equilibrium existence theorems in kkm spaces abstract an abstract convex space satisfying the kkm principle is called a kkm space this class of spaces contains g convex spaces properly in this work we show that a large number of results in kkm theory on g convex spaces also hold on kkm spaces examples of such results are theorems of sperner and alexandroff pasynkoff fan browder type fixed point theorems horvath type fixed point theorems ky fan type minimax inequalities variational inequalities von neumann type minimax theorems nash type equilibrium theorems and himmelberg type fixed point theorems

equivalence of deterministic top down tree to string transducers is decidable we prove that equivalence of deterministic top down tree to string transducers is decidable thus solving a long standing open problem in formal language theory we also present efficient algorithms for subclasses for linear transducers or total transducers with unary output alphabet over a given top down regular domain language as well as for transducers with the single use restriction these results are obtained using techniques from multi linear algebra for our main result we introduce polynomial transducers and prove that for these validity of a polynomial invariant can be certified by means of an inductive invariant of polynomial ideals this allows us to construct two semi algorithms one searching for a certificate of the invariant and one searching for a witness of its violation via a translation into polynomial transducers we thus obtain that equivalence of general y dt transducers is decidable in fact our translation also shows that equivalence is decidable when the output is not in a free monoid but in a free group

fundamental study modular tree transducers abstract a new tree transducer called a modular tree transducer is introduced this device specifies operations on trees and can be considered as a formalization of the concept of nested simultaneous primitive recursion on trees roughly speaking a modular tree transducer is a special left linear and non overlapping term rewriting system of which the set of rules is partitioned into modules each module being equipped with a non negative integer the number of the module then a module with number i may call modules with numbers not less than i three properties are proved 1 modular tree transducers compute exactly the inductively defined class of primitive recursive functions on trees 2 the number of modules in modular tree transducers induces a strict hierarchy on the class of all modular tree transductions and 3 by appropriately restricting the calling structure between modules modular tree transducers characterize the compositions of macro tree transducers where the number of modules and the number of compositions coincide

approachability and fixed points for non convex set valued maps this paper studies the approachability of upper semicontinuous nonconvex set valued maps by single valued continuous functions and its applications to fixed point theory the use of approximate selections was initiated by j von neumann 41 in the proof of his well known minimax principle this remarkable property was extended to the normed space setting by cellina s and cellina and lasota 9 in the context of a degree theory for upper semicontinuous convex compact valued maps it also holds for maps with compact contractible values defined on finite polyhedra of iw ma cole11 40 and more generally defined on compact anrs mclennan 39 it was recently taken up by gbrniewicz granas and kryszewski 22 241 in the context of an index theory for non convex maps defined on compact anrs the content of this paper is divided into three parts the first part is devoted to background material concerning the types of spaces and set valued maps studied herein in the second part we define the abstract class d of approachable set valued maps that is the class of maps a x y

on solutions of generalized complementarity and eigenvector problems abstract from a new fan browder type fixed point theorem due to the second author we deduce an existence theorem for a solution of an equilibrium problem in section 3 this theorem is applied to generalized complementarity problems in section 4 and to eigenvector problems in section 5

fundamental properties of infinite trees infinite trees naturally arise in the formalization and the study of the semantics of programming languages this paper investigates some of their combinatorial and algebraic properties that are especially relevant to semantics

total diameter and area of closed submanifolds the total diameter of a closed planar curve c subset mathbf r 2 is the integral of its antipodal chord lengths we show that this quantity is bounded below by twice the area of c furthermore when c is convex or centrally symmetric the lower bound is twice as large both inequalities are sharp and the equality holds in the convex case only when c is a circle we also generalize these results to m dimensional submanifolds of mathbf r n where the area will be defined in terms of the mod 2 winding numbers of the submanifold about the n m 1 dimensional affine subspaces of mathbf r n

macro tree transducers attribute grammars and mso definable tree translations a characterization is given of the class of tree translations definable in monadic second order logic mso in terms of macro tree transducers the first main result is that the mso definable tree translations are exactly those tree translations realized by macro tree transducers mtts with regular look ahead that are single use restricted for this the single use restriction known from attribute grammars is generalized to mtts since mtts are closed under regular look ahead this implies that every mso definable tree translation can be realized by an mtt the second main result is that the class of mso definable tree translations can also be obtained by restricting mtts with regular look ahead to be finite copying i e to require that each input subtree is processed only a bounded number of times the single use restriction is a rather strong static restriction on the rules of an mtt whereas the finite copying restriction is a more liberal dynamic restriction on the derivations of an mtt

