fault detection and isolation based on fuzzy automata fuzzy automata are proposed for fault diagnosis the output of the monitored system is partitioned into linear segments which in turn are assigned to pattern classes templates with the use of membership functions a sequence of templates is generated and becomes input to fuzzy automata which have transitions that correspond to the templates of the properly functioning system if the automata reach their final states i e the input sequence is accepted by the automata with a membership degree that exceeds a certain threshold then normal operation is deduced otherwise a failure is diagnosed fault diagnosis of a dc motor and detection of abnormalities in the ecg signal are used as case studies

on the state minimization of fuzzy automata this paper investigates the minimization problem of fuzzy automata aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one the decision version of the minimization problem is as follows given a fuzzy automaton cal a and a natural number k i e a pair langle cal a k rangle is there a k state fuzzy automaton equivalent to cal a we prove that the above problem is decidable for fuzzy automata over totally ordered lattices and then obtain a procedure for minimizing a given fuzzy automaton to this end we introduce the concept of systems of fuzzy polynomial equations present a procedure for finding solutions of these systems and finally reduce the above decision problem to finding a solution of a system of fuzzy polynomial equations it is worth pointing out that although some algorithms in the literature were claimed to be minimization algorithms the term minimization there did not mean state minimization in our sense since these algorithms did not aim at a minimal fuzzy automaton but found reasonably small fuzzy automata

finite model approximations and asymptotic optimality of quantized policies in decentralized stochastic control we consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents the strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions in particular quantized team policies are asymptotically optimal this result is then applied to witsenhausen s celebrated counterexample and the gaussian relay channel problem for witsenhausen s counterexample our approximation approach provides to our knowledge the first rigorously established result that one can construct an varepsilon optimal strategy for any varepsilon 0 through a solution of a simpler problem

reducing nfas by invariant equivalences we give new general methods for constructing small non deterministic finite automata nfa from arbitrary ones given an nfa we compute the largest right invariant equivalence on the set of states and then merge the equivalent states to obtain a smaller automaton when applying this method to position automata we get a way to convert regular expressions into nfas which are always smaller than or equal to the position partial derivative and follow automata it can be arbitrarily smaller the construction can be dually made for left invariant equivalences and then the two can be combined for even better results

determinization of weighted finite automata over strong bimonoids we consider weighted finite automata over strong bimonoids where these weight structures can be considered as semirings which might lack distributivity then in general the well known run semantics initial algebra semantics and transition semantics of an automaton are different we prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated submonoids moreover for a given weighted finite automaton we construct the nerode automaton and myhill automaton both being crisp deterministic which are equivalent to the original automaton with respect to the initial algebra semantics respectively the transition semantics we prove necessary and sufficient conditions under which the nerode automaton and the myhill automaton are finite and we provide efficient algorithms for their construction also for a given weighted finite automaton we show sufficient conditions under which a given weighted finite automaton can be determinized preserving its run semantics

brzozowski type determinization for fuzzy automata abstract in this paper we adapt the well known brzozowski determinization method to fuzzy automata this method gives better results than all previously known methods for determinization of fuzzy automata developed by b lohlavek 4 li and pedrycz 20 ignjatovic et al 15 and jancic et al 18 namely as in the case of ordinary nondeterministic automata brzozowski type determinization of a fuzzy automaton results in a minimal crisp deterministic fuzzy automaton equivalent to the starting fuzzy automaton and we show that there are cases when all previous methods result in infinite automata while brzozowski type determinization results in a finite one the paper deals with fuzzy automata over complete residuated lattices but identical results can also be obtained in a more general context for fuzzy automata over lattice ordered monoids and even for weighted automata over commutative semirings

clinical monitoring with fuzzy automata abstract in this paper a framework for an intelligent bedside monitor is presented the monitor derives an abstraction of the current status of a patient by performing fuzzy state transitions on pre processed input continuously supplied by clinical instrumentation so far an implementation called diamon 1 has been used for off line evaluation of data of patients suffering from the adult respiratory distress syndrome ards

mergible states in large nfa quite often trivial problems stated for deterministic finite automata dfa are surprisingly difficult for the non deterministic case nfa in any non minimal dfa for a given regular language we can find two equivalent states which can be merged without changing the accepted language this is not the case for nfa where we can have non minimal automata with no mergible states in this paper we prove a very basic result for nfa that for a given regular language any nfa of size greater than a computable constant must contain mergible states even more we parameterized this constant in order to guarantee groups of an arbitrary number of mergible states

