automorphisms of real four dimensional lie algebras and the invariant characterization of homogeneous 4 spaces the automorphisms of all four dimensional real lie algebras are presented in a comprehensive way their action on the space of 4 4 real symmetric and positive definite matrices defines equivalence classes which are used for the invariant characterization of the four dimensional homogeneous spaces which possess an invariant basis

a new invariant for finite dimensional leibniz lie algebras abstract for an n dimensional leibniz lie algebra h over a field k we introduce a new invariant a h called the universal algebra of h as a quotient of the polynomial algebra k x i j i j 1 n through an ideal generated by n 3 polynomials we prove that a h admits a unique bialgebra structure which makes it an initial object among all commutative bialgebras coacting on h the new object a h is the key tool in answering two open problems in lie algebra theory first we prove that the automorphism group aut l b z h of h is isomorphic to the group u g a h o of all invertible group like elements of the finite dual a h o secondly for an abelian group g we show that there exists a bijection between the set of all g gradings on h and the set of all bialgebra homomorphisms a h k g based on this all g gradings on h are explicitly classified and parameterized a h is also used to prove that there exists a universal commutative hopf algebra associated to any finite dimensional leibniz algebra h

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

frequency domain blind mimo system identification based on second and higher order statistics we present a novel frequency domain framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs the system frequency response is obtained based on singular value decomposition svd of a matrix constructed based on the power spectrum and slices of polyspectra of the system output by appropriately selecting the polyspectra slices we can create a set of such matrices each of which could independently yield the solution of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance the freedom to select the polyspectra slices allows us to bypass the frequency dependent permutation ambiguity that is usually associated with frequency domain svd while at the same time allows us compute and cancel the phase ambiguity an asymptotic consistency analysis of the system magnitude response estimate is performed

subspace methods for blind estimation of time varying fir channels novel linear algorithms are proposed in this paper for estimating time varying fir systems without resorting to higher order statistics the proposed methods are applicable to systems where each time varying tap coefficient can be described with respect to time as a linear combination of a finite number of basis functions examples of such channels include almost periodically varying ones fourier series description or channels locally modeled by a truncated taylor series or by a wavelet expansion it is shown that the estimation of the expansion parameters is equivalent to estimating the second order parameters of an unobservable fir single input many output simo process which are directly computed under some assumptions from the observation data by exploiting this equivalence a number of different blind subspace methods are applicable which have been originally developed in the context of time invariant simo systems identifiability issues are investigated and some illustrative simulations are presented

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

linear prediction error method for blind identification of periodically time varying channels blind channel estimation for single input multiple output simo periodically time varying channels is considered using only the second order statistics of the data the time varying channel is assumed to be described by a complex exponential basis expansion model ce bem the linear prediction error method for blind identification of time invariant channels is extended to time varying channels represented by a ce bem sufficient conditions for identifiability are investigated the cyclostationary nature of the received signal is exploited to consistently estimate the time varying correlation function of the data from a single observation record the proposed method requires the knowledge of the active basis functions but not the channel length an upper bound suffices several existing methods require precise knowledge of the channel length equalization of the time varying channel given the estimated channel is investigated computer simulation examples are presented to illustrate the approach and to compare it with two existing approaches

blind mimo identification using the second characteristic function we propose a new approach for the blind identification of a multi input multi output mimo system as a substitute to using classical high order statistics hos in the form of time lagged joint cumulants or polyspectra we use the estimated hessian matrices of the second joint generalized characteristic function of time lagged observations evaluated at several preselected processing points these matrices admit straightforward consistent estimates whose statistical stability can be finely tuned by proper selection of the processing points in contrast to classical hos transforming the obtained matrix sequence into the frequency domain we obtain and solve a sequence of frequency dependent joint diagonalization problems this yields a set of estimated frequency response matrices which are transformed back into the time domain after resolving frequency dependent phase and permutation ambiguities the performance of the proposed algorithm depends on the choice of processing points yet compares favorably with other algorithms especially at moderate signal to noise ratio conditions as we demonstrate in simulation results