linear deterministic multi bottom up tree transducers in general top down and bottom up tree transducers lead to incomparable classes of tree transformations both for the nondeterministic and the deterministic case if deterministic top down tree transducers are extended by the capability to recognize regular tree properties and deterministic bottom up tree transducers are generalized by allowing states with arbitrary finite rank then the two devices now called deterministic top down tree transducers with regular look ahead and deterministic multi bottom up tree transducers respectively become equivalent z fulop a kuhnemann h vogler a bottom up characterization of deterministic top down tree transducers with regular look ahead inform process lett 91 2004 57 67 in this paper we focus on the class ld mbot of tree transformations which are computed by linear deterministic multi bottom up tree transducers we investigate the relationship among ld mbot and the classes of tree transformations computed by restricted deterministic bottom up tree transducers and by restricted deterministic top down tree transducers with regular look ahead in fact we show the inclusion diagram of nine such classes

fixed point theory for admissible multimaps defined on closed subsets of frechet spaces abstract this paper presents new fixed point results for a general class of maps defined on frechet spaces our results in particular apply to kakutani acyclic o neill approximable admissible with respect to gorniewicz and u c maps

new generalizations of basic theorems in the kkm theory abstract in the present paper we obtain a new kkm type theorem for intersectionally closed valued kkm maps and some useful new basic consequences typical examples of them are abstract forms of fan s matching theorem fan s geometric lemma the fan browder fixed point theorem maximal element theorems fan s minimax inequality variational inequalities and others

on the semi monotone operator theory and applications abstract in this paper eis a real banach space a e e e is a semi monotone operator we first study the variational inequality problem findu k such that a u u v u 0 wherek e is a closed convex subset then the operator equationa u u p and we also construct a degree theory for demi continuous semi monotone operators in reflexive banach spaces

definable transductions and weighted logics for texts a text is a word together with an additional linear order on it we study quantitative models for texts i e text series which assign to texts elements of a semiring we introduce an algebraic notion of recognizability following reutenauer and bozapalidis as well as weighted automata for texts combining an automaton model of lodaya and weil with a model of esik and nemeth after that we show that both formalisms describe the text series definable in a certain fragment of weighted logics as introduced by droste and gastin in order to do so we study certain definable transductions and show that they are compatible with weighted logics

on a generic property of geodesic flows in this paper we are concerned with a sufficient condition for a riemannian metric on a compact simply connected manifold to have infinitely many geometrically distinct closed geodesics 1969 gromoll meyer proved in gm that for every riemannian metric on a compact simply connected manifold m there are infinitely many geometrically distinct closed geodesics if the sequence bi m f i of betti numbers of the free loop space m is unbounded for some field f using the theory of minimal models vigue poirrier sullivan proved that the rational cohomology algebra h m i q of m is generated by a single element if and only if the sequence bi m i q i of betti numbers of the free loop space m of m is bounded it is a conjecture that the same statement holds for all fields of prime characteristic partial results are due to mccleary ziller mz and halperin vigue poirrier hv now we turn to the manifolds for which the hypothesis of gromoll meyer s theorem does not hold for example spheres and projective spaces then stability properties of the closed geodesics become important a closed geodesic is hyperbolic if the linearized poincare map has no eigenvalue of norm 1 from the bumpy metrics theorem due to abraham ab and anosov an2 and from a pertubation result due to klingenberg takens kt one can conclude a c4 generic metric on a compact manifold has either a non hyperbolic closed geodesic of twist type or all closed geodesics are hyperbolic in the first case there are infinitely many geometrically distinct closed geodesics in every tubular neighborhood of the closed geodesic of twist type due to a theorem by moser mo in the second case there are infinitely many closed geodesics if m is simply connected due to results by hingston hi and the author ra1 hence it follows from these results that a c4 generic metric on a compact simply connected manifold has infinitely many geometrically distinct closed geodesics we remark that it is an open question whether there is a riemannian metric on a simply connected compact manifold all of whose closed geodesics are hyperbolic in ra2 we show that the examples of metrics on the 2

sensitivity in mixed generalized vector quasiequilibrium problems with moving cones in this paper we consider a parametric generalized vector quasiequilibrium problem which is mixed in the sense that several different relations can simultaneously appear in this problem the moving cones and other data of the problem are assumed to be set valued maps defined in topological spaces and taking values in topological spaces or topological vector spaces the main result of this paper gives general verifiable conditions for the solution mapping of this problem to be semicontinuous with respect to a parameter varying in a topological space the result is proven with the help of notions of cone semicontinuity of set valued maps weaker than the usual concepts of semicontinuity and an assumption imposed on the set valued map whose values are the dual cones of the corresponding values of the moving cones