randomized sensor selection in sequential hypothesis testing we consider the problem of sensor selection for time optimal detection of a hypothesis we consider a group of sensors transmitting their observations to a fusion center the fusion center considers the output of only one randomly chosen sensor at the time and performs a sequential hypothesis test we study a sequential multiple hypothesis test with randomized sensor selection strategy we incorporate the random processing times of the sensors to determine the asymptotic performance characteristics of this test for three distinct performance metrics we show that for a generic set of sensors and binary hypothesis the time optimal policy requires the fusion center to consider at most two sensors we also show that for the case of multiple hypothesis the time optimal policy needs at most as many sensors to be observed as the number of underlying hypotheses

nonblocking check in fuzzy discrete event systems based on observation equivalence in this paper we deal with the synthesis about nonblocking check in fuzzy discrete event systems fdess by using abstraction and observation equivalence of fuzzy finite automaton ffa in fdess such a check imposes a great computational challenge because of the complexity incurred by the composition of plants and the supervisors with respect to ideas in modeling control system we present procedure based on ffa abstractions which removes internal transitions of irrelevant transitions allowing the nonblocking check to be performed on relatively small automata

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

further improvements of determinization methods for fuzzy finite automata in this paper we provide further improvements of determinization methods for fuzzy finite automata these methods perform better than all previous determinization methods for fuzzy finite automata developed by b lohlavek 3 li and pedrycz 38 ignjatovic et al 25 and jancic et al 33 in the sense that they produce smaller automata while require the same computation time the only exception is the brzozowski type determinization algorithm developed recently by jancic and iric 34 which produces a minimal crisp deterministic fuzzy automaton but the algorithms created here can also be used within the brzozowski type algorithm and improve its performance

a priori bounds and stability in the retarded nonlinear wave equation the object of this work is to give sufficient conditions to ensure that the zero solution of certain generalizations of u t 4x g u x t h t x flu o 0 xg x oifx o f b 0 and g x 0 2 a g f and h are at least continuous 3 we impose the boundary conditions u t o u t l o so that u t o u t l o 4 although mixed boundary conditions are generally satisfactory among other things it is crucial to have

fuzzy homomorphisms of algebras in this paper we consider fuzzy relations compatible with algebraic operations which are called fuzzy relational morphisms in particular we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations called uniform fuzzy relational morphisms and those which are partially uniform f functions called fuzzy homomorphisms both uniform fuzzy relations and partially uniform f functions were introduced in a recent paper by us uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras we give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms we establish certain relationships between them and fuzzy congruences and we prove homomorphism and isomorphism theorems concerning them we also point to some applications of uniform fuzzy relational morphisms

weak bisimulations for fuzzy automata abstract forward and backward bisimulations have been introduced recently by ciric et al 2012 9 as a means for modeling the equivalence between states of fuzzy automata and approximating the language equivalence as well as for use in the state reduction of fuzzy automata the main aim of the present paper is to introduce two new kinds of bisimulations weak forward and backward bisimulations which provide better approximations of the language equivalence than forward and backward bisimulations and when employed in the state reduction they provide better reductions we give procedures for deciding whether there exist weak forward and backward simulations and bisimulations and for computing the greatest ones whenever they exist using weak bisimulations in conjunction with the concept of a uniform fuzzy relation we determine necessary and sufficient conditions under which two fuzzy automata are weak bisimulation equivalent we also characterize uniform weak backward and forward bisimulations between two fuzzy automata in terms of isomorphisms between their nerode and reverse nerode automata

computing behavior of finite fuzzy machines algorithm and its application to reduction and minimization we define finite fuzzy machines and investigate their behavior algorithm and software are proposed for computing behavior for establishing equivalence and redundancy of states and for solving reduction and minimization problems computational complexity of the algorithm is discussed testing examples are supplied the results are valid for finite max min min max and max product fuzzy machines

sequential detection of markov targets with trajectory estimation the problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered assuming a markov evolution of the system in particular the pair signal observation forms a hidden markov model hmm a sequential procedure is proposed wherein the detection part is a sequential probability ratio test sprt and the estimation part relies upon a maximum a posteriori probability map criterion gated by the detection stage the parameter to be estimated is the trajectory of the state evolution of the system itself a thorough analysis of the asymptotic behavior of the test in this new scenario is given and sufficient conditions for its asymptotic optimality are stated i e for almost sure minimization of the stopping time and for first order minimization of any moment of its distribution an application to radar surveillance problems is also examined

