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

on the combinatorics of locally repairable codes via matroid theory this paper provides a link between matroid theory and locally repairable codes lrcs that are either linear or more generally almost affine using this link new results on both lrcs and matroid theory are derived the parameters n k d r delta of lrcs are generalized to matroids and the matroid analog of the generalized singleton bound by gopalan et al for linear lrcs is given for matroids it is shown that the given bound is not tight for certain classes of parameters implying a nonexistence result for the corresponding locally repairable almost affine codes that are coined perfect in this paper constructions of classes of matroids with a large span of the parameters n k d r delta and the corresponding local repair sets are given using these matroid constructions new lrcs are constructed with prescribed parameters the existence results on linear lrcs and the nonexistence results on almost affine lrcs given in this paper strengthen the nonexistence and existence results on perfect linear lrcs given by song et al

diagnosability of discrete event systems subject to permanent sensor failures this paper considers a failure diagnosis problem for discrete event systems subject to permanent sensor failures a notion of diagnosability subject to permanent sensor failures is introduced with respect to a certain nondeterministic observation mask for its verification an aggregated mealy automaton with a deterministic and state dependent observation mask is defined it is shown that the diagnosability of the aggregated mealy automaton is equivalent to the diagnosability of the original system subject to permanent sensor failures then a method for verifying the diagnosability of the aggregated mealy automaton is presented moreover the delay bound within which the occurrence of any failure string can be detected subject to permanent sensor failures is computed

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

decidability for a temporal logic used in discrete event system analysis the type of plant considered is one that can be modelled by a non deterministic finite state machine p the regulator is a deterministic finite state machine r the closed loop system is formed by connecting p and r in a regulator configuration formulae in a propositional temporal language are used to describe the behaviour of the closed loop system it is shown that there is a mechanical procedure which for a given p and r and a temporal formula will determine in a finite number of steps whether or not must be true this decidability result could be proven using other known results on temporal logic the proof given here shows that the behaviour of the closed loop system may safely be assumed to be ultimately periodic formulae of a given complexity say n will be true in all possible runs of the system just in case they are true in all ultimately periodic runs with the period and the onset of periodicity bounded by a certain function of n a synthesis result follows immediately from th

a method for the synthesis of controllers to handle safety liveness and real time constraints describes a synthesis method that automatically derives controllers for timed discrete event systems with nonterminating behavior modeled by timed transition graphs and specifications of control requirements expressed by metric temporal logic mtl formulas synthesis is performed by using 1 a forward chaining search that evaluates the satisfiability of mtl formulas over sequences of states generated by occurrences of actions and 2 a control directed backtracking technique that takes into consideration the controllability of actions this method has several interesting features first the issues of controllability safety liveness and real time are integrated in a single framework second the synthesis process does not require explicit storage of an entire transition structure over which formulas are checked and can be stopped at any moment giving an approximate but useful result third search and control mechanisms allow circumvention of the state explosion problem

on the decidability and complexity of diagnosability for labeled petri nets in this paper we investigate the decidability and complexity of the fault diagnosis problem in unbounded labeled petri nets first we show that checking diagnosability for unbounded petri nets is decidable we present a new necessary and sufficient condition for diagnosability which can be reduced to a model checking problem for unbounded petri nets then we show that checking diagnosability for unbounded petri nets is expspace complete this complexity result is further extended to various subclasses of petri nets to the best of our knowledge this is the first paper that establishes decidability and complexity results for diagnosability of unbounded petri nets

codes with local regeneration and erasure correction regenerating codes and codes with locality are two coding schemes that have recently been proposed which in addition to ensuring data collection and reliability also enable efficient node repair in a situation where one is attempting to repair a failed node regenerating codes seek to minimize the amount of data downloaded for node repair while codes with locality attempt to minimize the number of helper nodes accessed this paper presents results in two directions in one this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures by employing local codes having minimum distance 2 an upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed the second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes these codes termed here as codes with local regeneration are codes with locality over a vector alphabet in which the local codes themselves are regenerating codes we derive an upper bound on the minimum distance of vector alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property this property is possessed by both minimum storage regeneration msr and minimum bandwidth regeneration mbr codes we provide several constructions of codes with local regeneration which achieve this bound where the local codes are either msr or mbr codes also included in this paper is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance

on the average locality of locally repairable codes a linear block code with dimension k length n and minimum distance d is called a locally repairable code lrc with locality r if it can retrieve any coded symbol by at most r other coded symbols lrcs have been recently proposed and used in practice in distributed storage systems such as windows azure storage and facebook hdfs raid theoretical bounds on the maximum locality of lrcs r have been established the average locality of an lrc overline r directly affects the costly repair bandwidth disk i o and the number of nodes involved in the repair process of a missing data block there is a gap in the literature studying overline r in this paper we establish a lower bound on overline r of arbitrary n k d lrcs furthermore we obtain a tight lower bound on overline r for a practical case where the code rate r k n is greater than 1 1 sqrt n 2 finally we design three classes of lrcs that achieve the obtained bounds on overline r comparing with the existing lrcs our proposed codes improve the average locality without sacrificing such crucial parameters as the code rate or minimum distance

model uncertainty in discrete event systems earlier work concerning control of discrete event systems usually assumed that a correct model of the system to be controlled was available a goal of this work is to provide an algorithm for determining the correct model from a set of models the result of the algorithm is a finite language that can be used to test for the correct model or notification that the remaining models cannot be controllably distinguished we use the finite state machine model with controllable and uncontrollable events presented by ramadge and wonham

verification of hybrid automata diagnosability by abstraction a notion of diagnosability for hybrid systems is defined which generalizes the common notion of observability we propose an abstraction procedure to translate a hybrid automaton into a timed automaton in order to verify observability and diagnosability properties we introduce a procedure to check diagnosability and show that for the system class of our abstraction namely for a subclass of timed automata the durational graphs the verification problem belongs to the complexity class p we apply our procedure to an electromagnetic valve system for camless engines

the shift operator technique for so 7 in an su 2 3 basis ii applications reduced matrix elements of the tensor operator which forms part of so 7 generator basis are calculated for the three respective classes of so 7 representations v 0 0 v n0 v 0 1 v n0 0 0 v v n0 the calculation is based on the relations between quadratic products of shift operators established in a previous paper by the same authors

the matrix representation of so7 in an su2 3 basis vector coherent state vcs theory is applied to so7 in an su2 3 basis some reduced matrix elements of the tensor operator that forms part of the so7 algebra are derived by using the k matrix technique

internal labelling problem an algorithmic procedure combining the decomposition of casimir operators induced by the embedding of a subalgebra into a semisimple lie algebra with the properties of commutators of subgroup scalars an analytical algorithm for the computation of missing label operators with the commutativity requirement is proposed two new criteria for subgroups scalars to commute are given the algorithm is completed with a recursive method to construct orthonormal bases of states as examples to illustrate the procedure four labelling problems are explicitly studied

predictability of event occurrences in partially observed discrete event systems this paper studies the problem of predicting occurrences of a significant event in a partially observed discrete event system the predictability of occurrences of an event in a system is defined in the context of formal languages the predictability of a language is a stronger condition than the diagnosability of the language two necessary and sufficient conditions for predictability of occurrences of an event in systems modeled by regular languages are presented both conditions can be algorithmically tested the first condition employs diagnosers the second condition employs verifiers and results in a polynomial time in the number of states complexity test for verification of predictability when predictability holds diagnosers can be used online to predict the significant event

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

on codiagnosability and coobservability with dynamic observations codiagnosability and coobservability in discrete event systems where observations are dynamic are considered instead of having a fixed set of observable events the observation of an event is dynamic trace dependent in this paper a procedure is developed to transform the problem of coobservability to the problem of codiagnosability in the context of dynamic observations this proves that problems of coobservability are transformable to problems of codiagnosability and enables us to leverage the large literature available for codiagnosability to solve problems of coobservability furthermore in the case of dynamic observations the known polynomial complexity tests for the property of codiagnosability based on verifier automata with fixed observable event set s are no longer directly applicable a new testing procedure is developed that can handle transition based dynamic observations and remains of polynomial complexity in the state space of the system this new testing procedure employs a covering of the state space of the system based on cluster automata which enhances its computational efficiency based on cluster automata a new type of verifier automaton is built called the c verifier for verification of codiagnosability as an application of the above mentioned transformation the c verifier becomes a unified method for verifying both codiagnosability and coobservability

a linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing a discrete event system is a system whose behavior can be described by means of a set of time consuming activities performed according to a prescribed ordering events correspond to starting or ending some activity an analogy between linear systems and a class of discrete event systems is developed following this analogy such discrete event systems can be viewed as linear in the sense of an appropriate algebra the periodical behavior of closed discrete event systems i e involving a set of repeatedly performed activities can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra this problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph the potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized the case of a flowshop like production process is analyzed in detail

