deciding whether a finite set of words has rank at most two abstract given a finite subset x of a free monoid a we define the rank of x as r x min y x y the problem we study here is to decide whether or not r x 2 we propose an o n ln 2 m algorithm where n stands for the sum of the lenghts of the words in x and m stands for the length of the longest word

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

reliable h_ infty control of linear systems with adaptive mechanism this technical note studies the problem of designing reliable h controllers with adaptive mechanism for linear systems a new method for designing indirect adaptive reliable controller via state feedback is presented for actuator fault compensations based on the on line estimation of eventual faults the proposed reliable controller parameters are updated automatically to compensate the fault effects on systems a notion of adaptive h performance index is proposed to describe the disturbance attenuation performances of closed loop systems the design conditions are given in terms of solutions to a set of linear matrix inequalities lmis the resultant designs can guarantee the asymptotic stability and adaptive h performances of closed loop systems even in the cases of actuator failures the effectiveness of the proposed design method is illustrated via a numerical example

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

the equivalence problem of multitape finite automata abstract using a result of b h neumann we extend eilenberg s equality theorem to a general result which implies that the multiplicity equivalence problem of two nondeterministic multitape finite automata is decidable as a corollary we solve a long standing open problem in automata theory namely the equivalence problem for multitape deterministic finite automata the main theorem states that there is a finite test set for the multiplicity equivalence of finite automata over conservative monoids embeddable in a fully ordered group

a fast algorithm for the unique decipherability of multivalued encodings abstract multivalued encodings constitute an interesting generalization of ordinary encodings in that they allow each source symbol to be encoded by more than one codeword in this paper the problem of testing the property of unique decipherability of multivalued encodings is considered we provide an efficient algorithm whose time complexity is o c where c is the number of codewords and is the sum of their lengths it is remarkable that the running time equals that of the fastest algorithms for testing the much simpler property of unique decipherability of ordinary encodings

a note on multiset decipherable codes in a recent paper a lempel ibid vol it 32 p 714 16 1986 introduced the notion of a multiset decipherable msd code to handle some special problems of information transmission he showed that no msd code contains a full prefix code as a proper subcode he further conjectured that no msd code contains a full uniquely decipherable code as a proper subcode and that every msd code satisfies the kraft inequality a proof of the first conjecture and a disproof of the second are given

on unique multiset and set decipherability of three word codes the concepts of unique decipherability ud multiset decipherability msd and set decipherability sd of codes were developed to handle some special problems in the transmission of information in unique decipherability different sequences of codewords carry different information in multiset decipherability the information of interest is the multiset of codewords used in the encoding process so that order in which transmitted words are received is immaterial in set decipherability it is the set of codewords that is relevant information so the order and the multiplicity of words are immaterial lempel 1986 showed that the ud and msd properties coincide for two word codes and conjectured that every three word msd code is a ud code guzman 1995 showed that the ud msd and sd properties coincide for two word codes and conjectured that these properties coincide for three word codes in this paper we answer both conjectures positively for all three word codes c sub 1 c sub 2 c sub 3 satisfying c sub 1 c sub 2 spl les c sub 3 our procedures are based on techniques related to dominoes

fuzzy adaptive output feedback fault tolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults this paper studies the fuzzy adaptive output feedback fault tolerant control ftc problem for a class of single input and single output uncertain nonlinear systems with time varying nonaffine nonlinear faults in strict feedback form in the design procedure filtered signals are adopted to circumvent algebraic loop problems on implementing the usual controllers by using fuzzy logic systems to approximate the unknown nonlinearity effects and changes in model dynamics due to faults a fuzzy state observer is first presented to estimate the unmeasured states based on the online estimating information from the adaptive mechanism an observer based dynamic output feedback fault tolerant controller is designed via the backstepping technique it is shown that the stability and tracking performances of the closed loop system can be achieved even in the presence of unknown nonlinear faults in comparison with the existing approaches the ftc scheme can handle the nonaffine nonlinear faults effectively finally a simulation example is included to validate the advantages of the proposed approaches