canonization of max min fuzzy automata abstract in this paper we propose a canonization method for fuzzy automata i e a determinization method that is able to return a minimal fuzzy deterministic automaton equivalent to the original fuzzy automaton the canonization method is derived from the well known brzozowski s algorithm for ordinary nondeterministic automata for a given fuzzy automaton a we prove that the construction m r n r a returns a minimal fuzzy deterministic automaton equivalent to a in that construction r represents the reversal of a fuzzy automaton n is the determinization of a fuzzy automaton based on fuzzy accessible subset construction and m is the determinization of a fuzzy automaton via factorization of fuzzy states which also includes a simple reduction of a particular case of proportional fuzzy states the method is accomplished for fuzzy automata with membership values over the godel structure also called max min fuzzy automata these fuzzy automata are always determinizable and have been proved useful in practical applications

the relationship of controllability between classical and fuzzy discrete event systems we have known that the controllability of classical discrete event systems has already been extended into fuzzy discrete event systems in this paper firstly we recall some related definitions and results of the controllability for classical and fuzzy discrete event systems respectively secondly we are concerned with the relationship of the controllability between classical and fuzzy discrete event systems in particular we show that there is an equivalence of the controllability between the two systems to some extent some special proofs are also presented finally we use this equivalence to extend some general controllability properties of classical discrete event systems into fuzzy ones

minimization of fuzzy finite automata abstract in this paper we show that a fuzzy finite automation m 1 has an equivalent minimal fuzzy finite automation m we also show that m can be chsen so that if m 2 is equivalent to m 1 then m is a homomorphic image of m 2

functional differential equations and jensen s inequality on etudie les proprietes de stabilite et de limitation de l equation differentielle fonctionnelle x t f t x t ou x t s x t s pour h s 0 et h une constante positive fixee on utilise la methode de lyapunov directe

equivalent conditions on stability of functional differential equations where x s x t s for h 0 and each 4 e c there is at least one solution x t 4 satisfying 1 on an interval to to a with value at t denoted by x t t 4 moreover if there is an h h and if ix t to d l h for all t 2 to for which x to 4 can be defined then tl co details may be found in 2 7 8 111 for example throughout this paper we work with wedges denoted by wi r r which are continuous strictly increasing and which satisfy wi 0 0 these wedges are related to properties of continuous scalar functionals called liapunov functionals v r x c r which are differentiated along solutions of 1 by the relation

minimization algorithm of fuzzy finite automata in this paper a class of fuzzy finite automata corresponding to the mealy type of ordinary automata is formulated and also two types of statewise equivalence relations are introduced from the equivalence relations a minimal form is defined and a minimization algorithm of the mealy type of fuzzy finite automata is obtained

asymptotic optimality theory for decentralized sequential multihypothesis testing problems the bayesian formulation of sequentially testing m 3 hypotheses is studied in the context of a decentralized sensor network system in such a system local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations asymptotically optimal decentralized sequential tests are developed from a class of two stage tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage it is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most m 1 unambiguous likelihood quantizers ulq we first present in detail our results for the system with a single sensor and binary sensor messages and then extend to more general cases involving any finite alphabet sensor messages multiple sensors or composite hypotheses

nondeterministic automata equivalence bisimulations and uniform relations in this paper we study the equivalence of nondeterministic automata pairing the concept of a bisimulation with the recently introduced concept of a uniform relation in this symbiosis uniform relations serve as equivalence relations which relate states of two possibly different nondeterministic automata and bisimulations ensure compatibility with the transitions initial and terminal states of these automata we define six types of bisimulations but due to the duality we discuss three of them forward backward forward and weak forward bisimulations for each of these three types of bisimulations we provide a procedure which decides whether there is a bisimulation of this type between two automata and when it exists the same procedure computes the greatest one we also show that there is a uniform forward bisimulation between two automata if and only if the factor automata with respect to the greatest forward bisimulation equivalences on these automata are isomorphic we prove a similar theorem for weak forward bisimulations using the concept of a weak forward isomorphism instead of an isomorphism we also give examples that explain the relationships between the considered types of bisimulations

