pushdown automata multiset automata and petri nets in this paper we consider various classes of infinite state automata generated by simple rewrite transition systems these classes are defined by two natural hierarchies one given by interpreting concatenation of symbols in the rewrite system as sequential composition and the other by interpreting concatenation as parallel composition in this way we provide natural definitions for commutative parallel context free automata multiset parallel or random access pushdown automata and petri nets we provide example automata which demonstrate the strictness of this hierarchy in particular we provide a proof of an earlier conjecture by moller that multiset automata form a proper subset of petri nets this result contrasts with the result of caucal for the analogous question in the sequential case where the hierarchy collapses

entropy sensitivity of languages defined by infinite automata via markov chains with forbidden transitions a language l over a finite alphabet is growth sensitive or entropy sensitive if forbidding any finite set of factors f of l yields a sublanguage lf whose exponential growth rate entropy is smaller than that of l let x e be an infinite oriented edge labelled graph with label alphabet considering the graph as an infinite automaton we associate with any pair of vertices x y x the language lx y consisting of all words that can be read as labels along some path from x to y under suitable general assumptions we prove that these languages are growth sensitive this is based on using markov chains with forbidden transitions

automorphism groups of context free graphs abstract we give a characterization of the automorphism group of context free graphs this kind of graphs was introduced by muller and schupp as transition graphs of pushdown automata the automorphism group of a context free graph is proved to be finitely generated if and only if the stabilizer of a vertex is finite in particular it is true for deterministic graphs an algorithm is given to construct a set of generators it is then shown that a finitely generated group is context free if and only if it is the automorphism group of a deterministic rooted context free graph

cellular automata between sofic tree shifts we study the sofic tree shifts of a s where s is a regular rooted tree of finite rank in particular we give their characterization in terms of unrestricted rabin automata we show that if x a s is a sofic tree shift then the configurations in x whose orbit under the shift action is finite are dense in x and as a consequence of this we deduce that every injective cellular automata t x x is surjective moreover a characterization of sofic tree shifts in terms of general rabin automata is given we present an algorithm for establishing whether two unrestricted rabin automata accept the same sofic tree shift or not this allows us to prove the decidability of the surjectivity problem for cellular automata between sofic tree shifts we also prove the decidability of the injectivity problem for cellular automata defined on a tree shift of finite type

modular strategies for recursive game graphs many problems in formal verification and program analysis can be formalized as computing winning strategies for two player games on graphs in this paper we focus on solving games in recursive game graphs which can model the control flow in sequential programs with recursive procedure calls while such games can be viewed as the pushdown games studied in the literature the natural notion of winning in our framework requires the strategies to be modular with only local memory that is resolution of choices within a module does not depend on the context in which the module is invoked but only on the history within the current invocation of the module while reachability in global pushdown games is known to be exptime complete we show reachability in modular games to be np complete we present a fixed point computation algorithm for solving modular games such that in the worst case the number of iterations is exponential in the total number of returned values from the modules if the strategy within a module does not depend on the global history but can remember the history of the past invocations of this module that is if memory is local but persistent we show that reachability becomes undecidable

on 2d elliptic discontinuous galerkin methods we discuss the discretization using discontinuous galerkin dg formulation of an elliptic poisson problem two commonly used dg schemes are investigated the original average flux proposed by bassi and rebay j comput phys 1997 131 267 and the local discontinuous galerkin ldg siam j numer anal 1998 35 2440 2463 scheme in this paper we expand on previous expositions discontinuous galerkin methods theory computation and applications springer berlin 2000 135 146 siam j sci comput 2002 24 2 524 547 int j numer meth engng 2003 58 2 1119 1148 by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the dg method through consideration of standard c0 type expansion bases as opposed to elementally orthogonal expansions with the matrix formulation we are able to apply static condensation techniques to improve efficiency of the direct solver when high order expansions are adopted the use of c0 type expansions also permits the direct enforcement of dirichlet boundary conditions through a lifting approach where the ldg flux does not require further stabilization in our construction we also adopt a formulation of the continuous dg fluxes that permits a more general interpretation of their numerical implementation in particular it allows us to determine the conditions under which the ldg method provides a near local stencil finally a study of the conditioning and the size of the null space of the matrix systems resulting from the dg discretization of the elliptic problem is undertaken copyright 2005 john wiley sons ltd