many endpoints and few interior points of geodesics in the sense of all except those in a set of first baire category the space of all convex surfaces in ir endowed with hausdorfl s metric is a baire space we shall see how abnormal convex surfaces may be by proving that most of them are so

farthest points on convex surfaces in the very enjoyable book 3 p 44 of craft falconer and guy we read we take a convex surface c in r3 steinhaus asked what can be said qualitatively about the set of all farthest points from a point x our aim here is to investigate this question let s be the space of all closed convex surfaces i e boundaries of open bounded convex sets in r3 and denote for any s s and x s by fx the set of all farthest points from x and by cx the set of all points joined with x by at least two segments i e shortest paths we shall see that to any point x on a closed convex surface we may associate in a natural way a point or a jordan arc jx fx lying in the cut locus of x this will provide the topological characterization of fx further we shall prove an easily stated remarkable geometric property of fx any three of its points if it contains at least three form an obtuse or right geodesic triangle moreover the preceding result is shown to hold for a large class of geodesic triangles with vertices in the cut locus interestingly the extreme case of a right triangle does not imply the degeneracy of the surface for the reader to be familiar with aleksandrov s book 1 see also 2 4 would be of considerable help the usual intrinsic metric of s s induced by the euclidean distance in r3 will be denoted by let x s and denote by ex the cut locus of x i e the set of all endpoints different from x of maximal by inclusion segments starting at x also let e be the set of all endpoints of s i e points not interior to any segment of s the set

transfer method for characterizing the existence of maximal elements of binary relations on compact or noncompact sets this paper systematically studies the existence of maximal elements for unordered binary relations on compact or noncompact sets in a general topological space this is done by developing a method called transfer method to derive various necessary and sufficient conditions that characterize the existence of maximal elements for a binary relation in terms of 1 generalized transitivity conditions under certain topological assumptions 2 topological conditions under certain generalized transitivity assumptions and 3 generalized convexity conditions under certain topological assumptions there are two basic approaches in the literature to prove the existence by providing sufficient conditions one assumes certain convexity and continuity conditions for a topological vector space and the other assumes certain weakened transitivity and continuity conditions for a general topological space the results unify those two aproaches and generalize almost all of the existing results in the literature

macro tree translations of linear size increase are mso definable the first main result is that if a macro tree translation is of linear size increase i e if the size of every output tree is linearly bounded by the size of the corresponding input tree then the translation is mso definable i e definable in monadic second order logic this gives a new characterization of the mso definable tree translations in terms of macro tree transducers they are exactly the macro tree translations of linear size increase the second main result is that given a macro tree transducer it can be decided whether or not its translation is mso definable and if it is then an equivalent mso transducer can be constructed similar results hold for attribute grammars which define a subclass of the macro tree translations

vector complementarity problems with a variable ordering relation in this paper we investigate vector complementarity problems with a variable ordering relation we establish existence results of a solution of a vector complementarity problem under an inclusive type condition we obtain equivalence results among a vector complementarity problem a vector variational inequality problem and other related problems

generalized vector complementarity type problems in topological vector spaces in this paper we introduced the generalized vector variational inequality type problem and the generalized vector complementarity type problem in the setting of topological vector space by utilizing a modified version of the fan kkm theorem we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption further we prove that solution sets of both the problems are equivalent to each other under some suitable conditions the results of this paper generalize and improve several results that appeared recently in the literature

on the symmetric vector quasi equilibrium problems abstract in this paper we using a particular technique consider the symmetric vector quasi equilibrium problems in the hausdorff topological vector space as applications of our existence theorem a coincidence point theorem and the existence of vector optimization problem for a pair of vector valued mappings are obtained moreover we answer an open question raised by fu in j y fu symmetric vector quasi equilibrium problems j math anal appl 285 2003 708 713