on multiset decipherable codes corresp in certain applications it is necessary to communicate a description of a sequence of events where the information of interest is which one of a set of possible events has occurred including multiplicity but where the order of occurrence is irrelevant typical examples are online compilations of inventories construction of histograms or updating of relative frequencies suitable codes for this purpose need not be uniquely decipherable ud in fact all that is required of such a code is that given a finite message over the code every possible parsing of the message into codewords must yield the same multiset of codewords a code with this property is referred to as a multiset decipherable msd code an msd code is said to be proper if it is not a ud code it is shown that for every n 3 there exist proper msd codes with n words for n 2 every msd code is necessarily a ud code and all evidence points to the same conclusion for n 3 it is further shown that no msd code contains a full prefix code or a full suffix code as a proper subcode and it is conjectured that despite the weaker decipherability condition every msd code satisfies the kraft inequality

a fast test for unique decipherability based on suffix trees corresp the classical algorithm for testing unique decipherability of codes is improved by using mccreight s algorithm for constructing suffix trees the complexity of the algorithm is o nm where n is the number of codewords and m is their total length efficiency is gained by avoiding repeatedly comparing subwords of the codewords

reliable state feedback control of t s fuzzy systems with sensor faults this paper is concerned with reliable state feedback control synthesis for takagi and sugeno t s fuzzy systems with sensor multiplicative faults by considering the influence of sensor faults on both the system states and premise variables of fuzzy controllers a class of new convex reliable stabilization conditions are proposed for t s fuzzy systems using the properties of fuzzy product inference engines furthermore the obtained result is extended to the h infty reliable control case the resulting controllers are reliable in that they provide guaranteed asymptotic stability and h infty performance when all sensors are operational as well as when some sensor experiences failures different from the proposed approach the influence of sensor faults on premise variables is not considered in the existing results then it might not guarantee the stability and control performance for t s fuzzy systems with premise variables dependent on the system states a numerical example is given to illustrate the effectiveness of the proposed method

the finest homophonic partition and related code concepts let c be a finite set of n words having total length l where all words are taken over a r element alphabet the set c is called numerically decipherable if any two factorizations of the same word over the given alphabet into words in c have the same length an o nl sup 2 time and o n k l space algorithm is presented for computing the finest homophonic partition of c provided that this set is numerically decipherable the latter property can be decided by another algorithm requiring o nl time and o n k l space the two algorithms are based on a technique related to dominoes

multiplicity one theorems for fourier jacobi models for every genuine irreducible admissible smooth representation pi of the metaplectic group widetilde rm sp 2n over a p adic field and every smooth oscillator representation omega psi of widetilde rm sp 2n we prove that the tensor product pi otimes omega psi is multiplicity free as a smooth representation of the symplectic group rm sp 2n similar results are proved for general linear groups and unitary groups

parallel complexity of the regular code problems abstract the regular code problem rcp seeks to decide whether a right linear grammar g generates a code i e whether or not l g is free over l g here l g is the language generated by g the regular free monoid problem rfmp seeks to decide whether a right linear grammar g generates a free monoid both problems can be reduced to the linear context free grammar emptiness problem which in turn can be reduced to matrix inversion in the case of rcp the reductions give rise to an nc algorithm in the rfmp case the reduction yields only an exptime algorithm

the inclusion problem for some classes of deterministic multitape automata abstract a natural and sufficiently large class of deterministic one way multitape automa is defined with decidable inclusion problem this class is also the largest with decidable equivalence problem at this moment

codes orderings and partial words codes play an important role in the study of the combinatorics of words in this paper we introduce pcodes that play a role in the study of combinatorics of partial words partial words are strings over a finite alphabet that may contain a number of do not know symbols pcodes are defined in terms of the compatibility relation that considers two strings over the same alphabet that are equal except for a number of insertions and or deletions of symbols we describe various ways of defining and analyzing pcodes in particular many pcodes can be obtained as antichains with respect to certain partial orderings using a technique related to dominoes we show that the pcode property is decidable

the spin l function on gsp6 via a non unique model we give two global integrals that unfold to a non unique model and represent the partial spin l function on rm pgsp 6 we deduce that for a wide class of cuspidal automorphic representations pi the partial spin l function is holomorphic except for a possible simple pole at s 1 and that the presence of such a pole indicates that pi is an exceptional theta lift from rm g 2 these results utilize and extend previous work of gan and gurevich who introduced one of the global integrals and proved these facts for a special subclass of these pi upon which the aforementioned model becomes unique the other integral can be regarded as a higher rank analogue of the integral of kohnen skoruppa on rm gsp 4