the compact discontinuous galerkin cdg method for elliptic problems we present a compact discontinuous galerkin cdg method for an elliptic model problem the problem is first cast as a system of first order equations by introducing the gradient of the primal unknown or flux as an additional variable a standard discontinuous galerkin dg method is then applied to the resulting system of equations the numerical interelement fluxes are such that the equations for the additional variable can be eliminated at the element level thus resulting in a global system that involves only the original unknown variable the proposed method is closely related to the local discontinuous galerkin ldg method b cockburn and c w shu siam j numer anal 35 1998 pp 2440 2463 but unlike the ldg method the sparsity pattern of the cdg method involves only nearest neighbors also unlike the ldg method the cdg method works without stabilization for an arbitrary orientation of the element interfaces the computation of the numerical interface fluxes for the cdg method is slightly more involved than for the ldg method but this additional complication is clearly offset by increased compactness and flexibility compared to the br2 f bassi and s rebay j comput phys 131 1997 pp 267 279 and ip j douglas jr and t dupont in computing methods in applied sciences second internat sympos versailles 1975 lecture notes in phys 58 springer berlin 1976 pp 207 216 methods which are known to be compact the present method produces fewer nonzero elements in the matrix and is computationally more efficient

a new proof of the howe conjecture let j q denote the space of g invariant distributions supported on ad g9 q if g e g set ad g f z f f g zg if q is a locally constant compactly supported function on g resp g define tq q to be the linear functional on j q defined by tq o t t 0 the set q will be fixed throughout the paper so we will abbreviate tq to t the g invariance of the distributions in j q means t ad g f t f if l is a compact open subgroup of g denote as c g l the space of compactly supported functions on g which are right l invariant similary if l is an open compact lattice in g let c g l be the space of compactly supported functions on g which are l invariant in hol howe conjectured that if q is a compact subset of g resp 9 then the restriction of the distributions in j q to c b l resp c g l is finite dimensional a more common formulation of the group version of the howe conjecture replaces the space c g l with the hecke algebra 7 g l of compactly supported l biinvariant functions on g since 7 g l c c g l apriori our formulation with c g l implies the hecke algebra formulation it is a simple matter to show that in fact the two formulations are equivalent if f e c 9 l then the function f g lf kgk 1 dk belongs to the hecke algebra and the map f 1 f is a surjection the linear functional on j q induced by f is a positive multiple of the linear functional induced by f thus the two spaces of linear functionals are equal and so the two formulations are equivalent

free products in r thompson s group v we investigate some product structures in r thompson s group v primarily by studying the topological dynamics associated with v s action on the cantor set c we draw attention to the class d v c of groups which have embeddings as demonstrative subgroups of v which class can be used to assist in forming various products note that d v c contains all finite groups the free group on two generators and q z and is closed under passing to subgroups and under taking direct products of any member by any finite member if g v and h d v c then g oh embeds into v finally if g h d v c then g h embeds in v using a dynamical approach we also show the perhaps surprising result that z z does not embed in v even though v has many embedded copies of z and has many embedded copies of free products of various pairs of its subgroups

time implicit high order discontinuous galerkin method with reduced evaluation cost an efficient and robust time integration procedure for a high order discontinuous galerkin method is introduced for solving nonlinear second order partial differential equations the time discretization is based on an explicit formulation for the hyperbolic term and an implicit formulation for the parabolic term the procedure uses an iterative algorithm with reduced evaluation cost the size of the linear system to be solved is greatly reduced thanks to partial uncoupling in space between low order and high order degrees of freedom numerical examples are presented for the nonlinear convection diffusion equation in one and two dimensions including steady and unsteady flow problems the performance of the present method is investigated in terms of cpu time and compared to a fully implicit method a von neumann stability analysis is carried out in order to determine the stability and damping properties of the method besides a fairly reduced cpu effort numerical results demonstrate better convergence properties of the present algorithm when compared to the fully implicit method