six dimensional nilpotent lie algebras abstract we give a full classification of six dimensional nilpotent lie algebras over an arbitrary field including fields that are not algebraically closed and fields of characteristic 2 to achieve the classification we use the action of the automorphism group on the second cohomology space as isomorphism types of nilpotent lie algebras correspond to orbits of subspaces under this action in some cases these orbits are determined using geometric invariants such as the gram determinant or the arf invariant as a byproduct we completely determine for a four dimensional vector space v the orbits of gl v on the set of two dimensional subspaces of v v

how to calculate all point symmetries of linear and linearizable differential equations the systematic method for calculating all point symmetries of partial differential equations pdes with non trivial lie point symmetry algebras does not currently apply to linear pdes consider an

the construction of solvable lie algebras from equidimensional nilpotent algebras abstract the study of gradings of solvable lie algebras l of finite dimensionover a field f of zero characteristic led the authors to the discovery of equidimensional nilpotent algebras l uniquely determined by l up to f isomorphy conversely for any finite dimensional lie algebra l over f an algorithm is developed which yields in parametric form all solvable lie algebras l determining l as the corresponding nilpotent algebra the exposition is independent of lie grading theory it organizes in a novel way the classification of solvable lie algebras of given dimension around the same task for nilpotent algebras every isomorphy class of solvable f algebras is obtained in this way

verification of reactive systems via instantiation of parameterised boolean equation systems verification problems for finite and infinite state processes like model checking and equivalence checking can effectively be encoded in parameterised boolean equation systems pbess solving the pbes then solves the encoded problem the decidability of solving a pbes depends on the data sorts that occur in the pbes we describe a pragmatic methodology for solving pbess viz by attempting to instantiate them to the sub fragment of boolean equation systems bess unlike solving pbess solving bess is a decidable problem based on instantiation verification using pbess can effectively be done fully automatically in most practical cases we demonstrate this by solving several complex verification problems using a prototype implementation of our instantiation technique in addition practical issues concerning this implementation are addressed furthermore we illustrate the effectiveness of instantiation as a transformation on pbess when solving verification problems involving systems of infinite size

an efficient subspace method for the blind identification of multichannel fir systems we present a novel method for the blind identification of linear single input multiple output simo finite impulse response fir systems based on second order statistics our approach called the truncated transfer matrix method ttm proceeds in two major steps first the svd analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second the block toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations the proposed ttm method is analytical no optimization procedure involved and it is robust to noise we find that the method comes with an increased computational cost but it significantly outperforms state of the art second order methods in low signal to noise ratio snr situations

on the identification of a lie algebra given by its structure constants i direct decompositions levi decompositions and nilradicals abstract methods are given for identifying a lie algebra l given by its structure constants the identification involves a transformation to a canonical basis in which the structure becomes obvious thus decomposable lie algebras are already decomposed into direct sums of indecomposable ones an indecomposable lie algebra that is not simple or solvable has its radical exhibited a solvable algebra has its nilradical displayed the methods all lead to simple algorithms that have been implemented as computer programs involving some symbolic manipulations

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

precoder design and blind identification of mimo channels in this paper blind identification problem based on second order statistics sos of received signals is investigated for multiple input multiple output mimo channels it is shown that precoders introduced in transmitters can provide certain extra information for blind identification problem and commonly used identifiability conditions on mimo channels can be relaxed a design criterion for the precoders in frequency domain is proposed two blind identification algorithms based on the knowledge of the precoders and sos of the received signals are then developed in these algorithms due to particular structure of the precoders the blind identification problem for a mimo channel is decomposed into several independent single input multiple output simo channel identification problems the presented algorithms are robust to an overestimated channel order and not sensitive to signal to noise ratio snr compared with the existing results a larger class of mimo finite impulse response fir channels can be identified by the new methods

bisimulation equivalence is decidable for all context free processes abstract a result originally due to baeten bergstra and klop shows that strong bisimulation equivalence for normed bpa processes is decidable on the other hand huynh and tian and groote and huttel have proved that all other standard equivalences are undecidable for normed bpa and thus for bpa in general the open problem remaining has been whether bisimulation is decidable for the full bpa language in this paper we answer this question in the affirmative using a proof technique based on the proof by caucal of the decidability of language equivalence for simple algebraic grammars the decision procedure relies on our main result extending that of caucal that the maximal bisimulation of any bpa transition graph is finitely representable as a thue congruence the decision procedure consists of two semi decision procedures one testing for non bisimilarity and one testing for bisimilarity