an improved algorithm for determinization of weighted and fuzzy automata for a given weighted finite automaton over a strong bimonoid we construct its reduced nerode automaton which is crisp deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics we show that the reduced nerode automaton is even smaller than the nerode automaton which was previously used in determinization related to this semantics we determine necessary and sufficient conditions under which the reduced nerode automaton is finite and provide an efficient algorithm which computes the reduced nerode automaton whenever it is finite in determinization of weighted finite automata over semirings and fuzzy finite automata over lattice ordered monoids this algorithm gives smaller crisp deterministic automata than any other known determinization algorithm

information structures causality and nonsequential stochastic control i design independent properties in control theory the usual notion of causality that at all times a system s output action only depends on its past and present inputs observations presupposes that all inputs and outputs can be ordered a priori in time in reality many distributed systems those subject to deadlock for instance are not sequential in this sense in a previous paper part i siam j control optim 30 1992 pp 1447 1475 the relationship between a less restrictive notion of causality deadlock freeness and the design independent properties of a potentially nonsequential generic stochastic control problem formulated within the framework of witsenhausen s intrinsic model was explored in the present paper part ii the properties of individual designs are examined in particular a property of a design s information partition that is necessary and sufficient to ensure its deadlock freeness is identified and shown to be sufficient to ensure its possession of an expected reward it is also shown by example that there exist nontrivial deadlock free designs that cannot be associated with any deadlock free information structure the first result provides an intuitive design dependent characterization of the cause effect notion of causality and suggests a framework for the optimization of constrained nonsequential stochastic control problems the second implies that this characterization is finer than existing design independent characterizations including properties c witsenhausen and ci part i

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

optimal transmission rate control policies in a wireless link under partial state information we consider the problem of phy layer transmission rate control for maximum throughput on a wireless link over a finite time horizon for each link state there exists a most advantageous transmission rate for the controller the controller needs to rely on incomplete link state information in the form of positive acknowledgements acks and negative acknowledgements nacks for transmitted packets we cast the problem as a partially observed markov decision processes pomdp we focus on the special case of time invariant or slowly time varying link quality with two states and two control options in that case the optimal control problem is a state estimation one and the optimal strategy is of threshold structure where the thresholds are certain values of the belief of being in one of the two states the policy admits a simple interpretation increase rate when the number of successive acks exceeds a threshold and decrease rate when the number of successive nacks exceeds a threshold

finite l fuzzy machines abstract for finite l fuzzy machines we develop behaviour reduction and minimization theory here l stands for l 0 1 where l is a totally ordered set with universal bounds 0 and 1 and the operations are join and meet the most essential results include investigating behaviour equivalence reduction and minimization problems and their algorithmical decidability

determinization of fuzzy automata by means of the degrees of language inclusion determinization of fuzzy finite automata is understood here as a procedure of their conversion into equivalent crisp deterministic fuzzy automata which can be viewed as being deterministic with possible infinitely many states but with fuzzy sets of terminal states particularly significant determinization methods are those that provide a minimal crisp deterministic fuzzy automaton equivalent to the original fuzzy finite automaton called canonization methods one canonization method for fuzzy finite automata the brzozowski type determinization has been developed recently by jancic and ciric in 10 here we provide another canonization method for a fuzzy finite automaton cal a a sigma delta tau over a complete residuated lattice cal l based on the degrees of inclusion of the right fuzzy languages associated with states of cal a into the left derivatives of the fuzzy language recognized by cal a the proposed procedure terminates in a finite number of steps whenever the membership values taken by delta sigma and tau generate a finite subsemiring of the semiring reduct of cal l this procedure is generally faster than the brzozowski type determinization and if the basic operations in the residuated lattice cal l can be performed in constant time it has the same computational time as all other determinization procedures provided in 8 11 and 12

automata theory based on complete residuated lattice valued logic reduction and minimization automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by qiu recently in this paper we define a kind of mealy type of l vfas mlfas a generalization of l vfas two kinds of statewise equivalence relations are introduced and a minimal form is defined we study the existence of the minimal form of an mlfa then we show that any two states can be distinguished by some word with finite length also a minimization algorithm of the mlfas is presented in addition we obtain a minimization algorithm for l vfas as well finally we define l valued languages l vls and l valued regular languages l vrls recognized by l vfas and provide some properties of l vrls