alternating automata the weak monadic theory of trees and its complexity beginning with the fundamental article of chandra et al 2 the notation of alternation has clarified several results concerning the complexity of logical theories muller and schupp 9 extended the idea of alternation to automata working on trees although such automata are a generalization of rabin s model 12 of nondeterministic automata working on infinite trees complementation and thus all boolean operations are easy for such automata in particular complementation costs no extra states there is of course no free lunch and in the alternating model one must pay for projection thus alternating automata do not give a simple proof of rabin s fundamental theorem 12 on the decidability of the full monadic theory of the tree indeed one must appeal to the powerful forgetful determinacy theorem of gurevitch and harrington 3 to show that alternating automata can be simulated by nondeterministic rabin automata

parabolic transfer for real groups this paper is the second of two articles in real harmonic analysis in the first paper a14 we established asymptotic formulas for some natural distributions on a real group in this paper we shall establish important relationships among the distributions as the group varies the group is the set of real points of a connected reductive group g over r the distributions are weighted orbital integrals jm f on g r and their invariant counterparts im f here m g is a levi subgroup of g while mg reg r is a strongly g regular conjugacy class in m r the relationships are defined by the invariant transfer of functions on g r to functions attached to endoscopic groups of g this necessitates our working with the invariant distributions im f we refer the reader to the introduction of a14 for some general remarks on these objects the distributions im f are the generic archimedean terms in the invariant trace formula we cannot review the trace formula here the reader might consult the introductions to a13 and its two predecessors for a brief summary the purpose of the paper a13 was to stabilize the invariant trace formula subject to a condition on the fundamental lemma that has been established in some special cases the stable trace formula is a milestone of sorts it is expected to lead to reciprocity laws which relate fundamental arithmetic data attached to automorphic representations on different groups the stable trace formula of a13 relies upon the results of this paper as well as a paper a16 in preparation this has been our guiding motivation the relevant identities among the nonarchimedean forms of the distributions im f were actually established in a13 they were a part of the global argument that culminated in the stable trace formula as such they are subject to the condition on the fundamental lemma mentioned above our goal here is to establish the outstanding archimedean identities we shall do so by purely local means which are independent of the fundamental lemma to simplify the introducton we assume that the derived group of g is simply connected the identities then relate the invariant distributions ong r with stable distributions on endoscopic groups g r we recall that a stable distribution on g r depends only on the average values assumed by a test function over strongly regular stable conjugacy classes in greg r which is to say intersections of g reg r

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

simulation preorder over simple process algebras we consider the problem of simulation preorder equivalence between infinite state process and finite state ones first we describe a general method how to utilize the decidability of bisimulation problems to solve certain instances of the corresponding simulation problems for certain process classes the method allows us to design effective reductions of simulation problems to their bisimulation counterparts and some new decidability border for the problem of simulation preorder equivalence are decidable in exptime between pushdown and finite state ones on the other hand simulation preorder is undecidable between pa and finite state process in both directions these results also hold for those pa and finite state process which are deterministic and normed and trace equivalence is also shown to be undecidable for pa finally we prove that simulation preorder in both directions and simulation equivalence are interact able between all classes of infinite state systems in the hierarchy of process rewrite systems and finite state ones this result is obtained by showing that the problem whether a bpa or bpp process simulation a finite state one is pspace hard and the other direction is co np hard consequently simulation equivalence between bpa or bpp and finite state processes is also co np hard

fast time implicit explicit discontinuous galerkin method for the compressible navier stokes equations an efficient and robust time integration procedure for a high order discontinuous galerkin method is introduced for solving the unsteady compressible navier stokes equations the time discretization is based on an explicit formulation for the convective fluxes and an implicit formulation for the viscous fluxes the implicit procedure uses a fast iterative algorithm based on a partial uncoupling of variables in neighboring elements introduced in previous works by the authors in the present work the method is associated to a newton krylov jacobian free method this association allows to reduce memory requirements and operation counts by avoiding the complete construction of the jacobian matrix and solving a problem of reduced size numerical examples in two space dimensions indicate that the performance of the present method is seen to be significantly improved in terms of cpu time

