a new algorithm for testing diagnosability of fuzzy discrete event systems failure diagnosis and detection of fuzzy discrete event systems play a significant role in the study of complex systems in this paper we investigate the diagnosability of fuzzy discrete event systems by proposing a new algorithm based on the concept of undistinguishable strings moreover a necessary and sufficient condition for fuzzy diagnosability is obtained in terms of certain properties of the diagnoser which is constructed with respect to the minimal observable event the computing process to check the diagnosability of fuzzy dess and some examples serving to illuminate the applications are developed and described

failure detection framework for stochastic discrete event systems with guaranteed error bounds this paper studies the online fault detection for stochastic discrete event systems dess under partial observability of events prior works have only studied the verification of the stochastic diagnosability s diagnosability property to the best of our knowledge this is a first paper that investigates the online detection schemes and also introduces the notions of their missed detections mds and false alarms fas due to the probabilistic nature of the problem mds and fas are possible even for s diagnosable systems and we establish that s diagnosability is a necessary and sufficient condition for achieving any desired levels of md and fa rates we also provide a detection scheme that can achieve the specified md and fa rates based on comparing a suitable detection statistic that we define with a suitable detection threshold that we algorithmically compute we also algorithmically compute the corresponding detection delay bound the detection scheme also works for non s diagnosable systems with the difference that in this case there exists a lower bound for achievable md rate that increases as the fa rate requirement is made more stringent by decreasing it

a polynomial algorithm for testing diagnosability of discrete event systems failure diagnosis in large and complex systems is a critical task in the realm of discrete event systems sampath et al 1995 proposed a language based failure diagnosis approach they introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system the complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types we give an algorithm for testing diagnosability that does not construct a diagnoser for the system and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types

polynomial time verification of diagnosability of partially observed discrete event systems the problem of verifying the properties of diagnosability and i diagnosability is considered we present new polynomial time algorithms for deciding diagnosability and i diagnosability these algorithms are based on the construction of a nondeterministic automaton called a verifier

current state opacity formulations in probabilistic finite automata a system is said to be current state opaque if the entrance of the system state to a set of secret states remains opaque uncertain to an intruder at least until the system leaves the set of secret states this notion of opacity has been studied in nondeterministic finite automata settings where the intruder observes a subset of events for example via some natural projection mapping and has been shown to be useful in characterizing security requirements in many applications including encryption using pseudorandom generators and coverage properties in sensor networks one limitation of the majority of existing analysis is that it fails to provide a quantifiable measure of opacity for a given system instead it simply provides a binary characterization of the system being opaque or not opaque in this paper we address this limitation by extending current state opacity formulations to systems that can be modeled as probabilistic finite automata under partial observation we introduce three notions of opacity namely 1 step based almost current state opacity 2 almost current state opacity and 3 probabilistic current state opacity all of which can be used to provide a measure of a given system s opacity we also propose verification methods for these probabilistic notions of opacity and characterize their corresponding computational complexities

procrustes problems in finite dimensional indefinite scalar product spaces abstract some applications from multidimensional scaling in an environment of indefinite scalar products are investigated in particular the construction of points from given distances is considered and two variants of procrustes problems are discussed it is found that both procrustes problems can be solved with the help of h polar decompositions or g h polar decompositions of specified matrices furthermore a method for the numerical computation of h or g h polar decompositions of nonsingular matrices is described

description of quantum spin using functions on the sphere s2 an overview of isomorphic correspondences between spin algebra and algebras of functions on the sphere is given in addition the authors show that in one case the induced product between the spin function and another function is expressible by the action of a first order differential operator correcting the ordinary product this deformation leads to the geometric quantization of classical spin the classical limit is studied for a class of correspondences

diagnosability of stochastic discrete event systems we investigate diagnosability of stochastic discrete event systems we define the notions of a and aa diagnosability for stochastic automata these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by sampath et al through the construction of a stochastic diagnoser we determine offline conditions necessary and sufficient to guarantee a diagnosability and sufficient to guarantee aa diagnosability we also show how the stochastic diagnoser can be used for on line diagnosis of failure events we illustrate the results through two examples from hvac systems

