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

fuzzy equivalence relations and their equivalence classes in this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice we give certain characterizations of fuzzy semi partitions and fuzzy partitions over a complete residuated lattice as well as over a linearly ordered complete heyting algebra in the latter case for a fuzzy equivalence relation over a linearly ordered complete heyting algebra we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it most of the presented results are new but some of them are generalizations of known results given in a way which simplifies and clarifies them

a categorical approach to minimal realization for a fuzzy language abstract in this study we provide a general theory of minimal realization for a given fuzzy language in a category theory setting we introduce categorical characterizations of a run map reachability map and observability map for a crisp deterministic fuzzy automaton finally we show that all minimal realizations for a given fuzzy language are isomorphic to the nerode realization for the same case

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

the accuracy of cell vertex finite volume methods on quadrilateral meshes for linear first order hyperbolic equations in two dimensions we restate the cell vertex finite volume scheme as a finite element method on structured meshes consisting of distorted quadrilaterals the global error is shown to be of second order in various mesh dependent norms provided that the quadrilaterals are close to parallelograms in the sense that the distance between the midpoints of the diagonals is of the same order as the measure of the guadrilateral on tensor product nonuniform meshes the cell vertex scheme coincides with the familiar box scheme in this case second order accuracy is shown without any additional assumption on the regularity of the mesh which explains the insensitivity of the cell vertex scheme to mesh stretching in the coordinate directions observed in practice 17 refs

the locally stabilized finite volume method for incompressible flow a locally stabilized finite volume method for the two dimensional incompressible flow governed by stationary stokes and navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem the optimal l 2 error estimate of u h p h determined by stokes equations is also deduced some numerical examples are provided to check the efficiency of this method

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

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

on domain decomposition algorithms for covolume methods for elliptic problems in this paper some new two level additive schwarz domain decomposition methods are constructed and used as preconditioners for gmres for the nonsymmetric systems arising from the covolume methods for elliptic problems without any restriction on the coarse mesh size the convergence of the preconditioned gmres is obtained for both circumcentric and barycentric covolume methods with inexact solvers for subproblems the rates of convergence are shown to be independent of the number of subregions and these methods are optimal for generous overlap

the finite volume element method for diffusion equations on general triangulations this paper develops discretization error estimates for the finite volume element method on general triangulations of a polygonal domain in mathcal r 2 using a special type of control volume the theory applies to diffusion equations of the form begin gathered nabla a nabla u f quad text in omega hfill u 0 quad text on partial omega hfill end gathered under fairly general conditions the theory establishes o h estimates of the error in a discrete mathcal h 1 seminorm under an additional assumption concerning local uniformity of the triangulation the estimate is improved to o h 2

on the existence and construction of t transitive closures in this paper it is shown that any fuzzy relation r on an arbitrary universe x has a t transitive closure the triangular norm t involved is not subject to any conditions this existential result can be turned into an explicit expression in the case of a left continuous triangular norm t furthermore this continuity restriction vanishes in the case of a finite universe x in that case the explicit expression can also be operationalized

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

the method of variably scaled radial kernels for solving two dimensional magnetohydrodynamic mhd equations using two discretizations the crank nicolson scheme and the method of lines mol abstract mhd equations have many applications in physics and engineering the model is coupled equations in velocity and magnetic field and has a parameter namely hartmann the value of hartmann number plays an important role in the equations when this parameter increases using different meshless methods makes the oscillations in velocity near the boundary layers in the region of the problem in the present paper a numerical meshless method based on radial basis functions rbfs is provided to solve mhd equations for approximating the spatial variable a new approach which is introduced by bozzini et al 2015 is applied the method will be used here is based on the interpolation with variably scaled kernels the methodology of the new technique is defining the scale function c on the domain r d then the interpolation problem from the data locations x j r d transforms to the new interpolation problem in the data locations x j c x j r d 1 bozzini et al 2015 the radial kernels used in the current work are multiquadrics mq inverse quadric iq and wendland s function of course the latter one is based on compactly supported functions to discretize the time variable two techniques are applied one of them is the crank nicolson scheme and another one is based on mol the numerical simulations have been carried out on the square and elliptical ducts and the obtained numerical results show the ability of the new method for solving this problem also in appendix we provide a computational algorithm for implementing the new technique in matlab software