on the approximation of upper semi continuous correspondences and the equilibriums of generalized games in section 1 we explain some of the definitions and terminology that we use in section 2 we prove several theorems concerning the approximation of upper semi continuous correspondences having for range a locally convex space theorems 1 and 2 and corollary 1 generalize certain approximation theorems by g haddad 16 pp 1352213541 g haddad and j m lasry 17 pp 299 3001 and j p aubin and a cellina 2 pp 86891 see also f s de blasi lo and j m lasry and r robert 21 although some of the details of the proofs of theorems 1 and 2 are new the basic ideas are taken from the above mentioned papers theorem 3 shows that the correspondences in the approximating families can be chosen so that they are regular see section 1 this theorem see the remark following its proof contains a classical result of m hukuhara 18 pp 56573 theorem 3 is proved using theorem 2 and propositions 1 and 4 variants of propositions 2 3 and 4 were given in 193 in section 3 we give among others theorem 5 which concerns the existence of equilibriums of generalized games abstract economies the main purpose of this result is to replace the continuity hypothesis in the w shafer h sonnenschein equilibrium theorem for generalized games by an upper semi continuity one the proof of theorem 5 is based on the results on the approximation of upper semi continuous correspondences obtained in section 2 theorem 5 us used in section 4 in section 4 we establish theorems 6 and 7 these theorems show that certain statements concerning the equilibrium of generalized games are equivalent to certain statements concerning minimax inequalities of k fan type theorems 1 2 3 5 6 and 7 are the main results of this paper 267 0022 247x 88 3 00

fixed points for kakutani factorizable multifunctions abstract a multifunction is called a kakutani multifunction if there exist two nonempty convex sets x and y each in a hausdorff topological vector space such that x y is upper semi continuous with nonempty compact convex values we prove the following extension of the kakutani fixed point theorem let x x be a multifunction from a simplex x into itself if can be factorized by an arbitrary finite number of kakutani multifunctions then has a fixed point the proof relies on a simplicial approximation technique and the brouwer fixed point theorem extensions to infinite dimensional spaces and applications to game theory are given

a constructive method for abstract algebraic software specification abstract a constructive method for abstract algebraic software specification is presented where the operations are not implicitly specified by equations but by an explicit recursion on the generating operations of an algebra characterizing the underlying data structure the underlying algebra itself may be equationally specified since we cannot assume that all data structures will correspond to free algebras this implies that we distinguish between generating and defined operations and that the underlying algebra has a mechanism of well founded decomposition w r t the generating operations we show that the explicit specification of operations using so called structural recursive schemata offers advantages over purely equational specifications especially concerning the safeness of enrichments the ease of semantics description and the separation between the underlying data structure and the operations defined on it

geodesics on s2 and periodic points of annulus homeomorphisms we show that an area preserving homeomorphism of the open or closed annulus which has at least one periodic point must in fact have infinitely many interior periodic points a consequence is the theorem that every smooth riemannian metric ons2 with positive gaussian curvature has infinitely many distinct closed geodesics

geodesic flows with positive topological entropy twist maps and hyperbolicity we prove a perturbation lemma for the derivative of geodesic flows in high dimension this implies that a c 2 generic riemannian metric has a nontrivial hyperbolic basic set in its geodesic flow

on typical degenerate convex surfaces various properties are given concerning geodesics on and distance functions from points in typical degenerate convex surfaces i e surfaces obtained by gluing together two isometric copies of typical in the sense of baire category convex bodies by identifying the corresponding points of their boundaries

equilibria and fixed points of set valued maps with nonconvex and noncompact domains and ranges abstract let c be a nonempty subset of a topological vector space e we state and prove new various fixed point theorems of fan browder type for set valued maps f c 2 e such that c f c called expansive without assuming that the sets c and f c are convex or compact or equal and e is hausdorff let k be a convex subset of e and let c be a nonempty subset of k our proofs use a technique based on the investigations of the images of maps and restated for maps f c k r of g x z yuan s results concerning the existence of equilibrium points and minimax inequalities for maps f k k r examples are provided

the generating power of total deterministic tree transducer abstract attributed tree transducers are abstract models used to study properties of attribute grammars one abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input instead of derivation trees of a context free grammar in this paper we show that with respect to the generating power this is not an abstraction i e we show that attributed tree transducers and attribute grammars generate the same class of term or tree languages to prove this a number of results concerning the generating power of top down tree transducers are established which are interesting in their own we also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes the latter result is achieved by proving a hierarchy of classes of tree languages generated by context free hypergraph grammars with respect to their rank

simple closed geodesics on most alexandrov surfaces abstract we study the existence of simple closed geodesics on most in the sense of baire category alexandrov surfaces with curvature bounded below compact and without boundary we show that it depends on both the curvature bound and the topology of the surfaces

continuous selection and fixed point theorems in this paper we obtain continuous selection theorems with range in a g convex space or in a space related to a g convex space and noncompact domain some applications to fixed point theorems and coincidence theorems are given we obtain some new results as well as generalizations of many known results

