extensions of the method of poles for code construction the method of poles is a method introduced by franaszek 1969 for constructing a rate 1 1 finite state code from k ary data into a constrained channel of finite type whose capacity is strictly greater than log k the method is based on the computation of a set of states called poles with each pole is associated a set of paths going from this pole to others each set verifies an entropy condition the code produced by the method of poles has a sliding block decoder if each set of paths satisfies moreover an optimization condition based on the sum of the path lengths of the set we give a new optimization condition which guarantees the sliding block window decoding property and has a lower computational complexity than the previous one we also extend the method of poles to the more general case of sofic constrained channels

stability properties of functional equations describing the scientific laws recently several authors have studied functional equations in order to find the general form of scientific laws which are invariant under the so called admissible transformations of the variables see e g 2 3 131 the problem has its origin in the theory of dimensional analysis see e g 11 12 14 but there are also close connections to economics production theory etc see 6 the functional equations considered by the above authors and solved in special cases have the form

multidimensional sofic shifts without separation and their factors for d 2 we exhibit mixing d shifts of finite type and sofic shifts with large entropy but poorly separated subsystems in the sofic examples the only minimal subsystem is a single point these examples consequently have very constrained factors in particular no non trivial full shift is a factor we also provide examples to distinguish certain mixing conditions and develop the natural class of block gluing shifts in particular we show that block gluing shifts factor onto all full shifts of strictly smaller entropy

minimality and observability of group systems abstract group systems are a generalization of willems type linear systems that are useful in error control coding it is shown that the basic ideas of willems s treatment of linear systems are easily generalized to linear systems over arbitrary rings and to group systems the interplay between systems behaviors and trellises evolution laws is discussed with respect to completeness minimality controllability and observability it is pointed out that for trellises of group systems and willems type linear systems minimality is essentially the same as observability the development is universal algebraic in nature and holds unconditionally for linear systems over the real numbers

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

rules for creating certain sophic systems abstract let a be a finite set a code is a subset of the a of all finite sequences on a with the property of unique deciphering codes are related with sofic systems in two ways considering the right resolving cover with state space of a sofic system s for the set of labels of minimal paths from to itself is a rational code called the first return code conversely a rational code generates a sofic system by concatenation we show that a necessary and sufficient condition for a sofic system to be of finite type resp almost finite type is that all first return codes are local resp with unique splitting to the right and left local codes and codes with unique splitting are related to classical families local codes are circular and finite local codes are identical to finite circular codes finite codes with unique splitting are identical to finite codes with finite deciphering delay to the same side restivo proved that finite circular codes generate subshifts of finite type we show finally that finite codes with unique splitting to the right and left generate almost finite type subshifts but those two results do not hold when the finiteness hypothesis is dropped

complexity and sliding block decodability a constrained system or sofic system s is the set of symbol strings generated by the finite length paths through a finite labeled directed graph karabed and marcus 1988 extending the work of adler coppersmith and hassner 1983 used the technique of state splitting to prove the existence of a noncatastrophic rate p q finite state encoder from binary data into s for any input word length p and codeword length q satisfying p q spl les cap s the shannon 1948 capacity for constrained systems that are almost finite type they further proved the existence of encoders enjoying a stronger form of decodability namely sliding block decodability in particular their result implies the existence of a 100 efficient rate 1 2 sliding block code for the charge constrained runlength limited constraint with parameters d k c 1 3 3 an almost finite type system with capacity precisely 1 2 we describe two quite different constructions of such codes the constructions highlight connections between the problem of determining sliding block decodability of a finite state encoder and certain problems of colorability for graphs and sets using these connections we show that the problem of determining the existence of a block decodable input tag assignment for a given rate p q finite state encoder is np complete for p 1 we also prove np completeness results for several related problems in combinatorics and coding

minimum scope for sliding block decoder mappings some properties of state splitting are established the properties are then used to develop an algorithm for searching the sliding block decoder mapping of minimum scope obtained by state splitting the algorithm is applied to the d k constraints of magnetic recording

sofic systems and encoding data techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input restricted channels this generalizes the earlier work of adler coppersmith and hassner on the same problem