diagnosability of fuzzy discrete event systems a fuzzy approach in order to more effectively cope with the real world problems of vagueness fuzzy discrete event systems fdess were proposed by lin and ying recently then we and cao and ying investigated the supervisory control of fdess independently in this paper we are concerned with another important issue of fdess the failure diagnosis more specifically 1 we propose a ldquofuzzy diagnosabilityrdquo approach by introducing a fuzzy diagnosability function to characterize the diagnosability degree which takes values in the interval 0 1 rather than 0 1 2 based on the observability of events we formalize the construction of the diagnosers that are used to perform fuzzy diagnosis 3 a number of basic properties of the diagnosers are investigated in particular we present a necessary and sufficient condition for failure diagnosis of fdess our results generalize the important consequences of the diagnosability for crisp discrete event systems dess introduced by sampath et al the newly proposed approach allows us to deal with the problem of diagnosability for both crisp dess and fdess 4 in addition a method for checking the fuzzy diagnosability for fdess is proposed also some examples are provided to illustrate the application of the diagnosability of fdess

verification of detectability in probabilistic finite automata abstract in this paper we analyze state estimation in stochastic discrete event systems sdes that can be modeled as probabilistic finite automata pfas for a given pfa we obtain the necessary and sufficient conditions that guarantee exact state estimation at least asymptotically with increasing certainty as more information is acquired from observing the behavior of the given pfa by defining the notion of aa detectability and providing necessary and sufficient conditions that can be used to verify it the characterization and analysis of aa detectability is transformed to a problem of classification between two or more pfas which capture the recurrent behavior of an underlying markov process that is obtained by ignoring output behavior and focusing on state transitions in the given pfa our approach combines techniques used in classification between two or more pfas with state estimation methods used in logical discrete event systems des we prove that the proposed verification of aa detectability is of polynomial complexity with respect to the size of the state space of the given pfa

robust disjunctive codiagnosability of discrete event systems against permanent loss of observations recently the so called robust diagnosability of dess against permanent loss of observations rdplo has been introduced in this regard the language generated by the system is said to be robustly diagnosable if it is possible to detect the failure occurrence within a bounded delay even when some sensors permanently fail to communicate the occurrence of the events to the diagnoser in this technical note we extend the definition of rdplo to the decentralized case considering the disjunctive architecture leading to the definition of robust disjunctive codiagnosability against permanent loss of observations rdcplo the technical note also addresses the issue of online implementation and we propose an efficient scheme to carry out online robust decentralized diagnosis against permanent loss of observations other contributions of the technical note are the development of algorithms for the verification of the rdcplo and the computation of the delay bound for robust decentralized diagnosis

algebraic approaches for fault identification in discrete event systems in this note we develop algebraic approaches for fault identification in discrete event systems that are described by petri nets we consider faults in both petri net transitions and places and assume that system events are not directly observable but that the system state is periodically observable the particular methodology we explore incorporates redundancy into a given petri net in a way that enables fault detection and identification to be performed efficiently using algebraic decoding techniques the guiding principle in adding redundancy is to keep the number of additional petri net places small while retaining enough information to be able to systematically detect and identify faults when the system state becomes available the end result is a redundant petri net embedding that uses 2k additional places and enables the simultaneous identification of 2k 1 transition faults and k place faults that may occur at various instants during the operation of the petri net the proposed identification scheme has worst case complexity of o k m n operations where m and n are respectively the number of transitions and places in the given petri net

reliable communication over channels with insertions deletions and substitutions a new block code is introduced which is capable of correcting multiple insertion deletion and substitution errors the code consists of nonlinear inner codes which we call watermark codes concatenated with low density parity check codes over nonbinary fields the inner code allows probabilistic resynchronization and provides soft outputs for the outer decoder which then completes decoding we present codes of rate 0 7 and transmitted length 5000 bits that can correct 30 insertion deletion errors per block we also present codes of rate 3 14 and length 4600 bits that can correct 450 insertion deletion errors per block

probabilistic detection of fsm single state transition faults based on state occupancy measurements this note discusses a probabilistic methodology for detecting single permanent or transient functional changes in the state transition mechanism of a deterministic finite state machine fsm the associated probabilistic detector observes the empirical frequencies with which different states are occupied and detects faults by analyzing the discrepancy between the observed state occupancy measurements and the expected frequencies in addition to state occupancy measurements the detector requires a statistical characterization of the input but does not need to know the order with which states appear or the exact input sequence that is applied to the fsm these features can be useful in settings where the input state order may not be known due to synchronization communication or other constraints