computation of the greatest right and left invariant fuzzy quasi orders and fuzzy equivalences abstract right invariant fuzzy quasi orders for fuzzy automata are broadly studied in the recent literature as they arise as solutions to particular systems of fuzzy relation equations and inequalities some of their applications include determinization and state reduction procedures as well as simulations and bisimulations for fuzzy automata in this paper we provide a procedure for computing the greatest right invariant fuzzy quasi order for a given fuzzy automaton over a complete residuated lattice the proposed procedure terminates in a finite number of steps whenever the underlying structure of the fuzzy automaton is locally finite when the previous condition is not satisfied we show that the greatest right invariant fuzzy quasi order can be obtained by taking the limit value of the convergent array of fuzzy quasi orders for fuzzy automata over bl algebras on the real unit interval 0 1 analogous procedures for computing the greatest left invariant fuzzy quasi order as well as the greatest right and left invariant fuzzy equivalences for a fuzzy automaton are also presented in addition the faster algorithm for computing the greatest right invariant equivalence on a nondeterministic automaton is also presented

fuzzy finite state automata can be deterministically encoded into recurrent neural networks there has been an increased interest in combining fuzzy systems with neural networks because fuzzy neural systems merge the advantages of both paradigms on the one hand parameters in fuzzy systems have clear physical meanings and rule based and linguistic information can be incorporated into adaptive fuzzy systems in a systematic way on the other hand there exist powerful algorithms for training various neural network models however most of the proposed combined architectures are only able to process static input output relationships they are not able to process temporal input sequences of arbitrary length fuzzy finite state automats ffas can model dynamical processes whose current state depends on the current input and previous states unlike in the case of deterministic finite state automats dfas ffas are not in one particular state rather each state is occupied to some degree defined by a membership function based on previous work on encoding dfas in discrete time second order recurrent neural networks we propose an algorithm that constructs an augmented recurrent neural network that encodes a ffa and recognizes a given fuzzy regular language with arbitrary accuracy we then empirically verify the encoding methodology by correct string recognition of randomly generated ffas in particular we examine how the networks performance varies as a function of synaptic weight strengths

asymptotic efficiency of a sequential multihypothesis test a sequential multihypothesis test known as the m ary sequential probability ratio test msprt is generalized to account for nonuniform decision costs bounds on error probabilities and asymptotic expressions for the stopping time and error probabilities are given a key result of this correspondence is a proof that the generalized msprt is asymptotically efficient

equivalence in automata theory based on complete residuated lattice valued logic automata theory based on complete residuated lattice valued logic called l valued finite automata abbr l vfas was introduced by the second author in 2001 in this paper we deal with the problems of equivalence between l valued sequential machines abbr l vsms and l vfas we define l vsms and particularly present a method for deciding the equivalence between l vsms as well an algorithm procedure for deciding the equivalence between l vsms is constructed we analyze the complexity and efficiency of the algorithm procedure and obtain the relative results to l vfas moreover the definitions of l valued languages abbr l vls and l valued regular languages abbr l vrls recognized by l vfas are given and some related properties are also discussed we show an equivalent relation between l vrls and conventional regular languages by using l valued pumping lemma we get a necessary and sufficient condition for an l vl to be nonconstant

a stochastic sensor selection scheme for sequential hypothesis testing with multiple sensors we study the problem of binary sequential hypothesis testing using multiple sensors with associated observation costs an off line randomized sensor selection strategy in which a sensor is chosen at every time step with a given probability is considered the objective of this work is to find a sequential detection rule and a sensor selection probability vector such that the expected total observation cost is minimized subject to constraints on reliability and sensor usage first the sequential probability ratio test is shown to be the optimal sequential detection rule in this framework as well efficient algorithms for obtaining the optimal sensor selection probability vector are then derived in particular a special class of problems in which the algorithm has complexity that is linear in the number of sensors is identified an upper bound for the average sensor usage to estimate the error incurred due to wald s approximations is also presented this bound can be used to set a safety margin for guaranteed satisfaction of the constraints on the sensor usage

controlled sensing for multihypothesis testing the problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings in the fixed sample size setting for binary hypothesis testing the optimal exponent for the maximal error probability corresponds to the maximum chernoff information over the choice of controls and a pure stationary open loop control policy is asymptotically optimal within the larger class of all causal control policies for multihypothesis testing in the fixed sample size setting lower and upper bounds on the optimal error exponent are derived it is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open loop control policy in the sequential setting a test based on earlier work by chernoff for binary hypothesis testing is shown to be first order asymptotically optimal for multihypothesis testing in a strong sense using the notion of decision making risk in place of the overall probability of error another test is also designed to meet hard risk constrains while retaining asymptotic optimality the role of past information and randomization in designing optimal control policies is discussed