a stabilized multi level method for non singular finite volume solutions of the stationary 3d navier stokes equations this paper proposes and analyzes a stabilized multi level finite volume method fvm for solving the stationary 3d navier stokes equations by using the lowest equal order finite element pair without relying on any solution uniqueness condition this multi level stabilized fvm consists of solving the nonlinear problem on the coarsest mesh and then performing one newton correction step on each subsequent mesh thus only solving a large linear system an optimal convergence rate for the finite volume approximations of nonsingular solutions is first obtained with the same order as that for the usual finite element solution by using a relationship between the stabilized fvm and a stabilized finite element method then the multi level finite volume approximate solution is shown to have a convergence rate of the same order as that of the stabilized finite volume solution of the stationary navier stokes equations on a fine mesh with an appropriate choice of the mesh size h j h j 1 2 j 1 ldots j finally numerical results presented validate our theoretical findings

the finite volume method based on stabilized finite element for the stationary navier stokes problem a finite volume method based on stabilized finite element for the two dimensional stationary navier stokes equations is investigated in this work a macroelement condition is introduced for constructing the local stabilized formulation for the problem we obtain the well posedness of the fvm based on stabilized finite element for the stationary navier stokes equations moreover for quadrilateral and triangular partition the optimal h 1 error estimate of the finite volume solution u h and l 2 error estimate for p h are introduced finally we provide a numerical example to confirm the efficiency of the fvm

variational multiscale a posteriori error estimation for multi dimensional transport problems this paper presents an explicit a posteriori error estimator for the multi dimensional transport equation based on an approximation to the variational multiscale theory the technique is adequate for methods with a local error distribution such as stabilized methods yielding efficiencies close to one for both the hyperbolic and diffusive limit regarding the hyperbolic limit previous work is extended to multi dimensions adequate norms are proposed for the computation of the error and proper error intrinsic time scales are calculated for the bilinear quadrilateral and the linear triangle furthermore the model considers the element interface error along the element edges enabling the error prediction in the diffusive limit the success of the method can be explained by the fact that in stabilized methods the element local problem captures most of the error and the proposed error intrinsic time scales are an approximation to the solution of the dual problem the proposed technology which can be implemented straightforwardly in existing codes is extremely economical because it is a simple explicit postprocessing

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

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

algebraic properties of la languages in this study we introduce the concepts of l valued regular substitution la substitution deterministic l valued regular substitution dla substitution l valued fuzzy homomorphism and its inverse images homomorphism and its inverse images for a lattice ordered monoid l we also study the properties of la languages and dla languages under the above mentioned algebraic operations the algebraic characterization of the l valued regular language is given

optimal biquadratic finite volume element methods on quadrilateral meshes in this paper an optimal biquadratic finite volume element scheme is established and analyzed for elliptic equations on quadrilateral meshes it is proved that the new scheme has optimal o h 2 convergence rate in h 1 norm and o h 3 convergence rate in l 2 norm with the assumption that each element is an h 2 parallelogram

the mortar finite volume method with the crouzeix raviart element for elliptic problems abstract we construct and analyse a mortar finite volume method for the discretization for selfadjoint elliptic boundary value problems in r 2 this method is based on the mortar crouzeix raviart non conforming finite element spaces we prove the optimal order h 1 norm and l 2 norm error estimates between the exact solution and the mortar finite volume approximation of the elliptic problems

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

derivatives of rational expressions with multiplicity this paper addresses the problem of turning a rational i e regular expression into a finite automaton we formalize and generalize the idea of partial derivatives introduced in 1995 by antimirov in order to obtain a construction of an automaton with multiplicity from a rational expression describing a formal power series with coefficients in a semiring we first define precisely what is such a rational expression with multiplicity and which hypothesis should be put on the semiring of coefficients in order to keep the usual identities we then define the derivative of such a rational expression as a linear combination of expressions called derived terms and we show that all derivatives of a given expression are generated by a finite set of derived terms that yields a finite automaton with multiplicity whose behaviour is the series denoted by the expression we also prove that this automaton is a quotient of the standard or glushkov automaton of the expression finally we propose and discuss some possible modifications to our definition of derivation