comments on polynomial time verification of decentralized diagnosability of discrete event systems versus decentralized failure diagnosis of discrete event systems complexity clarification an article on codiagnosability verification of discrete event systems was reported by moreira et al claiming an improvement in complexity over a paper by qiu and kumar this note clarifies an oversight in the complexity analysis of moreira et al s paper further the results of moreira et al s paper were obtained in a more restricted setting of projection masks in contrast to the more general non projection masks allowed in qiu and kumar s paper which was overlooked finally in the special case when the projection masks are used the complexity of qiu and kumar s paper is lower compared to the non projection masks case and equals the corrected complexity of moreira et al s paper

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

pencils of complex and real symmetric and skew matrices abstract this expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices the treatment is in the spirit of the well known book of gantmacher on matrix theory and may be regarded as a supplement to gantmacher s chapters on pencils of matrices

state based decentralized diagnosis of bi fuzzy discrete event systems recently we have introduced bi fuzzy discrete event systems bfdess and established their supervisory control theory under full observations and partial observations respectively compared with the models of discrete event systems and fuzzy discrete event systems bfdess are more satisfactory models to characterize some high uncertainty systems in this paper we study the fault diagnosis problems of bfdess first the framework of state based decentralized diagnosis is introduced then the notion of state based codiagnosability is defined and a necessary and sufficient condition for state based codiagnosability is provided in particular a polynomial time algorithm for state based codiagnosability verification and an online decentralized diagnosis method are presented in addition a compact state based decentralized diagnosis framework is introduced and the notion of state based jointly diagnosability and its verification algorithm are proposed finally the implication relationships between the two diagnosabilities are investigated

polynomial time verification of decentralized diagnosability of discrete event systems the first step in the diagnosis of failure occurrences in discrete event systems is the verification of the system diagnosability several works have addressed this problem using either diagnosers or verifiers for both centralized and decentralized architectures in this technical note we propose a new algorithm to verify decentralized diagnosability of discrete event systems the proposed algorithm requires polynomial time in the number of states and events of the system and has lower computational complexity than all other methods found in the literature in addition it can also be applied to the centralized case

classes of normal matrices in indefinite inner products abstract we study classes of matrices defined by various normality properties with respect to an indefinite complex inner product the relationships between many such properties all of them equivalent to the normality in case of a definite inner product are described in particular a canonical form is developed for the class of matrices that are polynomials of a self adjoint matrix

initial state detectability of stochastic discrete event systems with probabilistic sensor failures abstract initial state estimation is an important problem in discrete event systems in this problem the initial state of the system is unknown and one wants to determine the initial state of the system based on its observation in this paper we investigate the problem of initial state detection of partially observed discrete event systems in the stochastic setting we consider two sources of randomness in this problem stochastic dynamic of the system and probabilistic sensor failures specifically we model a stochastic discrete event system by a probabilistic finite state automaton and we use a probabilistic projection function as the observation model the notion of stochastic initial state detectability si detectability is introduced in order to capture whether or not the probability of detecting the initial state converges to one even in the presence of potential sensor failures an approach for the verification of si detectability is proposed we also investigate the complexity of the si detectability verification problem and we show that this problem is pspace complete

decentralized diagnosis of stochastic discrete event systems we investigate the decentralized diagnosis of stochastic discrete event systems sdess by using multiple local stochastic diagnosers each possessing its own sensors to deal with different information we formalize the notions of decentralized diagnosis for sdess by defining the concept of codiagnosability for stochastic automata in which any communication among the local stochastic diagnosers or to any coordinators is not involved these notions are weaker than the corresponding notions of decentralized diagnosis of classical dess a stochastic system being codiagnosable means that a fault can be detected by at least one local stochastic diagnoser within a finite delay we construct a codiagnoser from a given stochastic system with a finite number of projections whose each diagnosis component uses the complete model of the system we also deal with a number of basic properties of the codiagnoser in particular a necessary and sufficient condition of the codiagnosability for sdess is presented which generalizes the corresponding results of centralized diagnosis for sdess also we give a computing method in detail to check the codiagnosability of sdess as an application of our results some examples are described