constructions of optimal cyclic r delta locally repairable codes a code is said to be an r local locally repairable code lrc if each of its coordinates can be repaired by accessing at most r other coordinates when some of the r coordinates are also erased the r local lrc cannot accomplish the local repair which leads to the concept of r delta locality a q ary n k linear code mathcal c is said to have r delta locality delta ge 2 if for each coordinate i there exists a punctured subcode of mathcal c with support containing i whose length is at most r delta 1 and whose minimum distance is at least delta the r delta lrc can tolerate delta 1 erasures in every local code i e punctured subcode which degenerates to an r local lrc when delta 2 a q ary r delta lrc is called optimal if it meets the singleton like bound for r delta lrcs a class of optimal q ary cyclic r local lrcs with lengths n mid q 1 were constructed by tamo barg goparaju and calderbank based on the q ary reed solomon codes in this paper we construct a class of optimal q ary cyclic r delta lrcs delta ge 2 with length n mid q 1 which generalizes the results of tamo et al moreover we construct a new class of optimal q ary cyclic r local lrcs with lengths n mid q 1 and a new class of optimal q ary cyclic r delta lrcs delta ge 2 with lengths n mid q 1 the constructed optimal lrcs with length n q 1 have the best known length for a given finite field with size q when the minimum distance is larger than 4

generalized detectability for discrete event systems in our previous work we investigated detectability of discrete event systems which is defined as the ability to determine the current and subsequent states of a system based on observation for different applications we defined four types of detectabilities weak detectability strong detectability weak periodic detectability and strong periodic detectability in this paper we extend our results in three aspects 1 we extend detectability from deterministic systems to nondeterministic systems such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems 2 we develop polynomial algorithms to check strong detectability the previous algorithms are based on observer whose construction is of exponential complexity while the new algorithms are based on a new automaton called detector 3 we extend detectability to d detectability while detectability requires determining the exact state of a system d detectability relaxes this requirement by asking only to distinguish certain pairs of states with these extensions the theory on detectability of discrete event systems becomes more applicable in solving many practical problems

fractional repetition codes with flexible repair from combinatorial designs fractional repetition fr codes are a class of regenerating codes for distributed storage systems with an exact table based repair process that is also uncoded i e upon failure a node is regenerated by simply downloading packets from the surviving nodes in this paper we present the constructions of fr codes based on steiner systems and resolvable combinatorial designs such as affine geometries hadamard designs and mutually orthogonal latin squares the failure resilience of our codes can be varied in a simple manner we construct codes with normalized repair bandwidth beta strictly larger than one these cannot be obtained trivially from codes with beta 1 furthermore we present the kronecker product technique for generating new codes from existing ones and elaborate on their properties fr codes with locality are those where the repair degree is smaller than the number of nodes contacted for reconstructing the stored file for these codes we establish a tradeoff between the local repair property and the failure resilience and construct codes that meet this tradeoff much of prior work only provided lower bounds on the fr code rate in this paper for most of our constructions we determine the code rate for certain parameter ranges

coherent state theory of the noncompact symplectic group an extended coherent state theory is presented for the noncompact sp 3 r group which reveals a simple relationship between the sp 3 r algebra and its contracted u 3 boson limit the relationship is used to derive a remarkably accurate analytic expression for sp 3 r matrix elements for the generic lowest weight representations the expression is shown to be exact whenever the states involved are multiplicity free with respect to the u 3 subalgebra it is further shown how exact matrix elements are easily calculated in general dyson and holstein primakoff type u 3 boson expansions are given

boson realization of sp 4 i the matrix formulation holstein and primakoff derived long ago the boson realization of a su 2 lie algebra for an arbitrary irreducible representation irrep of the su 2 group the corresponding result for su 1 1 sp 2 is also well known this raises the question of whether it is possible to obtain in an explicit analytic and closed form and for any integer d the boson realization of a sp 2d lie algebra for an arbitrary irrep of the sp 2d group which is a problem of considerable physical interest the case d 2 already illustrates the problem in its full generality and thus in this paper we concentrate on sp 4 the dyson realization is well known and the passage to bosons satisfying the appropriate hermiticity conditions can be done by a similarity transformation through an operator k what we want though is an explicit boson realization for sp 2d similar to the one that exists for sp 2 in sec vi we show how we can get it for sp 4 if the operator k is known unfortunately while the matrix form of k2 can be ex

an algorithm for calculating indistinguishable states and clusters in finite state automata with partially observable transitions this paper presents a new algorithm for efficiently calculating pairs of indistinguishable states in finite state automata with partially observable transitions the need to obtain pairs of indistinguishable states occurs in several classes of problems related to control under partial observation diagnosis or distributed control with communication for discrete event systems the algorithm obtains all indistinguishable state pairs in polynomial time in the number of states and events in the system another feature of the algorithm is the grouping of states into clusters and the identification of indistinguishable cluster pairs clusters can be employed to solve control problems for partially observed systems