active classification for pomdps a kalman like state estimator author s zois ds levorato m mitra u abstract 1991 2012 ieee the problem of state tracking with active observation control is considered for a system modeled by a discrete time finite state markov chain observed through conditionally gaussian measurement vectors the measurement model statistics are shaped by the underlying state and an exogenous control input which influence the observations quality exploiting an innovations approach an approximate minimum mean squared error mmse filter is derived to estimate the markov chain system state to optimize the control strategy the associated mean squared error is used as an optimization criterion in a partially observable markov decision process formulation a stochastic dynamic programming algorithm is proposed to solve for the optimal solution to enhance the quality of system state estimates approximate mmse smoothing estimators are also derived finally the performance of the proposed framework is illustrated on the problem of physical activity detection in wireless body sensing networks the power of the proposed framework lies within its ability to accommodate a broad spectrum of active classification applications including sensor management for object classification and tracking estimation of sparse signals and radar scheduling

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

on the finite volume element method the finite volume element method fve is a discretization technique for partial differential equations it uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations then restricts the admissible functions to a finite element space to discretize the solution this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with fve based on triangulations with linear finite element spaces and a general type of control volume we establisho h estimates of the error in a discreteh 1 semi norm under an additional assumption of local uniformity of the triangulation the estimate is improved too h 2 results on the effects of numerical integration are also included

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

a finite volume method based on the crouzeix raviart element for elliptic pde s in two dimensions we introduce and analyse a finite volume method for the discretization of elliptic boundary value problems in mathbb r 2 the method is based on nonuniform triangulations with piecewise linear nonconforming spaces we prove optimal order error estimates in the l 2 norm and a mesh dependent h 1 norm

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

pumping lemma in context free grammar theory based on complete residuated lattice valued logic residuated lattices are important algebras and have close links with various important algebras automata theory based on complete residuated lattice valued logic called l valued automata has been established by the second author in 2001 and 2002 as a continuation of automata theory based on complete residuated lattice valued logic in this paper we mainly deal with the problem concerning pumping lemma in l valued context free languages l cfls as a generalization of the notion in the theory of formal grammars the definition of l valued context free grammars l cfgs is introduced we also discuss a special case of l cfgs l right or left linear grammars and show the equivalence between l linear grammars and l regular grammars this result shows that we generalize the pumping lemma in l valued regular languages l rls more recently established by the second author

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

the relationships among several types of fuzzy automata we discuss the relationships among several types of fuzzy automata in which all fuzzy sets are defined by membership functions whose codomains are a lattice ordered monoid l these automata include nondeterministic l valued finite automata with l move nondeterministic l valued finite automata deterministic l valued finite automata and l valued finite state automata we consider all that come with fuzzy initial states and fuzzy final states or with crisp initial states or crisp final states some comparative results concerning the power of fuzzy automata used in the existing literature to recognize fuzzy languages are given systematically

asymptotically optimal nonlinear mmse multiuser detection based on multivariate gaussian approximation in this paper a class of nonlinear minimum mean squared error multiuser detectors is derived based on a multivariate gaussian approximation of the multiple access interference for large systems this approach leads to expressions identical to those describing the probabilistic data association pda detector thus providing an alternative analytical justification for this structure a simplification to the pda detector based on approximating the covariance matrix of the multivariate gaussian distribution is suggested resulting in a soft interference cancellation scheme corresponding multiuser soft input soft output detectors delivering extrinsic log likelihood ratios are derived for application in iterative multiuser decoders finally a large system performance analysis is conducted for the simplified pda showing that the bit error rate ber performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector methods from statistical neurodynamics are shown to provide a closely related alternative large system prediction numerical results demonstrate that for large systems the ber is accurately predicted by the analysis and found to be close to optimal performance

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

a discontinuous finite volume method for a coupled fracture model abstract in this paper we present a discontinuous finite volume method for a hybrid dimensional coupled fracture model on triangular meshes in matrix and fracture the pressure is approximated by the discontinuous and continuous piecewise linear elements and in order to retain local conservation property the velocity is sought in the discontinuous lowest order raviart thomas element space and piecewise linear element space the proposed numerical scheme is only associated with the pressure so we avoid solving an indefinite saddle point problem in addition the discontinuous method eliminates the continuity of approximate functions across the interelement boundary so it has the advantage of high localizability and easy handling of complicated geometries optimal order error estimates for the pressure and velocity are proved and numerical experiments are carried out to confirm our theoretical analysis