computation of diagnosable fault occurrence indices for systems with repeatable faults certain faults such as intermittent or non persistent faults may occur repeatedly for discrete event systems prone to repeated faults jiang kumar and garcia in 2003 introduced the notion of l diagnosability requiring the diagnosis of the l th occurrence of a fault within a bounded delay the present paper studies the identification of the set of all indices l for which the system is not l diagnosable these are precisely the occurrence indices for which a repeatable fault cannot be diagnosed we present an algorithm of cubic complexity to determine whether a system is diagnosable for every fault occurrence index for those systems for which the answer is negative we show that the set of indices for which the system is non diagnosable possesses the property that it is either finite or consists of a finite number of eventually periodic sets

unitary equivalence in an indefinite scalar product an analogue of singular value decomposition if h1 is an n n and h2 an m m invertible hermitian matrix and x and y are arbitrary complex m n matrices we call the last matrices equivalent if x u2yu1 for some h1 unitary matrix u1 and some h2 unitary matrix u2 it is well known that if h1 and h2 are positive definite then without loss of generality we can assume that they are identities and x and y are equivalent if and only if the diagonalizable matrices x x and y y have the same spectrum in the present paper we show that in general the jordan form of x x where x is the h1 h2 adjoint of x x h 11x h2 defines a finite number of nonequivalent classes of matrices and that each such class is defined by its integer matrix explicit formulas for all classes having the same jordan form of x x are presented the necessary and sufficient conditions for an operator to be presentable as uz with h unitary u and h self adjoint h consistent z h polar decomposition of the operator are found

detectability in stochastic discrete event systems abstract a discrete event system possesses the property of detectability if it allows an observer to perfectly estimate the current state of the system after a finite number of observed symbols i e detectability captures the ability of an observer to eventually perfectly estimate the system state in this paper we analyze detectability in stochastic discrete event systems sdes that can be modeled as probabilistic finite automata more specifically we define the notion of a detectability which characterizes our ability to estimate the current state of a given sdes with increasing certainty as we observe more output symbols the notion of a detectability is differentiated from previous notions for detectability in sdes because it takes into account the probability of problematic observation sequences that do not allow us to perfectly deduce the system state whereas previous notions for detectability in sdes considered each observation sequence that can be generated by the underlying system we discuss observer based techniques that can be used to verify a detectability and provide associated necessary and sufficient conditions we also prove that a detectability is a pspace hard problem

from classic observability to a simple fuzzy observability for fuzzy discrete event systems in order to determine uncertainties from restricted available information fuzzy discrete event systems fdess or fuzzy discrete event dynamic systems fdedss were recently proposed these frameworks include fuzzy states and events occurring simultaneously with different membership degrees fuzzy states and events have been used to describe uncertainties that occur often in practical problems such as treatment planning for hiv aids patients sensory information processing for robotic control and fault diagnosis problems in order to measure information associated with fdess or fdedss the classical discrete event system des observability has been turned into fuzzy observability for fdess or fdedss the newly proposed method allows ease of defining degrees of observability so that uncertainties in fdess or fdedss can be dealt with effectively this gives an opportunity to design better decision making systems to calculate the observability degree a simple fuzzy observability checking method is introduced and two examples are elaborated upon to illustrate the presented method finally the newly proposed method is tested on a heating ventilating and air conditioning hvac system

on the convergence to ergodic behaviour of quantum wavefunctions we study the decrease of fluctuations of diagonal matrix elements of observables and of husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi classical regime h 0 the model studied is a spin su 2 one in a classically strongly chaotic regime we show that the fluctuations are gaussian distributed with a width 2 decreasing as the square root of planck s constant this is consistent with random matrix theory rmt predictions and previous studies on these fluctuations 1 2 we further study the width of the probability distribution of dependent fluctuations and compare it to the gaussian orthogonal ensemble goe of rmt

stability of self adjoint square roots and polar decompositions in indefinite scalar product spaces continuity properties of factors in polar decompositions of matrices with respect to indefinite scalar products are studied the matrix having the polar decomposition and the indefinite scalar product are allowed to vary closely related properties of a self adjoint with respect to an indefinite scalar product perturbed matrix to have a self adjoint square root or to have a representation of the form xx are also