relational codes of words we consider words i e strings over a finite alphabet together with a similarity relation induced by a compatibility relation on letters this notion generalizes that of partial words the theory of codes on combinatorics on words is revisited by defining r s codes for arbitrary similarity relations r and s we describe an algorithm to test whether or not a finite set of words is an r s code coding properties of finite sets of words are explored by finding maximal and minimal relations with respect to relational codes

equations over finite sets of words and equivalence problems in automata theory abstract several observations concerning equations over monoids of finite sets of words are made monoids considered are the monoid of finite prefix codes the monoid of all finite sets and the monoid of all finite multisets as well as some others as an application some known decidability results in automata theory are extended finally several open questions are raised

brief performance gain margins of the two stage lq reliable control this paper presents the performance gain margins of the recently developed two stage lq reliable control which is a discrete time version of veillette s reliable lq regulator such that the performance cost is guaranteed to be within a certain bound it is shown that the desired gain margins satisfy a unified gain margin constraint and a solution to solve this constraint is obtained in terms of linear matrix inequalities an application of the proposed unified gain margin constraint to design a reliable guaranteed cost controller is illustrated a numerical example is also given to show the effectiveness of the proposed results

the ehrenfeucht conjecture a compactness claim for finitely generated free monoids abstract we survey recent results on the so called ehrenfeucht conjecture which states for each language l over a finite alphabet there exists a finite subset f of l such that for each pair g h of morphisms on the equation g x h x holds for all x in l if and only if holds for all x in f we point out that the conjecture is closely related to the theory of equations in free monoids we also state a suprising consequence of the conjecture if it holds even noneffectively for all dol languages then the hdol sequence equivalence problem is decidable furthermore we give examples of when the conjecture is known to hold in particular we establish it for all binary languages as well as for all languages when attention is restricted to bounded delay morphisms of some fixed delay

unique decipherability in formal languages abstract we consider several language theoretic aspects of various notions of unique decipherability or unique factorization in formal languages given a language l at some position within the chomsky hierarchy we investigate the language of words ud l in l that have unique factorization over l we also consider similar notions for weaker forms of unique decipherability such as numerically decipherable words nd l multiset decipherable words msd l and set decipherable words sd l although these notions of unique factorization have been considered before it appears that the languages of words having these properties have not been positioned in the chomsky hierarchy up until now we show that ud l nd l msd l and sd l need not be context free if l is context free in fact nd l and msd l need not be context free even if l is finite although ud l and sd l are regular in this case we show that if l is context sensitive then so are ud l nd l msd l and sd l we also prove that the membership problem resp emptiness problem for these classes is pspace complete resp undecidable we finally determine upper and lower bounds on the length of the shortest word of l not having the various forms of unique decipherability into elements of l

transducers and repetitions the factor transducer of a word associates to each of its factors or subwords their first occurrence optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given analogue results and a simple algorithm are given for the case of subsequential suffix transducers algorithms are applied to repetition searching in words le transducteur des facteurs d un mot associe a chacun de ses facteurs leur premiere occurrence on donne des bornes optimales sur la taille du transducteur minimal d un most ainsi qu un algorithme pour sa construction on donne des resultats analogues et un algorithme simple dans le cas du transducteur sous sequentiel des suffixes d un mot on donne une application a la detection de repetitions dans les mots

convergent fault estimation for linear systems with faults and disturbances the problem of convergent fault estimation for a class of linear systems with faults and disturbances is addressed for the first time in this technical note a differential equation based convergence theorem of mean sequence of estimates is proposed which provides an iterative mean estimation technique that has not been fully reported yet in the literature based on the technique a convergent fault estimation strategy for the linear system in consideration is designed and the convergence of mean sequence of fault estimates is proved theoretically an iterative algorithm is given subsequently to compute the fault estimates numerical simulation results demonstrate the effectiveness and merits of the proposed method