the existence of solutions for the system of vector quasi equilibrium problems in topological order spaces abstract this paper introduces two kinds of quasiconcave mappings which are different from the usual quasiconcave function we establish a result for the existence of solutions for the system of vector quasi equilibrium problems in the frame of topological order by providing a maximal elements version of the well known browder fixed points theorem

symmetric vector quasi equilibrium problems the symmetric vector quasi equilibrium problem is introduced under suitable assumptions the symmetric vector quasi equilibrium problem is solvable as its applications a coincidence point theorem and the existence of vector optimization problem for a pair of vector valued mappings are reduced

curve shortening and the topology of closed geodesics on surfaces we study flat knot types of geodesics on compact surfaces m2 for every flat knot type and any riemannian metric g we introduce a conley index associated with the curve shortening flow on the space of immersed curves on m2 we conclude existence of closed geodesics with prescribed flat knot types provided the associated conley index is nontrivial

recent results in analytical fixed point theory we survey recent results in analytical fixed point theory firstly we state resolutions of long standing problems in infinite dimensional topology the schauder conjecture the compact ar problem and the banach problem on the hilbert cube secondly we list some fixed point theorems on kakutani maps generalized upper hemicontinuous maps fan browder maps approximable maps acyclic maps and admissible or better admissible class b of maps some related results are also given

well posedness for convex symmetric vector quasi equilibrium problems abstract in this paper the notion of a generalized levitin polyak well posedness is defined for symmetric vector quasi equilibrium problems sufficient conditions are given for the generalized levitin polyak well posedness moreover it is shown that the results can be refined in the convex case

extreme points of the distance function on convex surfaces we first see that in the sense of baire categories many convex surfaces have quite large cut loci and infinitely many relative maxima of the distance function from a point then we find that on any convex surface all these extreme points lie on a single subtree of the cut locus with at most three endpoints finally we confirm both in the sense of measure and in the sense of baire categories steinhaus conjecture that almost all points admit a single farthest point on the surface

comments on abstract convexity structures on topological spaces abstract all results in some properties of abstract convexity structures on topological spaces by s w xiang and h yang s w xiang h yang some properties of abstract convexity structures on topological spaces nonlinear analysis 67 2007 803 808 and a further characteristic of abstract convexity structures on topological spaces by s w xiang and s xia s w xiang s xia a further characteristic of abstract convexity structures on topological spaces j math anal appl 335 2007 716 723 are shown to be consequences of known ones or can be stated in more general forms

optimal approximate fixed point results in locally convex spaces abstract let c be a convex subset of a locally convex space we provide optimal approximate fixed point results for sequentially continuous maps f c c first we prove that if f c is totally bounded then it has an approximate fixed point net next it is shown that if c is bounded but not totally bounded then there is a uniformly continuous map f c c without approximate fixed point nets we also exhibit an example of a sequentially continuous map defined on a compact convex set with no approximate fixed point sequence in contrast it is observed that every affine not necessarily continuous self mapping of a bounded convex subset of a topological vector space has an approximate fixed point sequence moreover we construct an affine sequentially continuous map from a compact convex set into itself without fixed points

spaces and maps approximation and fixed points abstract a general approximation property for topological spaces is studied in relation with fixed point theory for set valued maps a particular instance of this property is the admissibility in the sense of klee examples of convex sets of topological spaces equipped with a local topological convexity structure as well as general classes of approximative neighborhood retracts are shown to have this approximation property a general topological principle on the preservation of the fixed point property under this space approximation is proved it allows the passage from basic classes of spaces to more elaborate ones for general classes of nonconvex set valued maps

on multiple context free grammars abstract multiple context free grammars mcfg s is a subclass of generalized context free grammars introduced by pollard 1984 in order to describe the syntax of natural languages the class of languages generated by mcfg s called multiple context free languages or shortly mcfl s properly includes the class of context free languages and is properly included in the class of context sensitive languages first the paper presents results on the generative capacity of mcfg s and also on the properties of mcfl s such as formal language theoretic closure properties next it is shown that the time complexity of the membership problem for multiple context free languages is o ne where n is the length of an input string and e is a constant called the degree of a given mcfg head grammars hg s introduced by pollard and tree adjoining grammars tag s introduced by joshi et al 1975 are also grammatical formalisms to describe the syntax of natural languages the paper also presents the following results on the generative capacities of hg s tag s and 2 mcfg s which are a subclass of mcfg s 1 the class hl of languages generated by hg s is the same as the one generated by tag s 2 hl is the same as the one generated by left wrapping hg s or right wrapping hg s which is a proper subclass of hg s 3 hl is properly included in the one generated by 2 mcfg s as a corollary of 1 it is also shown that hl is a substitution closed full afl