verification of codiagnosability for discrete event systems modeled by mealy automata with nondeterministic output functions in the conventional framework for failure diagnosis of partially observed discrete event systems it is assumed that for each event the corresponding output symbol is determined uniquely however this assumption does not hold in discrete event systems such as a mobile system where an output symbol depends on not only an event but also a state at which the event occurs in this technical note we model such discrete event systems by mealy automata with nondeterministic output functions and consider a decentralized failure diagnosis problem that requires any occurrence of a failure should be detected by at least one local diagnoser within a uniformly bounded number of steps we introduce an extended version of codiagnosability as a condition for the existence of a decentralized diagnoser we then present an algorithm for verifying the extended codiagnosability condition

maximum likelihood failure diagnosis in finite state machines under unreliable observations in this paper we develop a probabilistic methodology for failure diagnosis in finite state machines based on a sequence of unreliable observations given prior knowledge of the input probability distribution but without actual knowledge of the applied input sequence the core problem we consider is to choose from a pool of known deterministic finite state machines fsms the one that most likely matches the given sequence of observations the problem becomes challenging because of sensor failures which may corrupt the observed sequence by inserting deleting and transposing symbols with certain probabilities that are assumed known we propose an efficient recursive algorithm for obtaining the most likely underlying fsm given the possibly erroneous observed sequence the proposed algorithm essentially allows us to perform online maximum likelihood failure diagnosis and is applicable to more general settings where one is required to choose the most likely underlying hidden markov model hmm based on a sequence of observations that may get corrupted with known probabilities the algorithm generalizes existing recursive algorithms for likelihood calculation in hmms by allowing loops in the associated trellis diagram we illustrate the proposed methodology using an example of diagnosis in the context of communication protocols

polynomial time verification of decentralized diagnosability of discrete event systems versus decentralized failure diagnosis of discrete event systems a critical appraisal in 1 the authors claim that there is an oversight in 2 in the sense that the proposed verifier is in general nondeterministic and the computational complexity analysis is incorrect the authors in 1 also claim that the complexity of the verification algorithm presented in 3 is reduced when considering the more restrictive setting of projection masks in contrast to the more general non projection masks case and equals the complexity of the verification algorithm presented in 2 in this note we show that the computational complexity analysis of 2 is actually correct and that the complexity of the verification algorithm presented in 3 is not reduced without additional modification of the algorithm not yet proposed in the literature if projection masks are used and therefore is not equal to the complexity of the algorithm presented in 2

safe diagnosability of stochastic discrete event systems recently safe diagnosability of discrete event systems dess was investigated by paoli and lafortune which was viewed as the first necessary step of fault tolerant supervision in this paper we consider the problem of safe diagnosability in the framework of stochastic discrete event systems sdess we define the notion of safe diagnosability for stochastic automata in which fault detection occurs before any given forbidden string in the failed mode of system is executed the relationship between diagnosability and safe diagnosability for sdess is analyzed in particular a necessary and sufficient condition for safe diagnosability of sdess is presented by constructing the recognizer of illegal language and the safe diagnoser some examples are described to illustrate the results

a petri net diagnoser for discrete event systems modeled by finite state automata we propose in this paper a petri net approach to online diagnosis of discrete event systems dess modeled by finite state automata the diagnosis method is based on the construction of a petri net diagnoser pnd which is constructed in polynomial time and requires less memory than other methods proposed in the literature we also present methods for the conversion of the pnd to both sequential function chart and ladder diagram for implementation on a programmable logic controller plc implementation issues are also addressed in the paper

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived

computation of minimal diagnosis bases of discrete event systems using verifiers abstract in order to diagnose the occurrence of a fault event in a discrete event system des it is first necessary to verify if the language of the system is diagnosable with respect to an observable event set and a fault event set in some cases the language of the system is also diagnosable even when a subset of the set of observable events under consideration is used as the actual observable event set among the benefits that such a reduction may bring we list the reduction in the number of sensors used in the diagnosis therefore reducing the cost of the system and the possibility to deploy the sensor redundancy to obtain a more reliable diagnosis decision in this work we propose two algorithms to find in a systematic way all minimal subsets of the observable event set that ensure the diagnosability of the des minimal diagnosis bases the methods are based on the construction of verifiers and have lower computational complexity than another method recently proposed in the literature