fuzzy adaptive fault tolerant control of multi agent systems with interactions between physical coupling graph and communication graph abstract this paper considers the fuzzy fault tolerant control problem for multi agent systems with interactions between physical coupling graph and communication graph the dynamics of agents are interconnected by a signed physical coupling graph and the control protocols are computed by using the information flow prescribed in a signed communication graph a novel fuzzy adaptive fault tolerant control method for agents with antagonistic interactions to achieve bipartite consensus is proposed firstly in the presence of actuator bias faults and unknown nonlinear functions different from the traditional method to estimate the weight matrix only the weight vector needs to be estimated by exchanging the order of weight vectors and fuzzy basis functions in the fuzzy logic systems finally a simulation example is given to illustrate the effectiveness of the proposed controller

robust h_2 control of linear systems with mismatched quantization this paper is concerned with the h 2 control of linear systems with multiple quantization channels the quantization parameters of each channel are not required to be identical the resultant mismatches are represented by polytopic uncertainties a composite controller composed of linear and nonlinear parts is designed to meet the required h 2 performance and offset the quantization error resorting to a vertex separation technique and finsler lemma instead of matrix inverse operations new synthesis conditions for the desired linear part are derived in terms of linear matrix inequalities which are further extended to treat systems with norm bounded uncertainties a comparison of conservativeness between the proposed methods and the existing ones is demonstrated by two numerical examples

equations and monoid varieties of dot depth one and two abstract each level of the straubing s hierarchy of aperiodic monoids can be parametrized in a natural way this paper studies this parametrization for dot depth one and two monoids for level one it is shown that the m th level is defined by a finite sequence of equations if and only if m 1 2 or 3 for level two and for m 1 a sequence of equations is given which is satisfied in the m th level and shown to ultimately define the 1st level

adaptive fuzzy fault compensation tracking control for uncertain nonlinear systems with multiple sensor faults abstract this paper investigates the problem of fault compensation tracking control for a class of uncertain nonlinear strict feedback systems the presence of multiple sensor faults leads to that the existing feedback control based on perfect measurement will be completely invalid and cannot achieve the desired tracking control to solve this problem a new type control strategy is proposed a cubic absolute value lyapunov stability theory is used to online estimating the fault information and an adaptive signal compensation mechanism is proposed to eliminate the adverse effects caused by the sensor faults it is proved that by applying the presented method both the tracking performance and the boundedness of closed loop signals can be guaranteed finally simulation results are given to illustrate the established theoretical findings intuitively

dominoes over a free monoid abstract dominoes over a free monoid and operations on them are introduced related algebraic systems and their applications to decidability problems about morphisms on free monoids are studied a new simple algorithm for testing dol sequence equivalence is presented

multiplicities a deterministic view of nondeterminism abstract we discuss four important problems in automata theory each of which has three natural variants a deterministic one a nondeterministic one and as an in between case a nondeterministic one with multiplicities our goal is to support a general view that the third variant is much closer to the first one than to the second one

a decision procedure for finite decipherability and synchronizability of multivalued encodings a multivalued encoding is a variable length coding system in which more than one codeword may correspond to each source symbol the properties of unique decipherability decipherability with finite delay and synchronizability for multivalued encodings are characterized in particular the property of unique decipherability is considered and a recent conjecture about decipherability with finite delay is proved to be true the notion of a synchronizable multivalued code is also introduced and a necessary and sufficient condition for a multivalued code to be synchronizable is provided some auxiliary results are also obtained

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

a proof of ehrenfeucht s conjecture abstract ehrenfeucht s conjecture states that each subset s of a finitely generated free monoid has a finite subset t such that if two endomorphisms of the monoid agree on t then they agree on s it is the purpose of this note to verify the conjecture

efficient constructions of test sets for regular and context free languages we present a simple construction of linear size test sets for regular languages and of single exponential test sets for context free languages in the case of regular sets the size of our test set is exactly the number of transitions of the automaton this improves the best known upper bounds exponential for regular and doubly exponential for context free languages we give also an o n log n time algorithm for the morphism equivalence and an o n3log n time algorithm to test the gsm equivalence on a regular language an o n2log n time algorithm is given to test the equivalence of two deterministic gsm s as well as that of two deterministic finite transducers