automata theory based on complete residuated lattice valued logic pushdown automata automata theory based on complete residuated lattice valued logic called l valued automata has been proposed by qiu automata theory based on complete residuated latticed valued logic sci china ser f 44 6 2001 419 429 automata theory based on complete residuated latticed valued logic ii sci china ser f 45 6 2002 442 452 in this paper we discuss some properties of l valued context free grammars languages and pushdown automata we show that for such grammars chomsky and greibach normal forms can be equivalently constructed and we also prove that the languages accepted by final states and by empty stack in l valued pushdown automata are equivalent in particular we prove the equivalence between l valued context free grammars and l valued pushdown automata

minimal nfa problems are hard finite automata fa s are of fundamental importance in theory and in applications the following basic minimization problem is studied given a dfa deterministic fa find a minimum equivalent no

formal power series and regular operations on fuzzy languages in this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet and representation of fuzzy languages by these formal power series this representation generalizes the well known representation of fuzzy languages by their cut and kernel languages we show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages we use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series

the decentralized quickest detection problem two detectors making independent observations must decide when a markov chain jumps from state 0 to state 1 the decisions are coupled through a common cost function it is shown that the optimal decision is characterized by thresholds as in the decoupled case however the thresholds are time varying and their computation requires the solution of two coupled sets of dynamic programming equations a comparison to the decoupled case shows the structure of the coupling

dynamic sequential team multi hypothesis testing under uniformly distributed nonstationary observations abstract we consider a dynamic team of communicating decision makers performing bayesian sequential multi hypothesis testing under nonstationary observations a simple decision rule is shown to be member by member optimal if the observations are uniformly distributed if the observation costs are defined to reflect the quality of observations and if vague terminal decisions are allowed without additional penalty the vague terminal decisions can be made clear by performing a finite number of member by member optimal sequential decisions successively

multihypothesis sequential probability ratio tests ii accurate asymptotic expansions for the expected sample size for pt i see ibid vol 45 p 2448 61 1999 we proved in pt i that two specific constructions of multihypothesis sequential tests which we refer to as multihypothesis sequential probability ratio tests msprts are asymptotically optimal as the decision risks or error probabilities go to zero the msprts asymptotically minimize not only the expected sample size but also any positive moment of the stopping time distribution under very general statistical models for the observations in this paper based on nonlinear renewal theory we find accurate asymptotic approximations up to a vanishing term for the expected sample size that take into account the overshoot over the boundaries of decision statistics the approximations are derived for the scenario where the hypotheses are simple the observations are independent and identically distributed i i d according to one of the underlying distributions and the decision risks go to zero simulation results for practical examples show that these approximations are fairly accurate not only for large but also for moderate sample sizes the asymptotic results given here complete the analysis initiated by baum and veeravalli 1994 where first order asymptotics were obtained for the expected sample size under a specific restriction on the kullback leibler distances between the hypotheses

quickest linear search over correlated sequences consider a set of random sequences each consisting of independent and identically distributed random variables drawn from one of the two known distributions f 0 and f 1 the underlying distributions of different sequences are correlated induced by an inherent physical coupling in the mechanisms generating these sequences the objective is to design the quickest data adaptive and sequential search procedure for identifying one sequence generated according to f 1 the optimal design involves striking a balance between the average delay in reaching a decision and the rate of false alarms as two opposing figures of merit optimal and asymptotically optimal decision rules are derived which can take radically different forms depending on the correlation structure performance and sampling complexity analyses are provided to delineate the tradeoff between decision delay and quality the generalization to parallel sampling in which multiple sequences are sampled at the same time is also investigated

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

quickest change detection of a markov process across a sensor array recent attention in quickest change detection in the multisensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption in this work a more general scenario is considered where the change propagates across the sensors and its propagation can be modeled as a markov process a centralized bayesian version of this problem is considered with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process the problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework insights into the structure of the optimal stopping rule are presented in the limiting case of rare disruptions it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened under a certain condition on the kullback leibler k l divergence between the post and the pre change densities it is established that the threshold test is asymptotically optimal in the vanishing false alarm probability regime it is shown via numerical studies that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single sensor test or a test that incorrectly assumes that the change propagates instantaneously