codiagnosability of discrete event systems revisited a new necessary and sufficient condition and its applications abstract it has been argued for some time now based on classroom textbook and practical examples that the size of verifiers and diagnosers is comparable this belief has been corroborated by a recent paper where it is conjectured based on a rigorous statistical analysis that the size of the states of diagnosers is n 0 77 log k 0 63 on the average where k resp n is the number of events resp states of the plant automaton however there is another difficulty that hampers the use of diagnosers in diagnosability verification the search for cycle which has been proved to be factorial we present in this paper a necessary and sufficient condition for a language codiagnosability of des and based on this condition we propose a new test for its verification that is based on a diagnoser like automaton that has following advantages i the diagnosability verification test is based on the search for strongly connected components which is linear in the state size ii it has both observable and unobservable events of the plant in its event set and so the usual assumptions on language liveness and nonexistence of unobservable cycles of states connected with unobservable events only are no longer required and iii t codiagnosability can be computed by adding weights associated with transitions of the plant automaton and as a consequence k codiagnosability since it is a particular case of t codiagnosability when all weights are set equal to 1

new algorithms for verification of relative observability and computation of supremal relatively observable sublanguage in this technical note we present a new property of relative observability and based on this property we propose two algorithms the first one that has polynomial complexity verifies if a regular language is relatively observable the second algorithm computes the supremal relatively observable sublanguage of a given regular language although the latter has exponential complexity it is more efficient than a recently proposed algorithm which has double exponential complexity moreover the algorithm proposed here has polynomial complexity when the automaton that marks the specification language is state partition

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

polar decompositions in finite dimensional indefinite scalar product spaces general theory abstract several classes of polar decompositions of real and complex matrices with respect to a given indefinite scalar product are studied matrices that admit such polar decompositions are described in various ways in particular a full description of all polar decompositions of a given matrix up to the natural similarity between polar decompositions is given

robust diagnosis of discrete event systems against intermittent loss of observations in the usual approaches to fault diagnosis of discrete event systems it is assumed that not only all sensors work properly but also all information reported by sensors always reaches the diagnoser any bad sensor operation or communication failure between sensors and the diagnoser can be regarded as loss of observations of events initially assumed as observable in such situations it may be possible that either the diagnoser stands still or report some wrong information regarding the fault occurrence in this paper we assume that intermittent loss of observations may occur and we propose an automaton model based on a new language operation language dilation that takes it into account we refer to this problem as robust diagnosability against intermittent loss of observations or simply robust diagnosability where the context allows we present a necessary and sufficient condition for robust diagnosability in terms of the language generated by the original automaton and propose two tests for robust language diagnosability one that deploys diagnosers and another one that uses verifiers we also extend the results to robust codiagnosability against intermittent loss of observations

verification complexity of a class of observational properties for modular discrete events systems abstract a modular discrete event system is modeled by a set of module automata running synchronously in this paper we investigate the complexity of the verification problems of three different properties diagnosability predictability and detectability for partially observed modular discrete event systems we first show that deciding diagnosability for modular discrete event systems is pspace complete when the number of modules is unbounded then we show that deciding predictability and detectability for modular discrete event systems are both pspace hard problems these results reveal that in order to verify these properties for the complete system exploring the state space of the monolithic model may be unavoidable in the worst case

evidence for the validity of the berry robnik surmise in a periodically pulsed spin system we study the statistical properties of the spectrum of a quantum dynamical system whose classical counterpart has mixed phase space structure consisting of two regular regions separated by a chaotic one we make use of a simple symmetry of the system to separate the eigenstates of the time evolution operator into two classes in agreement with the percival classification scheme we then use a method firstly developed by bohigas et al 1990 to evaluate the fractional measure of states belonging to the regular class and finally present the level spacing statistics for each class the level spacing distribution of states belonging to the irregular part of the spectra as well as that of the complete set of levels corroborate the berry robnik surmise we further present a statistical study of the regular levels the presence of intermediate states states which belong to neither class as long as r is finite phase spatially mixed among the set of regular ones together with the small fractional measure of regular states strongly affects the corresponding level spacing statistics resulting in a non negligible deviation from the expected poisson distribution we see however the remarkable agreement of the irregular level spacing statistics as a direct confirmation of the berry robnik surmise