on meaningfulness of means abstract we are concerned with the definition of means or averaging operators i e aggregators m x1 xi xm where xi r represent measures on the reals corresponding to a given type of scale ordinal interval or ratio scale the adequate mean which varies between min x1 xm and max x1 xm should correspond to some comparison meaningfulness property or some functional equation that induces invariance or stability we characterize the averaging operators which present some natural properties continuity monotonicity neutrality unanimity etc and comparison meaningfulness or invariance and we show that operators like order statistics and ordered weighted averaging operators can be used to rank elements defined by vectors x1 xm in a meaningful way in the spirit of measurement theory

state splitting for variable length graphs corresp the state splitting algorithm of adler coppersmith and hassner for graphs with edges of fixed length is extended to graphs with edges of variable lengths this has the potential to improve modulation code construction techniques although the ideas of state splitting come from dynamical systems completely graph theoretic terms are used

characterization of the ordered weighted averaging operators this paper deals with the characterization of two classes of monotonic and neutral mn aggregation operators the first class corresponds to mn aggregators which are stable for the same positive linear transformations and presents the ordered linkage property the second class deals with mn idempotent aggregators which are stable for positive linear transformations with the same unit independent zeroes and ordered values these two classes correspond to the weighted ordered averaging operator owa introduced by yager in 1988 it is also shown that the owa aggregator can be expressed as a choquet integral

signal sets matched to groups recently linear codes over z sub m the ring of integers mod m have been presented that are matched to m ary phase modulation the general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes a definition is given for the notion of matching it is shown that any signal set in n dimensional euclidean space that is matched to an abstract group is essentially what d slepian 1968 called a group code for the gaussian channel if the group is commutative this further implies that any such signal set is equivalent to coded phase modulation with linear codes over z sub m some further results on such signal sets are presented and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed

on a functional equation concerning affine transformations abstract in this paper we prove that if the functional equation u rx p r p u x r p has a nonconstant solution u then and have to be of a very special form finally we obtain under suitable hypotheses the general solution of this equation

fuzzy differential game of guarding a movable territory in most earlier works of differential game problems which are based solely on crisp mathematics it is generally assumed that all information obtained by each player is perfect thus the games are treated with full information in many practical situations the information obtained by any player may contain some sort of uncertainties which are usually difficult to characterize either deterministically or stochastically we treat such uncertain information as fuzzy information and consider a differential game problem with fuzzy information as a fuzzy differential game problem in this paper we consider the fuzzy differential game of guarding a movable territory in a general problem of guarding a territory key concepts are the favorable region of the invader and the boundary curve for simplicity the movable territory is assumed to be a circle in this paper we will show that when the center of the territory is located outside the favorable region of the invader the value of the game exists otherwise the value does not exist a fuzzy control strategy is proposed and some computer simulations are provided in this paper

fuzzy controller theory limit theorems for linear fuzzy control rules abstract for a general fuzzy controller employing linear fuzzy control rules it is shown that as the number of rules grow the defuzzified output becomes a linear function of the input in particular for a sufficiently large number of rules the defuzzified output is approximately the same as the pi pid controller

multidimensional modulation and coding for band limited digital channels a class of multidimensional signals based on generalized group alphabets is introduced and its basic properties are derived the combination of generalized group alphabets and coding is also examined two coding schemes are considered g ungerboeck s scheme 1982 for combination with convolutional codes and v v ginzburg s 1984 scheme for combination with block codes it is concluded that the performance of these schemes makes them attractive for transmission over band limited digital channels

enumerative sequences of leaves and nodes in rational trees we prove that any n rational sequence s sn n 1 of nonnegative integers satisfying the kraft strict inequality n 1snk n 1 is the enumerative sequence of leaves by height of a rational k ary tree we give an efficient algorithm to get a k ary rational tree particular cases of this result had been previously proven we give some partial results in the case of equality especially we study the similar problem of characterizing the enumerative sequences of nodes of k ary rational trees and solve this question when the sequence has a primitive linear representation

convolutional codes over groups the basic algebraic structure theory of convolutional codes and their trellises is developed simultaneously for codes over groups rings and fields the first part which covers fundamental notions such as minimality and observability is semi tutorial in that most definitions are already standard within the modern behavioral theory as are some of the formally stated results however some of the pivotal results emphasizing the role of observability as the basic well behavedness condition for codes are new and several previous results are given simplified proofs the usefulness of the behavioral approach even for convolutional codes over fields is demonstrated by a new minimality test for encoders as well as by the straightforward derivation of some known minimality criteria for generator matrices from the basic minimality criteria for group trellises the second part of the paper deals with issues that are specific to codes over rings and groups the main result is a concise characterization the first such of those groups that can appear as the branch group of any group trellis it is further shown how such groups are presented by shift registers a new large class of noncommutative convolutional codes is also given