fourth order cumulant based blind identification of underdetermined mixtures in this paper we study two fourth order cumulant based techniques for the estimation of the mixing matrix in underdetermined independent component analysis the first method is based on a simultaneous matrix diagonalization the second is based on a simultaneous off diagonalization the number of sources that can be allowed is roughly quadratic in the number of observations for both methods explicit expressions for the maximum number of sources are given simulations illustrate the performance of the techniques

deciding bisimulation equivalences for a class of non finite state programs traditionally many automatic program verification techniques have been applicable only to finite state programs in this paper we extend some of these techniques to a class of infinite state programs that in addition to having a finite state control component may read store and write but not perform any other computations on data such programs are data independent in the sense that their behavior does not depend on the actual data values supplied we consider the problems of deciding strong equivalence and observation equivalence defined by bisimulations as in ccs between such programs these equivalences have major applications in verification of communication protocols we present reductions of these problems to the problem of deciding strong equivalence and observation equivalence between finite state programs for which polynomial time algorithms exist the equivalence problems on data independent programs are shown to be np hard in the size of the programs

lie algebras of vector fields in the real plane finite dimensional real analytic lie algebras of vector fields on r 2 are completely classified up to changes of local coordinates

automorphisms of real lie algebras of dimension five or less the lie algebra version of the krull schmidt theorem is formulated and proved this leads to a method for constructing the automorphisms of a direct sum of lie algebras from the automorphisms of its indecomposable components for finite dimensional lie algebras there is a well known algorithm for finding such components so the theorem considerably simplifies the problem of classifying the automorphism groups we illustrate this by classifying the automorphisms of all indecomposable real lie algebras of dimension five or less our results are presented very concisely in tabular form

bisimulation and divergence abstract behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated particular study is made of these preorders in the context of milner s calculus of communicating systems the precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms a verification technique based on the theory of the preorders is introduced and illustrated

blind mimo channel identification from second order statistics using rank deficient channel convolution matrix for multiuser systems several direct blind identification algorithms require that the linear multiple input multiple output mimo system have a full rank convolution matrix this condition requires that the system transfer function be irreducible and column reduced we show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodate more practical scenarios algorithms such as the outer product decomposition algorithm only require minor length adjustment to its processing window without the column reduced condition this result allows direct blind identification methods to be applicable to mimo without requiring a full rank channel convolution matrix

cumulant based blind identification of linear multi input multi output systems driven by colored inputs the blind identification problem of a linear multi input multi output mimo system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation however such a problem is ill posed and has no unique solution therefore we can only find a solution of the problem within an equivalence class we address the blind identification problem of the linear mimo system driven by unobservable colored inputs using higher order statistics hos particularly the fourth order cumulants of the outputs where the unobservable inputs are mutually independent but temporally colored linear processes we first define the set which is denoted by s of stable scalar transfer functions and then define the notion of a generalized permutation matrix which is abbreviated by a g matrix over s then it is shown that the transfer function matrix of an unknown system is identified only up to post multiplication by a g matrix this result is applied to identifying fir systems for blind signal separation

blind identification of multi channel arma models based on second order statistics this correspondence presents a new second order statistical approach to blind identification of single input multiple output simo autoregressive and moving average arma system models the proposed approach exploits the dynamical autoregressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block toeplitz structure of the channel convolution matrix used by classical subspace methods for the multi channel model with the same autoregressive ar polynomial sufficient conditions and an efficient identification algorithm are given such that the multi channel model can be uniquely identified up to a constant scaling factor furthermore an extension of the result to blind identification of multi channel models with different ar polynomials is presented simulation results are given to show the effectiveness of the proposed approach

blind system identification using precise and quantized observations this paper studies the blind identification of multi channel fir systems using precise and quantized observations first a new deterministic blind identification dbi algorithm is presented for multi channel fir systems using precise observations in which the system parameters can be consistently estimated and the common source signal can be stably recovered when the observed samples are quantized by a static finite level quantizer an iterative deterministic blind identification idbi method is then provided the asymptotic characters of the proposed idbi method are discussed and the quantization effect on the identification performance is analyzed numerical simulations are given to support the developed dbi method and idbi method