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

dynamic decentralized sequential detection under uniformly distributed observations decentralized sequential detection problems with communicating detectors are solved under the assumptions that the observations are independent and uniformly distributed and that decision errors are uniformly penalized for the cases of one step delayed sequential and nonsequential signaling explicit decision rules are proposed and exact conditions for their member by member optimality are derived these decision rules approximate high performance threshold rules with very strict thresholds when decision errors are heavily penalized

the basal ganglia optimize decision making over general perceptual hypotheses the basal ganglia are a subcortical group of interconnected nuclei involved in mediating action selection within cortex a recent proposal is that this selection leads to optimal decision making over multiple alternatives because the basal ganglia anatomy maps onto a network implementation of an optimal statistical method for hypothesis testing assuming that cortical activity encodes evidence for constrained gaussian distributed alternatives this letter demonstrates that this model of the basal ganglia extends naturally to encompass general bayesian sequential analysis over arbitrary probability distributions which raises the proposal to a practically realizable theory over generic perceptual hypotheses we also show that the evidence in this model can represent either log likelihoods log likelihood ratios or log odds all leading proposals for the cortical processing of sensory data for these reasons we claim that the basal ganglia optimize decision making over general perceptual hypotheses represented in cortex the relation of this theory to cortical encoding cortico basal ganglia anatomy and reinforcement learning is discussed

bisimulations for fuzzy automata bisimulations have been widely used in many areas of computer science to model equivalence between various systems and to reduce the number of states of these systems whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata we prove that a uniform fuzzy relation between fuzzy automata a and b is a forward bisimulation if and only if its kernel and co kernel are forward bisimulation fuzzy equivalence relations on a and b and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations as a consequence we get that fuzzy automata a and b are ufb equivalent i e there is a uniform forward bisimulation between them if and only if there is a special isomorphism between the factor fuzzy automata of a and b with respect to their greatest forward bisimulation fuzzy equivalence relations this result reduces the problem of testing ufb equivalence to the problem of testing isomorphism of fuzzy automata which is closely related to the well known graph isomorphism problem we prove some similar results for backward forward bisimulations and we point to fundamental differences because of the duality with the studied concepts backward and forward backward bisimulations are not considered separately finally we give a comprehensive overview of various concepts on deterministic nondeterministic fuzzy and weighted automata which are related to bisimulations

myhill nerode type theory for fuzzy languages and automata the myhill nerode theory is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right congruences and congruences on a free monoid in this paper we develop a general myhill nerode type theory for fuzzy languages with membership values in an arbitrary set with two distinguished elements 0 and 1 which are needed to take crisp languages in consideration we establish connections between extensionality of fuzzy languages w r t right congruences and congruences on a free monoid and recognition of fuzzy languages by deterministic automata and monoids and we prove the myhill nerode type theorem for fuzzy languages we also prove that each fuzzy language possess a minimal deterministic automaton recognizing it we give a construction of this automaton using the concept of a derivative automaton of a fuzzy language and we give a method for minimization of deterministic fuzzy recognizers in the second part of the paper we introduce and study nerode s and myhill s automata assigned to a fuzzy automaton with membership values in a complete residuated lattice the obtained results establish nice relationships between fuzzy languages fuzzy automata and deterministic automata

congruences and homomorphisms of fuzzy automata concepts of congruences and homomorphisms of fuzzy automata are defined and homomorphism theorem is proved lattices of congruences of fuzzy automata are described and an algorithm for computing the greatest congruence contained in an equivalence of a fuzzy automaton is presented it is used for minimization procedures for both fuzzy automata with and without outputs connections with previously known minimization algorithms are discussed

minimization of states in automata theory based on finite lattice ordered monoids in this study we consider a concept of complete l fuzzy matrix define complete lattice valued finite automata clfas and study their properties the definitions of statewise equivalence relations and automata equivalence relations of a clfa are given two algorithms are aimed at the minimization of states of a clfa

a sequential procedure for multihypothesis testing the sequential testing of more than two hypotheses has important applications in direct sequence spread spectrum signal acquisition multiple resolution element radar and other areas a useful sequential test which we term the msprt is studied in this paper the test is shown to be a generalization of the sequential probability ratio test under bayesian assumptions it is argued that the msprt approximates the much more complicated optimal test when error probabilities are small and expected stopping times are large bounds on error probabilities are derived and asymptotic expressions for the stopping time and error probabilities are given a design procedure is presented for determining the parameters of the msprt two examples involving gaussian densities are included and comparisons are made between simulation results and asymptotic expressions comparisons with bayesian fixed sample size tests are also made and it is found that the msprt requires two to three times fewer samples on average