spectral analysis of maximum entropy multitrack modulation codes the problem of calculating the power spectral density of a constrained maxentropic vector sequence a sup n a sup n a sub i sup n sub 0 spl les i spl les n 1 is considered the constraints of the constituent sequences a sub i sup n are defined by the sofic systems s sub i presented by the directed graphs g sub i 0 spl les i spl les n 1 but the vector sequence itself is constrained additionally and given by a function spl phi of constituent graphs g spl phi g sub 0 spl middot spl middot spl middot g sub n 1 this class of vector constraints is met in parallel multitrack recording the general case of a simultaneous recording on n tracks is considered assuming that the common vector constraint is track invariant

the construction of m ary d spl infin codes that achieve capacity and have the fewest number of encoder states the existence of 100 efficient i e capacity achieving fixed rate codes for input constrained noiseless channels is guaranteed provided the channel has rational capacity a class of m ary runlength limited m d spl infin constraints was shown in previous work to have rational capacity in this correspondence we present a code construction procedure for obtaining 100 efficient codes with the fewest number of encoder states for all m d spl infin constraints with rational capacity the decoders are sliding block decoders with sliding window size d 1

sliding block codes between constrained systems the construction of finite state codes between constrained systems called sofic systems introduced by r karabed and b marcus 1988 is continued it is shown that if sigma is a shift of finite type and s is a sofic system with k n h s h sigma where h denotes entropy there is a noncatastrophic finite state invertible code from sigma to s at rate k n if sigma and s satisfy a certain algebraic condition involving dimension groups and sigma and s satisfy a certain condition on their periodic points moreover if s is an almost finite type sofic system then the decoder can be sliding block

infinite to one codes and markov measures we study the structure of infinite to one continuous codes between subshifts of finite type and the behaviour of markov measures under such codes we show that if an infinite to one code lifts one markov measure to a markov measure then it lifts each markov measure to uncountably many markov measures and the fibre over each markov measure is isomorphic to any other fibre calling such a code markovian we characterize markovian codes through pressure we show that a simple condition on periodic points necessary for the existence of a code between two subshifts of finite type is sufficient to construct a markovian code several classes of markovian codes are studied in the process of proving illustrating and providing contrast to the main results a number of examples and counterexamples are given in particular we give a continuous code between two bernoulli shifts such that the defining vector of the image is not a clustering of the defining vector of the domain

minimal presentations for irreducible sofic shifts we re cast a theorem of willems 1989 in terms of symbolic dynamics we then present a new result which characterizes when an irreducible sofic shift i e constrained system has a unique minimal irreducible presentation

trellis group codes for the gaussian channel in this paper trellis group codes are introduced as an extension of slepian group codes to codes over sequence spaces a trellis group code is defined over r sup n as the orbit of a bi infinite seed sequence x sub 0 spl isin r sup n sup z under an infinite defining group of transformations this group of transformations is generated by a symbolic system the theory is developed by combining a nontrivial extension of the notion of an isometric labeling with results from the theory of symbolic dynamics over groups new results presented here include a useful characterization of uniform partitions and a symbolic dynamic classification of trellis group codes the theory is used to develop a class of rotationally invariant nonabelian trellis group codes for qam modulation it is also shown that the 8 state rotationally invariant trellis code designed by wei 1984 used in the v 32 and v 32 bis international modem standard belongs to this class

a strategy for a payoff switching differential game based on fuzzy reasoning in this paper a new concept of a payoff switching differential game is introduced in this new game any one player at any time may have several choices of payoffs for the future moreover the payoff switching process including the time of payoff switching and the outcome payoff of any one player is unknown to the other indeed the overall payoff which is a sequence of several payoffs is unknown until the game ends an algorithm for determining a reasoning strategy based on fuzzy reasoning is proposed in this algorithm the fuzzy theory is used to estimate the behavior of one player during a past time interval by deriving two fuzzy matrices gsm game similarity matrix and vgsm variation of gsm the behavior of the player can be quantified two weighting vectors are selected to weight the relative importance of the player s behavior at each past time instant finally a simple fuzzy inference rule is adopted to generate a linear reasoning strategy the advantage of this algorithm is that it provides a flexible way for differential game specialists to convert their knowledge into a reasonable strategy a practical example of guarding three territories is given to illustrate our main ideas