universal and dynamic locally repairable codes with maximal recoverability via sum rank codes locally repairable codes lrcs are considered with equal or unequal localities local distances and local field sizes an explicit two layer architecture with a sum rank outer code is obtained having disjoint local groups and achieving maximal recoverability mr for all families of local linear codes mds or not simultaneously up to a specified maximum locality r furthermore the local linear codes thus the localities local distances and local fields can be efficiently and dynamically modified without global recoding or changes in architecture or outer code while preserving the mr property easily adapting to new configurations in storage or new hot and cold data in addition local groups and file components can be added removed or updated without global recoding the construction requires global fields of size roughly g r for g local groups and maximum or specified locality r for equal localities these global fields are smaller than those of previous mr lrcs when r leq h global parities for unequal localities they provide an exponential field size reduction on all previous best known mr lrcs for bounded localities and a large number of local groups the global erasure correction complexity of the given construction is comparable to that of tamo barg codes or reed solomon codes with local replication while local repair is as efficient as for the cartesian product of the local codes reed solomon codes with local replication and cartesian products are recovered from the given construction when r 1 and h 0 respectively the given construction can also be adapted to provide hierarchical mr lrcs for all types of hierarchies and parameters finally subextension subcodes and sum rank alternant codes are introduced to obtain further exponential field size reductions at the expense of lower information rates

asymptotic interference alignment for optimal repair of mds codes in distributed storage the high repair bandwidth cost of n k maximum distance separable mds erasure codes has motivated a new class of codes that can reduce repair bandwidth over that of conventional mds codes in this paper we address n k d exact repair mds codes which allow for any single failed node to be repaired exactly with access to any arbitrary set of d survivor nodes we show the existence of exact repair mds codes that achieve minimum repair bandwidth matching the cut set lower bound for arbitrary admissible n k d i e k d n 1 moreover we extend our results to show the optimality of our codes for multiple node failure scenarios in which an arbitrary set of r n k failed nodes needs to repaired our approach is based on asymptotic interference alignment proposed by cadambe and jafar as a byproduct we also characterize the capacity of a class of multisource nonmulticast networks

explicit constructions of optimal access mds codes with nearly optimal sub packetization an n k l maximum distance separable mds array code of length n dimension k n r and sub packetization l is formed of l times n matrices over a finite field f with every column of the matrix stored on a separate node in the distributed storage system and viewed as a coordinate of the codeword repair of a failed node recovery of one erased column can be performed by accessing a set of d le n 1 surviving helper nodes the code is said to have the optimal access property if the amount of data accessed at each of the helper nodes meets a lower bound on this quantity for optimal access mds codes with d n 1 the sub packetization l satisfies the bound l ge r k 1 r in our previous work ieee trans inf theory vol 63 no 4 2017 for any n and r we presented an explicit construction of optimal access mds codes with sub packetization l r n 1 in this paper we take up the question of reducing the sub packetization value l to make it to approach the lower bound we construct an explicit family of optimal access codes with l r lceil n r rceil which differs from the optimal value by at most a factor of r 2 these codes can be constructed over any finite field f as long as f ge r lceil n r rceil and afford low complexity encoding and decoding procedures we also define a version of the repair problem that bridges the context of regenerating codes and codes with locality constraints lrc codes which we call group repair with optimal access in this variation we assume that the set of n sm nodes is partitioned into m repair groups of size s and require that the amount of accessed data for repair is the smallest possible whenever the d s k 1 helper nodes include all the other s 1 nodes from the same group as the failed node for this problem we construct a family of codes with the group optimal access property these codes can be constructed over any field f of size f ge n and also afford low complexity encoding and decoding procedures

abstraction based failure diagnosis for discrete event systems in this paper we introduce the idea of abstraction based diagnosability for large scale composed discrete event systems that consist of multiple subsystems to this end we determine sufficient conditions such that diagnosability of the original system follows from diagnosability of an abstracted system model on a smaller state space in addition we prove that also the reverse implication is true if an additional requirement for the abstraction is fulfilled then we show how our method can be applied to compute abstracted models for the diagnosability verification of composed systems without enumerating the whole system state space in this way considerable computational savings can be achieved as illustrated by a small manufacturing system example

verification of the observer property in discrete event systems the observer property is an important condition to be satisfied by abstractions of discrete event system des models this technical note presents a new algorithm that tests if an abstraction of a des obtained through natural projection has the observer property the procedure called op verifier can be applied to potentially nondeterministic automata with no restriction on the existence of cycles of non relevant events this procedure has quadratic complexity in the number of states the performance of the algorithm is illustrated by a set of experiments

