characterising notions of simulation we propose a modular approach to defining notions of simulation and modal logics which characterise them we use coalgebras to model state based systems relators to define notions of simulation for such systems and inductive techniques to define the syntax and semantics of modal logics for coalgebras we show that the expressiveness of an inductively defined logic for coalgebras w r t a notion of simulation follows from an expressivity condition involving one step in the definition of the logic and the relator inducing that notion of simulation moreover we show that notions of simulation and associated characterising logics for increasingly complex system types can be derived by lifting the operations used to combine system types to a relational level as well as to a logical level we use these results to obtain baltag s logic for coalgebraic simulation as well as notions of simulation and associated logics for a large class of non deterministic and probabilistic systems

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