adaptive h control in finite frequency domain for uncertain linear systems this paper is concerned with the problem of adaptive h controller design in finite frequency domains for uncertain linear systems the uncertainties are assumed to be time invariant unknown but bounded which appear affinely in the matrices of system models an adaptive mechanism is introduced to construct a novel finite frequency h controller with time varying gains by using lyapunov theory and parseval s theorem the controller design conditions are given in terms of a set of linear matrix inequalities lmis it is shown that the proposed finite frequency controller with time varying gains can achieve better h performance than the traditional ones with fixed gains finally a numerical example of the f 18 aircraft model is given to illustrate the presented theoretical results

reliable control using redundant controllers this paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant the resulting closed loop control system is reliable in the sense that it provides guaranteed internal stability and h sub spl infin performance in terms of disturbance attenuation not only when all controllers are operational but also when some controller outages sensor and or actuator occur a numerical example is given to illustrate the proposed design procedures

robust adaptive fuzzy control of a class of uncertain switched nonlinear systems with mismatched uncertainties this paper studies the adaptive fuzzy control problem for a class of uncertain switched nonlinear systems with mismatched uncerta inties and external disturbances a new switched adaptive control technique for the problem studied is set up such that the considered switched systems can be stabilized under a class of switching signals characterized by the generalized average dwell time condition first the adaptive state feedback controller is designed based on tuning the estimations of the bounds on switching parameters instead of estimating the switching parameters directly next by using a switched observer to reconstruct the states of the system an output feedback controller is also presented in the design procedure fuzzy logic systems are used to approximate the unknown nonlinear functions to overcome the undesirable chattering phenomenon both control laws are developed using the continuous control strategy it is shown that both controllers can guarantee that all the signals in the resulting closed loop system are bounded finally two simulation examples are presented to demonstrate the effectiveness of the proposed control results

modularity of the rankin selberg l series and multiplicity one for sl 2 let f g be primitive cusp forms holomorphic or otherwise on the upper half plane h of levels n m respectively with unitarily normalized l functions l s f equation and l s g equation when p does not divide n resp m the inverse roots p p resp p p are nonzero with sum ap resp bp for every p prime to nm set lp s f g 1 p pp s 1 p pp s 1 p pp s 1 p pp s 1 let l s f g denote the incomplete euler product of lp s f g over all p not dividing nm this is closely related to the convolution l series sum over n 1 a sub n b sub n n s whose miraculous properties were first studied by rankin and selberg

on shalika periods and a theorem of jacquet martin let pi be a cuspidal automorphic representation of gl 4 bbb a with central character mu 2 it is known that pi has shalika period with respect to mu if and only if the l function l s s pi bigwedge 2 otimes mu 1 has a pole at s 1 jacquet and martin considered the analogous question for cuspidal representations pi d of the inner form gl 2 d bbb a and obtained a partial result via the relative trace formula in this paper we provide a complete solution to this problem via the method of theta correspondence and give necessary and sufficient conditions for the existence of shalika period for pi d we also resolve the analogous question in the local setting

accepting networks of splicing processors complexity results in this paper we consider a new bio inspired computing model the accepting network of splicing processors we define two computational complexity classes based on this model and show how they are related to the classical ones defined for turing machines namely np and pspace furthermore we approach the topic of problem solving using these newly defined devices in this context a linear time solution for one of the most interesting np complete problems the sat problem is presented the results presented here suggest once more that nondeterminism might be approached in a deterministic way by means of multiplicities

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

deciding multiset decipherability an o n sup 2 l time and o n k l space algorithm is provided for deciding whether or not a finite set c consisting of n words having total length l where all words are taken over a k element alphabet is a multiset decipherable code the algorithm is based on a technique related to dominoes at an easily stage it decides in o nl time and o n k l space whether or not the set c is uniquely decipherable

towards a classification of global integral constructions and functorial liftings using the small representations method abstract this is a survey article in which we discuss some recent approach toward the classification of global factorizable integrals and constructions of langlands functorial lifting using small representations to do that we use the language of unipotent orbits and their relation to fourier coefficients we also introduce the dimension equation and set our goal to classify all global integrals of a certain form which satisfies this equation