sliding block coding for input restricted channels work on coding arbitrary sequences into a constrained system of sequences called a sofic system is presented such systems model the input constraints for input restricted channels e g run length limits and spectral constraints for the magnetic recording channel in this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation a constructive proof is given of the existence of finite state invertible noncatastrophic codes from arbitrary n ary sequences to a sofic system s at constant rate p q provided only that shannon s condition p q

homothetic and translatable preferences utility representation and functional equations involved abstract i provide a full characterization of those preferences total preorders defined on r n that admit a representation by means of a continuous homogeneous of degree one and translative utility order preserving function in addition i pay attention to the functional form of the kind of representation obtained including some qualifications such as being continuous and or monotonic in particular a full description of the functions f r 3 r that are continuous homogeneous of degree one translative and monotonic is presented further applications to utility theory and social choice theory are also provided

on the structure of a sofic shift space the structure of a sofic shift space is investigated and krieger s embedding theorem and boyle s factor theorem are generalized to a large class of sofic shifts

sofic shifts with synchronizing presentations abstract a sofic shift s is a symbolic dynamical system that can be viewed as a set of all bi infinite sequences obtained by reading the labels of all bi infinite paths in a finite directed labeled graph g the presentation g is synchronizing if for every vertex v there is a word x v such that every path in g labeled with x v has v as a terminal vertex we present an example of a subshift of finite type that has no unique minimal deterministic presentation and we show that if a sofic shift has a synchronizing deterministic presentation sdp then it has a unique minimal one irreducible sofic shifts subshifts of finite type and nonwandering systems have synchronizing deterministic presentations we give an intrinsic characterization of a sofic shift s that has an sdp in terms of the syntactic monoid m s of the factor language f s of s another characterization of sofic shifts with sdp s is given in terms of the predecessor sets we show that a sofic shift can have at most one bi synchronizing presentation

the method of poles a coding method for constrained channels a method for solving coding problems involving channels restricted by finite state constraints is presented the method was introduced by p a franaszek 1969 and is based on the computation of a set of principal states it is proved that state independent decoding is guaranteed the main result is that the transducer constructed using the method is a local automaton in its output the method is also related to recent work in symbolic dynamics by r l adler 1987 b marcus 1985 and others typical applications are coding methods for magnetic storage

the dynamics of group codes state spaces trellis diagrams and canonical encoders a group code c over a group g is a set of sequences of group elements that itself forms a group under a component wise group operation a group code has a well defined state space sigma sub k at each time k each code sequence passes through a well defined state sequence the set of all state sequences is also a group code the state code of c the state code defines an essentially unique minimal realization of c the trellis diagram of c is defined by the state code of c and by labels associated with each state transition the set of all label sequences forms a group code the label code of c which is isomorphic to the state code of c if c is complete and strongly controllable then a minimal encoder in controller canonical feedbackfree form may be constructed from certain sets of shortest possible code sequences called granules the size of the state space sigma sub k is equal to the size of the state space of this canonical encoder which is given by a decomposition of the input groups of c at each time k if c is time invariant and nu controllable then mod sigma sub k mod pi sub 1

rotationally invariant nonlinear trellis codes for two dimensional modulation a general parity check equation is presented that defines rotationally invariant trellis codes of rate k k 1 for two dimensional signal sets this parity check equation is used to find rate k k 1 codes for 4psk 8psk 16psk and qam signal sets by systematic code searches the mpsk codes exhibit smaller free euclidean distances than nonrotationally invariant linear codes with the same number of states however since the nonlinear codes have a smaller number of nearest neighbors their performance at moderate signal to noise ratios is close to that of the best linear codes the rotationally invariant qam codes with 8 32 64 and 256 states achieve the same free euclidean distance as the best linear codes transparency of user information under phase rotations is accomplished either by conventional differential encoding and decoding or by integrating this function directly into the code trellis

determining presentations of sofic shifts a sofic shift is a symbolic dynamical system which consists of all sequences of labels occurring in bi infinite paths in a finite labelled directed graph the graph defines a presentation of the sofic shift determining presentations of a sofic shift s are a generalization of resolving or deterministic presentations the collection of minimal determining presentations is a conjugacy invariant of s we give a procedure for constructing all minimal determining presentations of an irreducible sofic shift which is a generalization of the construction of the fischer covers of s