a q1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh abstract in this paper we study a q 1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh it is known that the coercivity is the basement for some other theoretical results stability h 1 and l 2 error estimates etc and the existing results were mainly obtained on h 1 parallelogram meshes with scalar diffusion coefficients for the cases of full diffusion tensors and arbitrary convex quadrilateral meshes we obtain a necessary and sufficient condition for the positive definiteness of the cell matrix related to the cell bilinear form based on this result a sufficient condition is suggested to guarantee the coercivity of the scheme more interesting is that this sufficient condition covers the traditional h 1 parallelogram mesh assumption and has an explicit expression by which one can easily judge on any diffusion tensor and any mesh with arbitrary mesh size h 0 moreover an h 1 error estimate is obtained without the h 1 parallelogram assumption and some numerical results are also provided to validate the theoretical results

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

a new family of soft output adaptive receivers exploiting nonlinear mmse estimates for tdma based wireless links decision directed adaptive receivers suffer performance degradation on time varying and intersymbol interference impaired links because of two major problems the use of predicted channel estimates due to the unavoidable decision delay of any detector and the unreliability of hard decisions used for channel estimation and tracking it is shown here that combining a recursive nonlinear symbol estimator with a channel estimator with a low prediction order may alleviate this performance degradation in particular it is here proposed to employ the nonlinear minimum mean square error nl mmse filtered and fixed lag smoothed estimates of the transmitted symbols in place of the usual hard decisions for channel estimation and tracking it is also shown that these nl mmse estimates can be recursively computed on the basis of a linear transformation of the vector of the a posteriori probabilities apps of the states of the channel this approach allows the prediction order of the channel estimates to be limited and at the same time limits the performance degradation due to erroneous hard decisions another result presented here is that the use of nl mmse estimates in place of hard decisions is not based on mere intuition only but is a straightforward consequence of the statement of the problem of mmse channel estimation when the overly optimistic assumption of correct decisions is dropped on the basis of this novel approach a new family of soft output adaptive receivers is presented for time division multiple access based radio communications the proposed family of adaptive receivers is based on an app computer and exploits the apps for both channel estimation and detection the versatility of the apps ensures that the architecture of the proposed receiver is flexible so that several estimators and detectors can be embedded in it

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

fuzzy language on free monoid in this paper we shall introduce the notion of fuzzy regular language adjunctive language and dense language and discuss their algebraic character and algebraic properties

on factorized l fuzzy automaton and its l fuzzy topological characterization abstract this paper is towards the study of l fuzzy automata via theory of factorizations where l is a complete residuated lattice we study the concept of factorization of l fuzzy sets and factorization of collection of l fuzzy sets such factorizations are used i to study the concept of minimal l fuzzy automaton and ii to introduce l fuzzy topologies for the study of concepts associated with an l fuzzy automaton specifically we introduce the notion of factorized l fuzzy automaton corresponding to a given l fuzzy automaton and study the minimality of such automaton further we associate l fuzzy topologies for factorized l fuzzy automaton and use these to characterize some algebraic concepts

finite volume methods for convection diffusion problems derivation stability and error analysis in both discrete h 1 and l 2 norms for cell centered finite volume approximations of convection diffusion problems are presented various upwind strategies are investigated the theoretical results are illustrated by numerical examples

variational multiscale a posteriori error estimation for systems the euler and navier stokes equations this paper extends explicit a posteriori error estimators based on the variational multiscale theory to systems of equations in particular the emphasis is placed on flow problems the euler and navier stokes equations three error estimators are proposed the standard the naive and the upper bound numerical results show that with a very economical algorithm the attained global and local efficiencies for the naive approach are reasonably close to unity whereas the standard and upper bound approaches give respectively approximate lower and higher error estimates

finite automata theory with membership values in lattices in this paper we study finite automata with membership values in a lattice which are called lattice valued finite automata the extended subset construction of lattice valued finite automata is introduced then the equivalences between lattice valued finite automata lattice valued deterministic finite automata and lattice valued finite automata with e moves are proved a simple characterization of lattice valued languages recognized by lattice valued finite automata is given then it is proved that the kleene theorem holds in the frame of lattice setting a minimization algorithm of lattice valued deterministic finite automata is presented in particular the role of the distributive law for the truth valued domain of finite automata is analyzed the distributive law is not necessary to many constructions of lattice valued finite automata but it indeed provides some convenience in simply processing lattice valued finite automata

finite volume schemes for hamilton jacobi equations we introduce two classes of monotone finite volume schemes for hamilton jacobi equations the corresponding approximating functions are piecewise linear defined on a mesh consisting of triangles the schemes are shown to converge to the viscosity solution of the hamilton jacobi equation