blind identification of digital communication channels with correlated noise blind identification consists of estimating the impulse response of a linear time invariant channel used for transmission of digital data by observing the channel output without knowledge of the transmitted symbol sequence we show how a previously proposed algorithm moulines et al 1995 based on second order statistics of the received signal can be modified to account for correlated noise

characterizing finite kripke structures in propositional temporal logic abstract we show that if two finite kripke structures can be distinguished by some ctl formula that contains both branching time and linear time operators then the structures can be distinguished by a ctl formula that contains only branching time operators our proof involves showing that for any finite kripke structure m it is possible to construct a ctl formula f m that uniquely characterizes m since one kripke structure may be a trivial unrolling of another we use a notion of equivalence between kripke structures that is similar to the notion of bisimulation studied by milner 15 our first construction of f m requires the use of the nexttime operator we also consider the case in which the nexttime operator is disallowed in ctl formulas the proof in this case requires another notion of equivalence equivalence with respect to stuttering and is much more difficult since it is possible for two inequivalent states to have exactly the same finite behaviors modulo stuttering but different infinite behaviors we also give a polynomial algorithm for determining if two structures are stuttering equivalent and discuss the relevance of our results for temporal logic model checking and synthesis procedures

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

discrete point symmetries of ordinary differential equations this paper describes a method that enables the user to construct systematically the set of all discrete point symmetries of a given ordinary differential equation ode of order two or greater provided that the ode has at least a one parameter lie group of point symmetries the method is easy to use and is based upon lie s method of constructing continuous symmetries the calculations are simple and computer algebra is not usually required various examples are used to illustrate the method the paper concludes with a proof that every ode whose lie group of point symmetries is isomorphic to the unimodular group has at least four inequivalent real discrete point symmetries

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

branching time and abstraction in bisimulation semantics in comparative concurrency semantics one usually distinguishes between linear time and branching time semantic equivalences milner s notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence in this paper we investigate whether observation equivalence really does respect the branching structure of processes and find that in the presence of the unobservable action of ccs this is not the case therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes in the sense that it preserves computations together with the potentials in all intermediate states that are passed through even if silent moves are involved on closed ccs terms branching bisimulation congruence can be completely axiomatized by the single axion scheme a y z y a y z where a ranges over all actions and the usual loaws for strong congruence we also establish that for sequential processes observation equivalence is not preserved under refinement of actions whereas branching bisimulation is for a large class of processes it turns out that branching bisimulation and observation equivalence are the same as far as we know all protocols that have been verified in the setting of observation equivalence happen to fit in this class and hence are also valid in the stronger setting of branching bisimulation equivalence

a sequential subspace method for blind identification of general fir mimo channels this correspondence addresses the problem of blindly identifying multiple input multiple output mimo finite impulse response fir channels without the conventional assumption of identical column degrees a subspace based algorithm is developed that identifies the channel s columns sequentially from the lowest degree columns to the highest degree ones compared with the previous generalized subspace method by gorokhov and loubaton 1997 the new method is simpler and more accurate

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

the structure of underlying lie algebras abstract every lie algebra over a field e gives rise to new lie algebras over any subfield f e by restricting the scalar multiplication this paper studies the structure of these underlying lie algebra in relation to the structure of the original lie algebra in particular the question how much of the original lie algebra can be recovered from its underlying lie algebra over subfields f by introducing the conjugate of a lie algebra we show that in some specific cases the lie algebra is completely determined by its underlying lie algebra furthermore we construct examples showing that these assumptions are necessary as an application we give for every positive n an example of a real 2 step nilpotent lie algebra which has exactly n different bi invariant complex structures this answers an open question by di scala lauret and vezzoni motivated by their work on quasi kahler chern flat manifolds in differential geometry the methods we develop work for general lie algebras and for general galois extensions f e in contrast to the original question which only considered nilpotent lie algebras of nilpotency class 2 and the field extension r c we demonstrate this increased generality by characterizing the complex lie algebras of dimension 4 which are defined over r and over q