on quotient machines of a fuzzy automaton and the minimal machine in this paper the concept of substitution property sp partition for a finite fuzzy automaton is formulated and the quotient automaton with respect to an sp partition is defined the state minimization problem for such automata by using the method of quotient machines is solved

computation of the greatest simulations and bisimulations between fuzzy automata recently two types of simulations forward and backward simulations and four types of bisimulations forward backward forward backward and backward forward bisimulations between fuzzy automata have been introduced if there is at least one simulation bisimulation of some of these types between the given fuzzy automata it has been proved that there is the greatest simulation bisimulation of this kind in the present paper for any of the above mentioned types of simulations bisimulations we provide an efficient algorithm for deciding whether there is a simulation bisimulation of this type between the given fuzzy automata and for computing the greatest one whenever it exists the algorithms are based on the method developed in ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 which comes down to the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations

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

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

determinism and fuzzy automata the concept of a fuzzy automaton as studied in the literature is a direct generalization of the classical concept of a non deterministic automaton in this paper we consider the question of whether there is a deterministic counterpart to the notion of a fuzzy automaton we propose a definition of deterministic fuzzy automata and show that they are equally powerful as fuzzy automata compared to the classical notion of a deterministic automaton the deterministic fuzzy automaton defined in our paper differs essentially only in that the final states form a fuzzy set moreover we show that deterministic fuzzy automata are equally powerful as nested systems of deterministic automata

multihypothesis sequential probability ratio tests i asymptotic optimality the problem of sequential testing of multiple hypotheses is considered and two candidate sequential test procedures are studied both tests are multihypothesis versions of the binary sequential probability ratio test sprt and are referred to as msprts the first test is motivated by bayesian optimality arguments while the second corresponds to a generalized likelihood ratio test it is shown that both msprts are asymptotically optimal relative not only to the expected sample size but also to any positive moment of the stopping time distribution when the error probabilities or more generally risks associated with incorrect decisions are small the results are first derived for the discrete time case of independent and identically distributed i i d observations and simple hypotheses they are then extended to general possibly continuous time statistical models that may include correlated and nonhomogeneous observation processes it also demonstrated that the results can be extended to hypothesis testing problems with nuisance parameters where the composite hypotheses due to nuisance parameters can be reduced to simple ones by using the principle of invariance these results provide a complete generalization of the results given by veeravalli and baum see ibid vol 41 p 1994 97 1995 where it was shown that the quasi bayesian msprt is asymptotically efficient with respect to the expected sample size for i i d observations

analysis and control of fuzzy discrete event systems using bisimulation equivalence in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently in this paper we deal with the analysis and control of fuzzy discrete event systems by using bisimulation equivalence in practice we design a supervisor such that the controlled system is bisimilar to the specification also a model theorem showing that a supervisor exists over a certain finite fuzzy state space is obtained furthermore the notion of fuzzy state controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor

optimal decision making on the basis of evidence represented in spike trains experimental data indicate that perceptual decision making involves integration of sensory evidence in certain cortical areas theoretical studies have proposed that the computation in neural decision circuits approximates statistically optimal decision procedures e g sequential probability ratio test that maximize the reward rate in sequential choice tasks however these previous studies assumed that the sensory evidence was represented by continuous values from gaussian distributions with the same variance across alternatives in this article we make a more realistic assumption that sensory evidence is represented in spike trains described by the poisson processes which naturally satisfy the mean variance relationship observed in sensory neurons we show that for such a representation the neural circuits involving cortical integrators and basal ganglia can approximate the optimal decision procedures for two and multiple alternative choice tasks

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development

pumping lemma in automata theory based on complete residuated lattice valued logic a note abstract automata theory based on complete residuated lattice valued logic called l valued automata was established in qiu automata theory based on completed residuated lattice valued logic i science in china f 44 6 2001 419 429 qiu automata theory based on completed residuated lattice valued logic ii science in china f 45 6 2002 442 452 in this note we deal with the pumping lemma in l valued automata theory after recalling some preliminaries related to complete residuated lattices and l valued automata we define a number of l valued accepting predicates in particular the pumping lemma for l valued automata theory is set up we show that if those related l valued predicates are defined by using connective instead of then the pumping lemma may not hold again furthermore we investigate the l valued automata with e transitions and present the equivalence between the l valued automata without e transitions and those with e transitions finally a number of related questions is addressed