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

on the accuracy of the finite volume element method based on piecewise linear polynomials we present a general error estimation framework for a finite volume element fve method based on linear polynomials for solving second order elliptic boundary value problems this framework treats the fve method as a perturbation of the galerkin finite element method and reveals that regularities in both the exact solution and the source term can affect the accuracy of fve methods in particular the error estimates and counterexamples in this paper will confirm that the fve method cannot have the standard o h2 convergence rate in the l2 norm when the source term has the minimum regularity only being in l2 even if the exact solution is in h2

uniform convergence of finite volume element method with crouzeix raviart element for non self adjoint and indefinite elliptic problems in this paper we consider the finite volume element method based on the crouzeix raviart element and prove the existence uniqueness and uniform convergence of the finite volume element approximations for the non self adjoint and indefinite elliptic problems under minimal elliptic regularity assumption

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

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

on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations in this paper we study systems of fuzzy relation inequalities and equations of the form u v i v i u i i where u is an unknown and v i i i are given fuzzy relations the dual systems v i u u v i i i their conjunctions the systems of the form u v i v i u i i and certain special types of these systems we call them weakly linear systems for each weakly linear system with a complete residuated lattice as the underlying structure of truth values we prove the existence of the greatest solution and we provide an algorithm for computing the greatest solution which works whenever the underlying complete residuated lattice is locally finite otherwise we determine some sufficient conditions under which the algorithm works the algorithm is iterative and each its single step can be viewed as solving of a particular linear system weakly linear systems emerged from the fuzzy automata theory but we show that they also have important applications in other fields e g in the concurrency theory and social network analysis

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

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

additive average schwarz method for a crouzeix raviart finite volume element discretization of elliptic problems with heterogeneous coefficients in this paper we introduce an additive schwarz method for a crouzeix raviart finite volume element discretization of a second order elliptic problem with discontinuous coefficients where the discontinuities are both inside the subdomains and across and along the subdomain boundaries we show that depending on the distribution of the coefficient in the model problem the parameters describing the generalized minimal residual method gmres convergence rate of the proposed method depend linearly on the mesh parameters inlineequation not available see fulltext also under certain restrictions on the distribution of the coefficient the convergence of the gmres method is independent of jumps in the coefficient

minimization of lattice finite automata and its application to the decomposition of lattice languages in this paper we study the minimization of lattice valued finite automata with membership values in a distributive lattice and its relationships to the decomposition of lattice valued regular languages first we establish the equivalence of nondeterministic lattice finite automata la and deterministic lattice finite automata dla furthermore we provide some characterization of lattice valued regular languages and regular operations on family of lattice valued regular languages in the sequel we introduce some notions that help clarify the concept of minimal dlas and present an effective algorithm to obtain a minimal dla from a given la using the construction of minimal dla we introduce some simple classes of lattice valued regular languages such as l unitary and l prefix ones we demonstrate that any lattice valued regular language can be decomposed as disjoint joins of such kinds of simple languages

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

weighted finite automata over strong bimonoids we investigate weighted finite automata over strings and strong bimonoids such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold we define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions moreover we show that in this case the given weighted automata can be determinized

mortar upwind finite volume element method for convection diffusion problems abstract in this paper we consider the mortar upwind finite volume element method with local linear conforming finite element space for the convection diffusion problems and show that the mortar upwind finite volume element approximations derived are convergent with optimal order in the h 1 norm

on the construction and analysis of high order locally conservative finite volume type methods for one dimensional elliptic problems locally conservative finite volume type methods based on continuous piecewise polynomial functions of degree r ge 2 are introduced and analyzed in the context of indefinite elliptic problems in one space dimension the new methods extend and generalize the classical finite volume method based on piecewise linear functions we derive a priori error estimates in the l2 h1 and l infty norm and discuss superconvergence effects for the error and its derivative explicit residual based a posteriori error bounds in the l2 and energy norm are also derived we compute the experimental order of convergence and show the results of an adaptive algorithm based on the a posteriori error estimates