context free event domains are recognizable the possibly non distributive event domains which arise from winskel s event structures with binary conflict are known to coincide with the domains of configurations of stark s trace automata we prove that whenever the transitive reduction of the order on finite elements in an event domain is a context free graph in the sense of muller and schupp the event domain may also be generated from a finite trace automaton where both the set of states and the concurrent alphabet are finite we show that the set of graph grammars which generate event domains is a recursive set we obtain altogether an effective procedure which decides from an unlabeled graph grammar whether it generates an event domain and which constructs in that case a finite trace automaton recognizing that event domain

on distinguished square integrable representations for galois pairs and a conjecture of prasad we prove an integral formula computing multiplicities of square integrable representations relative to galois pairs over p adic fields and we apply this formula to verify two consequences of a conjecture of dipendra prasad one concerns the exact computation of the multiplicity of the steinberg representation and the other the invariance of multiplicities by transfer among inner forms

infinite hypergraphs i basic properties abstract basic properties of the category of infinite directed hyperedge labelled hypergraphs are studied an algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions it is then shown that two expressions define the same hypergraphs if and only if they are congruent with respect to some rewriting system these results will be used in the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions

fundamental study the modular decomposition of countable graphs definition and construction in monadic second order logic we consider the notion of modular decomposition for countable graphs the modular decomposition of a graph given with an enumeration of its set of vertices can be defined by formulas of monadic second order logic another result is the definition of a representation of modular decompositions by low degree relational structures such relational structures can also be defined in the considered graph by monadic second order formulas

pushdown processes a pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton a winning condition in such a game is defined in terms of states appearing infinitely often in the play it is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton an exptime procedure for finding a winner in a pushdown game is presented the procedure is then used to solve the model checking problem for the pushdown processes and the propositional calculus the problem is shown to be dexptime complete

generalized orbital integrals of some euler poincare functions of a reductive p adic group abstract schneider and stuhler have defined euler poincare functions of irreducible representations of reductive p adic groups and calculated their orbital integrals orbital integrals belong to a larger family of invariant distributions appearing in the geometric side of the arthur selberg trace formula we calculate the value of these distributions on the euler poincare functions of tempered representations using the arthur local trace formula

cfl condition and boundary conditions for dgm approximation of convection diffusion we propose a general method for the design of discontinuous galerkin methods dgms for nonstationary linear equations the method is based on a particular splitting of the bilinear forms that appear in the weak dgm we prove that an appropriate time splitting gives a stable linear explicit scheme whatever the order of the polynomial approximation numerical results are presented

the dimensions of spaces of siegel cusp forms of general degree abstract in this paper we give a dimension formula for spaces of siegel cusp forms of general degree with respect to neat arithmetic subgroups the formula was conjectured before by several researchers cf 40 43 45 75 the dimensions are expressed by special values of shintani zeta functions for spaces of symmetric matrices at non positive integers this formula was given by shintani for only a small part of the geometric side of the trace formula see 64 to be precise it is the contribution of unipotent elements corresponding to the partitions 2 j 1 2 n 2 j where n denotes the degree and 0 j n hence our work is to show that all the other contributions vanish therefore one finds that shintani s formula means the dimension itself combining our formula and an explicit formula of the shintani zeta functions which was discovered by ibukiyama and saito cf 44 42 61 we can derive an explicit dimension formula for the principal congruence subgroups of level greater than two cf 43 45 in this explicit dimension formula the dimensions are described by degree n weight k level n and the bernoulli numbers b m

inverse monoids trees and context free languages this paper is concerned with a study of inverse monoids presented by a set x subject to relations of the form e i f i i i where e i and f i are dyck words i e idempotents of the free inverse monoid on x some general results of stephen are used to reduce the word problem for such a presentation to the membership problem for a certain subtree of the cayley graph of the free group on x in the finitely presented case the word problem is solved by using rabin s theorem on the second order monadic logic of the infinite binary tree some connections with the theory of rational subsets of the free group and the theory of context free languages are explored