error correcting regenerating and locally repairable codes via rank metric codes this paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings one being storage using existing regenerating codes and the second being storage using locally repairable codes the concatenated coding scheme brings together a maximum rank distance code as an outer code and either a globally regenerating or a locally repairable code as an inner code in addition error resilience for combination of locally repairable codes with regenerating codes is considered this concatenated coding system is designed to handle two different types of adversarial errors the first type includes an adversary that can replace the content of an affected node only once while the second type studies an adversary that is capable of polluting data an unbounded number of times the paper establishes an upper bound on the resilience capacity for a locally repairable code this paper also proves that the proposed concatenated coding approach attains the upper bound on the resilience capacity in the presence of the first type of adversary for both minimum storage regenerating codes and locally repairable codes further this paper presents mechanisms that combine the presented concatenated coding scheme with subspace signatures to achieve error resilience for the second type of errors

communication efficient secret sharing a secret sharing scheme is a method to store information securely and reliably particularly in a threshold secret sharing scheme a secret is encoded into n shares such that any set of at least t 1 shares suffice to decode the secret and any set of at most t 2 shares reveal no information about the secret assuming that each party holds a share and a user wishes to decode the secret by receiving information from a set of parties the question we study is how to minimize the amount of communication between the user and the parties we show that the necessary amount of communication termed decoding bandwidth decreases as the number of parties that participate in decoding increases we prove a tight lower bound on the decoding bandwidth and construct secret sharing schemes achieving the bound particularly we design a scheme that achieves the optimal decoding bandwidth when d parties participate in decoding universally for all t 1 le d le n the scheme is based on a generalization of shamir s secret sharing scheme and preserves its simplicity and efficiency in addition we consider the setting of secure distributed storage where the proposed communication efficient secret sharing schemes not only improve decoding bandwidth but further improve disk access complexity during decoding

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

the shift operator technique for so 7 in an su 2 3 basis i theory shift operators for the chain of lie groups so 7 su 2 3 are constructed and several properties are examined quite a number of relations connecting quadratic products of shift operators are built up finally the connection between matrix elements of the shift operators and reduced matrix elements of the tensor operator which forms part of the so 7 generator basis is explained

failure diagnosis of discrete event systems with linear time temporal logic specifications the paper studies failure diagnosis of discrete event systems dess with linear time temporal logic ltl specifications the ltl formulas are used for specifying failures in the system the ltl based specifications make the specification specifying process easier and more user friendly than the formal language automata based specifications and they can capture the failures representing the violation of both liveness and safety properties whereas the prior formal language automaton based specifications can capture the failures representing the violation of only the safety properties such as the occurrence of a faulty event or the arrival at a failed state prediagnosability and diagnosability of dess in the temporal logic setting are defined the problem of testing prediagnosability and diagnosability is reduced to the problem of model checking an algorithm for the test of prediagnosability and diagnosability and the synthesis of a diagnoser is obtained the complexity of the algorithm is exponential in the length of each specification ltl formula and polynomial in the number of system states and the number of specifications the requirement of nonexistence of unobservable cycles in the system which is needed for the diagnosis algorithms in prior methods to work is relaxed finally a simple example is given for illustration

the complexity of codiagnosability for discrete event and timed systems in this paper we study the fault codiagnosis problem for discrete event systems given by finite automata fa and timed systems given by timed automata ta we provide a uniform characterization of codiagnosability for fa and ta which extends the necessary and sufficient condition that characterizes diagnosability we also settle the complexity of the codiagnosability problems both for fa and ta and show that codiagnosability is pspace complete in both cases for fa this improves on the previously known bound exptime and for ta it is a new result we then generalize the previous results to the case of dynamic observers finally we show that the codiagnosis problem for ta under bounded resources is 2exptime complete

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

the basis for the symmetric irreducible representations of so 9 an explicit basis is constructed for the symmetric irreducible representation irrep of su 9 so 9 so 5 su1 2 su2 2 it is also indicated how good angular momentum states can be constructed the techniques used are based on the well known tensor algebra for the infinitesimal generators of simple lie groups

the predictability of discrete event systems perturbation analysis and the automaton and language model are approaches developed recently for the study of discrete event systems dess the prediction of a trajectory of a new system is the essential idea of perturbation analysis the automaton theory models a trajectory of a des by a string in a particular language the author formulates the trajectory prediction as a projection of a string onto a language a sufficient condition is found for one language to be predictable from another language examples are given to show the application of this concept