fixed point theorems for better admissible multimaps on almost convex sets abstract we obtain new fixed point theorems on multimaps in the class b p defined on almost convex subsets of topological vector spaces our main results are applied to deduce various fixed point theorems coincidence theorems almost fixed point theorems intersection theorems and minimax theorems consequently our new results generalize well known works of kakutani fan browder himmelberg lassonde and others

strong vector f complementary problem and least element problem of feasible set abstract in this paper we introduce several classes of strong vector f complementary problems and give some existence results for these problems in banach spaces we also discuss the least element problems of feasible sets and present their relations with the strong vector f complementary problems

look ahead removal for total deterministic top down tree transducers top down tree transducers are a convenient formalism for describing tree transformations they can be equipped with regular look ahead which allows them to inspect a subtree before processing it in certain cases such a look ahead can be avoided and the transformation can be realized by a transducer without look ahead removing the look ahead from a transducer if possible is technically highly challenging for a restricted class of transducers with look ahead namely those that are total deterministic ultralinear and bounded erasing we present an algorithm that for a given transducer from that class 1 decides whether it is equivalent to a total deterministic transducer without look ahead and 2 constructs such a transducer if the answer is positive for the whole class of total deterministic transducers with look ahead we present a similar algorithm which assumes that a so called difference bound is known for the given transducer the designer of a transducer can usually also determine a difference bound for it

fixed point theorems for the ψ set contraction mapping on almost convex sets abstract in this paper we first discuss the properties of the almost convex subsets of a hausdorff topological vector space then in the setting of the almost convex sets we establish some fixed point theorems for the two k k m and b d type set valued mappings with either set contraction or 1 set contraction next we also establish new cycle point theorems for three set valued mappings our results generalize the results of chang et al t h chang c l yen kkm property and fixed point theorems j math anal appl 203 1996 224 235 and park s park fixed point theorems for better admissible multimaps on almost convex sets j math anal appl 329 2007 690 702

an operational and denotational approach to non context freeness the main result of this paper is a description of linguistically motivated non context free phenomena equivalently in terms of regular tree languages to express the recursive properties and both a logical and an operational perspective to establish the intended linguistic relations the result is exemplified with a particular non context free phenomenon namely cross serial dependencies in natural languages such as swiss german or dutch the logical description is specified in terms of binary monadic second order mso formulas and the operational description is achieved by means of a linear and non deleting macro tree transducer besides giving a grammatical presentation for the regular tree language we shall also specify an implementation in the form of a finite state tree automaton to emphasize the effectivity of our approach

tree transducers with external functions abstract in this paper we investigate the computational power of particular tree transducers viz macro tree transducers and attributed tree transducers the former tree transducers formalize the idea of syntax directed translation with the possibility of handling context the latter tree transducers can serve as a formal model for the reduction semantics of attribute grammars here we generalize these tree transducers by allowing the invocation of external functions during the usual rewriting process the main result of this paper is the characterization of macro tree transducers with external function calls in terms of attributed tree transducers with external function calls furthermore such tree transducers with external function calls induce in an obvious way two operators on the set of all classes of tree functions according to this point of view we define two classes of tree functions inductively in the same way as the class prec of primitive recursive tree functions except that the closure under the scheme of primitive recursion is replaced by the closure under macro tree transducers with external function calls and attributed tree transducers with external function calls respectively as a second result of this paper we prove that these two classes are equal to prec

attributed tree transducers cannot induce all deterministic bottom up tree transformations in this paper we give a deterministic bottom up tree transducer t and show that the tree transformation t induced by it can be induced by no attributed tree transducer

streaming tree transducers the theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as xml documents we introduce streaming tree transducers as an analyzable executable and expressive model for transforming unranked ordered trees and forests in a single pass given a linear encoding of the input tree the transducer makes a single left to right pass through the input and computes the output in linear time using a finite state control a visibly pushdown stack and a finite number of variables that store output chunks that can be combined using the operations of string concatenation and tree insertion we prove that the expressiveness of the model coincides with transductions definable using monadic second order logic mso existing models of tree transducers either cannot implement all mso definable transformations or require regular look ahead that prohibits single pass implementation we show a variety of analysis problems such as type checking and checking functional equivalence are decidable for our model