codes circulaires automates locaux et entropie abstract the theory of codes and finite automata is applied to prove the existence of codes suitable for coding arbitrary sequences into a constrained system of sequences called system of finite type the techniques are different from those used by adler coppersmith hassner and marcus in earlier work on the same problem

on the existence of open and bi continuing codes given an irreducible sofic shift x we show that an irreducible shift of finite type y of lower entropy is a factor of x if and only if it is a factor of x by an open bi continuing code if these equivalent conditions hold and y is mixing then any code from a proper subshift of x to y can be extended to an open bi continuing code on x these results are still valid when x is assumed to be only an almost specified shift i e a subshift satisfying an irreducible version of the specification property

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

determining merged relative scores the starting point in this paper is the following type of situation performances of people or technologies are measured by their scores with respect to different benchmarks relative to those of some base performance in order to arrive at a decision one wants to merge average aggregate the scores of each individual or technology into a single number which can then be compared with that of another individual or technology the situation is similar at least technically to price indices where present prices of different products are considered relative to prices of these products in a base year and we again want to merge these into one number in this paper one solves most of these problems one also states a few problems which are still open

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

characterization of weighted maximum and some related operations abstract the complete characterization of weighted maximum and minimum operations as well as the ordered weighted maximum and minimum is established the results are obtained via stability properties of the operations these properties are expressed by functional equations solutions of these equations correspond to the studied operations

conjoint axiomatization of min discrimin and leximin in many multi criteria decision making applications the preferential information is of an ordinal nature and appropriate aggregation procedures should be used in this paper we build a common axiomatic framework to characterize the minimum procedure as well as two of its refinements the discrimin and the leximin in practical situations this axiomatic framework could help to select the best suited procedure

a note on the shannon capacity of run length limited codes corresp it is proven that 100 percent efficient fixed rate codes for run length limited rll d k and rll charge constrained d k c channels are possible in only two eases namely d k c 0 1 1 and 1 3 3 specifically the binary shannon capacity of rll d k constrained systems is shown to be irrational for all values of d k 0 leq d for rll charge constrained systems with parameters d k c the binary capacity is irrational for all values of d k c 0 leq d except 0 1 1 and 1 3 3 which both have binary capacity 1 2

factor maps and invariant distributional chaos abstract the main aim of this article is to show that maps with the specification property have invariant distributionally scrambled sets and that this kind of scrambled set can be transferred from factor to extension under finite to one factor maps this solves some open questions in the literature of the topic we also show how our method can be applied in practice taking as example poincare map of time periodic nonautonomous planar differential equation z v t z 1 e i t z 2 z 3 n where and n are sufficiently small positive real numbers

characterization of some aggregation functions stable for positive linear transformations abstract this paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems the common properties involved in these characterizations are increasing monotonicity and stability for positive linear transformations additional algebraic properties related to associativity allow to completely specify the functions

merging relative scores abstract this paper considers the problem of scoring alternative technologies based on their performance on different benchmarks normalizing the scores relative to those of a base technology and then finding a merged or combined score based on the normalized or relative scores similar problems occur if we score alternative job candidates or students on the basis of different tests or criteria and seek to merge relative scores after normalization they also occur when we obtain index numbers such as price indices here we measure different items at different times normalize relative to some base time and merge the relative measures of the different items obtained at a fixed time we attempt to identify merging methods which will guarantee that certain types of conclusions based on them will be invariant if the base technology job candidate student or time is changed

codes and local constraints etude du probleme de l existance et de la construction de codes dont les elements des mots satisfont certaines contraintes concernant les sequences de lettres qu ils peuvent contenir l equivalence entre les notions de maximalite et de completude pour ces codes est etudiee

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

a first approach to fuzzy differential game problem guarding a territory abstract in this paper the fuzzy differential game problem is proposed and the problem of guarding a territory is considered we reformulate this differential game problem by considering that the locations of the territory and or of one s opponent are imprecisely known to the players thus treating them as fuzzy information a fuzzy control strategy is proposed for this fuzzy differential game problem it will be seen that in the limiting case the result of the fuzzy differential game problem approaches that of the unfuzzified case some computer simulation results are provided in this paper