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

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

safe diagnosability of fuzzy discrete event systems and a polynomial time verification since fuzzy discrete event systems fdess were significantly brought forward the study of fdess has received increasing attention recently this paper addresses the safe diagnosability under the framework of fdess the contributions are threefold first the notion of safe diagnosability for fuzzy systems is formalized a safe diagnosable fdes means that not only each failure can be detected in terms of fuzziness as well as the detection must be completed before any unsafe operation is executed then a necessary and sufficient condition of safe diagnosability of fdess is proposed by constructing the safe diagnoser finally we present an algorithm for verifying the safe diagnosability of fdess based on a constructive nondeterministic automaton namely verifier it is worth noting that both constructing the verifier and verifying the safe diagnosability of fdess can be realized with a polynomial complexity

robust nonblocking supervisory control of discrete event systems under partial observation in this paper we extend previous results on robust nonblocking supervisory control of discrete event systems with full observation to the case of control under partial observation where only a subset of events are observable and can be monitored the exact model of the plant is not known but is assumed to be among a finite set of possible models for each plant model a legal marked behavior is assumed given we manage to characterize the entire set of solutions of the robust control problem and obtain a set of necessary and sufficient conditions for the existence of a solution for the robust control problem

on lowest density mds codes let f sub q denote the finite field gf q and let h be a positive integer mds maximum distance separable codes over the symbol alphabet f sub q sup b are considered that are linear over f sub q and have sparse low density parity check and generator matrices over f sub q that are systematic over f sub q sup b lower bounds are presented on the number of nonzero elements in any systematic parity check or generator matrix of an f sub q linear mds code over f sub q sup b along with upper bounds on the length of any mds code that attains those lower bounds a construction is presented that achieves those bounds for certain redundancy values the building block of the construction is a set of sparse nonsingular matrices over f sub q whose pairwise differences are also nonsingular bounds and constructions are presented also for the case where the systematic condition on the parity check and generator matrices is relaxed to be over f sub q rather than over f sub q sup b

robust prognosability for a set of partially observed discrete event systems abstract in this paper we consider a robust failure prognosis problem for partially observed discrete event systems given a set of possible models each of which has its own nonfailure specification we consider a single prognoser such that for all possible models it predicts any failure prior to its occurrence we call such a prognoser a robust prognoser we introduce a notion of robust prognosability and show that it serves as a necessary and sufficient condition for the existence of a robust prognoser we then present a method for verifying the robust prognosability condition moreover we discuss online synthesis of a robust prognoser

exact repair mds code construction using interference alignment the high repair cost of n k maximum distance separable mds erasure codes has recently motivated a new class of mds codes called repair mds codes that can significantly reduce repair bandwidth over conventional mds codes in this paper we describe n k d exact repair mds codes which allow for any failed node to be repaired exactly with access to d survivor nodes where k d n 1 we construct exact repair mds codes that are optimal in repair bandwidth for the cases of k n 1 2 and d 2k 11 b k 3 our codes are deterministic and require a finite field size of at most 2 n k our constructive codes are based on interference alignment techniques

verification of robust diagnosability for partially observed discrete event systems in this paper we study robust failure diagnosis of discrete event systems given a set of possible models each of which has its own nonfailure specification we consider the existence of a single diagnoser such that for all possible models it detects any occurrence of a failure within a uniformly bounded number of steps we call such a diagnoser a robust diagnoser we introduce a notion of robust diagnosability and prove that it serves as a necessary and sufficient condition for the existence of a robust diagnoser we then present an algorithm for verifying the robust diagnosability condition

on the locality of codeword symbols consider a linear n k d q code c we say that the ith coordinate of c has locality r if the value at this coordinate can be recovered from accessing some other r coordinates of c data storage applications require codes with small redundancy low locality for information coordinates large distance and low locality for parity coordinates in this paper we carry out an in depth study of the relations between these parameters we establish a tight bound for the redundancy n k in terms of the message length the distance and the locality of information coordinates we refer to codes attaining the bound as optimal we prove some structure theorems about optimal codes which are particularly strong for small distances this gives a fairly complete picture of the tradeoffs between codewords length worst case distance and locality of information symbols we then consider the locality of parity check symbols and erasure correction beyond worst case distance for optimal codes using our structure theorem we obtain a tight bound for the locality of parity symbols possible in such codes for a broad class of parameter settings we prove that there is a tradeoff between having good locality and the ability to correct erasures beyond the minimum distance

so 2n 1 in an so 2n 3 su 2 su 2 basis ii detailed study of the symmetric representations of the so 7 group for pt i see ibid vol 15 p 2665 76 1982 the so 7 down arrow su 2 3 reduction is analysed in detail explicit forms for the different su 2 generators and the remaining ones are derived using the results of the previous paper basis states describing the symmetric irreducible unitary representations are introduced expressions for the reduced matrix elements of the occurring generators with respect to these basis states are determined

robust supervisory control of a class of timed discrete event systems under partial observation this paper studies robust supervisory control of timed discrete event systems proposed by brandin and wonham given a set of possible models which includes the exact model of the plant the objective is to synthesize a robust supervisor such that it achieves legal behavior for all possible models we show that controllability for each possible model and observability for a suitably defined aggregate model are necessary and sufficient conditions for the existence of a solution to the robust supervisory control problem moreover when there does not exist a solution a maximally permissive robust supervisor is synthesized under the assumption that all controllable events are observable

stochastic failure prognosability of discrete event systems we study the prognosis of fault i e its prediction prior to its occurrence in stochastic discrete event systems we introduce the notion of m steps stochastic prognosability called s m prognosability which allows the prediction of a fault at least m steps in advance we formalize the notion of a prognoser and also show that s m prognosability is necessary and sufficient for the existence of a prognoser that can predict a fault at least m steps prior to occurrence while achieving any arbitrary false alarm and missed detection rates we also provide a polynomial algorithm for the verification of s m prognosability finally we compare the notion of stochastic prognosability with that of stochastic diagnosability and show that the former is a stronger notion as can be expected

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

constructions of optimal r delta locally repairable codes via constacyclic codes locally repairable codes lrcs are introduced in distributed storage systems due to their low repair overhead an lrc is called optimal if its minimum distance attains the singleton like upper bound chen et al 2018 recently studied the constructions of optimal r delta lrcs with length n mid q 1 and r delta 1 mid n where many classes of optimal cyclic constructions were obtained in this paper by employing constacyclic mds codes we construct seven classes of optimal r delta lrcs with new parameters after adding these new optimal lrcs via constacyclic codes we have completely obtained all optimal r delta lrcs with length n mid q 1 and r delta 1 mid n for all possible parameters for the completeness in the coding theory it is worth noting that the optimal constacyclic lrcs with new parameters provide more alternatives to cyclic lrcs in the practical demands of distributed storage systems where specific values of n k r and delta are required moreover constacyclic lrcs also possess the encoding and decoding efficiency as cyclic lrcs

a new approach for diagnosability analysis of petri nets using verifier nets in this paper we analyze the diagnosability properties of labeled petri nets we consider the standard notion of diagnosability of languages requiring that every occurrence of an unobservable fault event be eventually detected as well as the stronger notion of diagnosability in k steps where the detection must occur within a fixed bound of k event occurrences after the fault we give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded petri nets and then present an algorithmic technique for testing the conditions based on linear programming our approach is novel and based on the analysis of the reachability coverability graph of a special petri net called verifier net that is built from the petri net model of the given system in the case of systems that are diagnosable in k steps we give a procedure to compute the bound k to the best of our knowledge this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in k steps of labeled unbounded petri nets are presented

so 2n 1 in an so 2n 3 su 2 su 2 basis i reduction of the symmetric representations the branching rule for the reduction of symmetric irreducible unitary representations iur of the simple lie group so 2n 1 into iur of its maximal subgroup so 2n 3 x su 2 x su 2 is established for all n or 3 after the particular case n 3 is analysed in detail a general proof is presented which is valid for all n or 3 all branching rules n 3 4 can be summed up in one formula also a dimension verification is carried out the generators of so 2n 1 not belonging to the semi simple subgroup can be combined into a mixed tensor spinor representation with respect to the simple groups which occur in the direct product the precise nature of that representation is indicated and discussed

the diagnosability of petri net models using minimal explanations for a bounded petri net model the diagnosability property is usually checked via its regular language represented by the reachability graph rg however this is problematic because the computational complexity of the diagnosability test is polynomial in the cardinality of the state space of the model which is typically very large this limitation can be overcome by using for the diagnosability test an rof automaton with a state space significantly smaller than rg that generates the same language as rg after projecting out all non faulty unobservable transitions rof is efficiently constructed based on the calculation of the minimal explanations of the fault and of the observable transitions

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

the symmetric irreducible representations of so7 in su2 3 basis the symmetric irreducible representations of so7 in su2 3 basis are constructed some reduced matrix elements and closed expressions of simple isoscalar factors for so7 contains implies su2 3 are obtained finally an example is given to show how to obtain physical states from these mathematical ones

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 generalized framework for inference based diagnosis of discrete event systems capturing both disjunctive and conjunctive decision making we have previously introduced an inference based framework for decentralized decision making comprising of multiple observers each with its own partial observation where inferencing over the ambiguities of the self and the others is used to issue local decisions and a global decision is taken to be the one possessing the minimum ambiguity level in this setting we previously introduced the notion of n inference vee diagnosability to characterize the existence of a disjunctive decentralized diagnosis scheme so that any fault can be detected within a bounded delay using at most n levels of inferencing by one of the diagnosers while the disjunctive scheme relies on one of the diagnosers making the failure decision the dual conjunctive scheme relies on none of the diagnosers making the nonfailure decision it is known that the two schemes are incomparable and in this paper we extend our earlier work to provide a more general framework introducing the notion of n inference diagnosability capturing both disjunctive and conjunctive schemes we also develop a method for verifying n inference diagnosability as well as discuss several of its useful properties

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

np completeness of sensor selection problems arising in partially observed discrete event systems we consider the three properties of diagnosability normality and observability of discrete event systems in each case we consider the problem of finding an observable event set with minimum cardinality such that the property under consideration holds we prove that these search problems are computationally hard by showing that the corresponding decision problems are np complete

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

extensions of infinitesimal perturbation analysis an extension of the concept of perturbation analysis pa is introduced that can be applied to cases where sample path discontinuity with respect to system parameters has prevented the application of simple pa rules both markov and generalized semi markov processes are considered the robustness of the extended pa is examined and it is found to be sufficiently robust

diagnosis of behaviors of interest in partially observed discrete event systems abstract in this paper we address the problem of diagnosing the behaviors of interest in discrete event systems to this end we introduce the notion of language diagnosability based on language specifications that generalizes diagnosability based on event specifications a polynomial time algorithm for verifying language diagnosability is developed building upon the verification algorithm we develop a polynomial time algorithm for computing the worst case detection delay of a given system the computation of the worst case detection delay involves the shortest path computation of a weighted directed graph we exploit a special weighting structure of the graph resulting from the verification algorithm which enables an algorithm with a lower complexity than the commonly used bellman ford shortest path algorithm

the computational complexity of decentralized discrete event control problems computational complexity results are obtained for decentralized discrete event control problems these results generalize the earlier work of tsitsiklis 1989 who showed that for a special class of centralized supervisory control problems under partial observation there is an algorithm for determining in polynomial time whether or not a solution exists the negative complexity results associated with tsitsiklis work also carry over to the decentralized case so that solution existence for the more general class is not decidable in polynomial time nor does there exist a polynomial time algorithm for producing supervisor solutions when such solutions exist

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

decentralized prognosis of failures in discrete event systems we study the prognosis of failures i e their prediction prior to their occurrence in discrete event systems in a decentralized setting where multiple prognosers use their local observations to issue local prognosis decisions we define the notion of correctness of a decentralized set of prognosers in terms of no missed detections each failure is prognosed prior to its occurrence and no false alarms an incorrect prognostic decision is never issued and introduce the notion of coprognosability as an existence condition when specialized to the centralized case i e the case of a single prognoser this condition turns out to be weaker than the one introduced by genc and lafortune in 2006 since a uniform bound on the number of steps within which a failure will occur is not required for comparison we also introduce the stronger notion of uniformly bounded coprognosability and identify the subclass of decentralized prognosers for which it serves as an existence condition we show that the two notions coincide when the underlying system and its nonfailure specification possess finite state representations and present a verification algorithm whose complexity is polynomial in the sizes of the system being prognosed and its nonfailure specification and is exponential in the number of the local prognosers we also introduce the notion of reaction bound for coprognosis as the earliest time beyond a prognostic decision when a failure can occur and present an algorithm for computing it the complexity of this algorithm is identical to that of the verification algorithm an algorithm with complexity linear in the size of the specification and the number of local prognosers is also presented for an online prognosis of failures we show that the notions of coprognosability and its uniformly bounded version are in general incomparable with the notion of codiagnosability that guarantees a uniformly bounded delay detection of a failure by a local diagnoser when the system cannot execute an unbounded sequence of unobservable events uniformly bounded coprognosability implies codiagnosability whereas coprognosability and codiagnosability remain incomparable

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

a temporal logic approach to discrete event control for the safety canonical class this paper presents a temporal logic formulation of discrete event control which forms a new theoretical basis for control analysis and synthesis of a class of discrete event systems des based on the formulation a basic supervisory control theory is developed for a control objective specified by an invariance formula belonging to the safety canonical class of manna and pneuli using the safety canonical class as a basis the refinement and generalization of the existing basic predicate framework are demonstrated a simple example illustrates the formal axiomatic means to perform control theoretic analysis and synthesis under the new formulation

locally recoverable codes on algebraic curves a code over a finite alphabet is called locally recoverable lrc code if every symbol in the encoding is a function of a small number at most r of other symbols of the codeword in this paper we introduce a construction of lrc codes on algebraic curves extending a recent construction of the reed solomon like codes with locality we treat the following situations local recovery of a single erasure local recovery of multiple erasures and codes with several disjoint recovery sets for every coordinate the availability problem for each of these three problems we describe a general construction of codes on curves and construct several families of lrc codes we also describe a construction of codes with availability that relies on automorphism groups of curves we also consider the asymptotic problem for the parameters of the lrc codes on curves we show that the codes obtained from asymptotically maximal curves for instance garcia stichtenoth towers improve upon the asymptotic versions of the gilbert varshamov bound for lrc codes