growth sensitivity of context free languages a language l over a finite alphabet is called growth sensitive if forbidding any set of subwords f yields a sub language lf whose exponential growth rate is smaller than that of l it is shown that every essentially ergodic non linear context free language of convergent type is growth sensitive ergodic means that the dependency di graph of the generating context free grammar is strongly connected and essentially ergodic means that there is only one nonregular strong component in that graph the methods combine 1 an algorithm for constructing from a given grammar one that generates the associated 2 block language and 2 a generating function technique regarding systems of algebraic equations furthermore the algorithm of 1 preserves unambiguity as well as the number of non regular strong components of the dependency di graph

complexity results on branching time pushdown model checking the model checking problem of pushdown systems pmc problem for short against standard branching temporal logics has been intensively studied in the literature in particular for the modal m calculus the most powerful branching temporal logic used for verification the problem is known to be exptime complete even for a fixed formula the problem remains exptime complete also for the logic ctl which corresponds to a fragment of the alternation free modal m calculus for the logic ctl the problem is known to be in 2exptime in this paper we show that the complexity of the pmc problem for ctl is in fact 2exptime complete moreover we give a new optimal algorithm to solve this problem based on automata theoretic techniques finally we prove that the program complexity of the pmc problem against ctl i e the complexity of the problem in terms of the size of the system is exptime complete

discrete series characters and the lefschetz formula for hecke operators this paper consists of three independent but related parts in the rst part xx1 6 we give a combinatorial formula for the constants appearing in the numerators of characters of stable discrete series representations of real groups see x3 as well as an analogous formula for individual discrete series representations see x6 moreover we give an explicit formula theorem 5 1 for certain stable virtual characters on real groups by theorem 5 2 these include the stable discrete series characters and thus we recover the results of x3 in a more natural way in the second part x7 we use the character formula given in theorem 5 1 to rewrite the lefschetz formula of gm for the local contribution at a single xed point component to the trace of a hecke operator on weighted cohomology in the same spirit as that of arthur s lefschetz formula a in terms of stable virtual characters on real groups see theorem 7 14 b we then sum the contributions of the various xed point components and show that in the case of middle weighted cohomology the resulting global lefschetz xed point formula agrees with arthur s lefschetz formula this gives a topological proof of arthur s formula

infinite hypergraphs ii systems of recursive equations abstract the results and tools which were developed in part i of this paper 4 are used to solve systems of recursive equations on hypergraphs and to characterize their solutions completely a hypergraph s initial solutions are called equational hypergraphs it is then shown that the context free graphs of muller and schupp 15 are equational

on infinite transition graphs having a decidable monadic theory we define a family of graphs whose monadic theory is in linear space reducible to the monadic theory s2s of the complete ordered binary tree this family contains strictly the context free graphs investigated by muller and schupp and also the equational graphs defined by courcelle using words as representations of vertices we give a complete set of representatives by prefix rewriting of rational languages this subset of possible representatives is a boolean algebra preserved by transitive closure of arcs and by rational restriction on vertices

inverse monoids decidability and complexity of algebraic questions this paper investigates the word problem for inverse monoids generated by a set c subject to relations of the form e f where e and f are both idempotents in the free inverse monoid generated by c it is shown that for every fixed monoid of this form the word problem can be solved both in linear time on a ram as well as in deterministic logarithmic space which solves an open problem of margolis and meakin for the uniform word problem where the presentation is part of the input exptime completeness is shown for the cayley graphs of these monoids it is shown that the first order theory with regular path predicates is decidable regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language as a corollary the decidability of the generalized word problem is deduced

on groups whose word problem is solved by a counter automaton we prove that a group g has a word problem that is accepted by a deterministic counter automaton with a weak inverse property if and only if g is virtually abelian we extend this result to larger classes of groups by considering a generalization of finite state automata counter automata and pushdown automata natural corollaries of our general result include a restricted version of herbst s classification of groups for which the word problem is a one counter language and a new classification of automata that accept context free word problems

verification of qualitative z constraints we introduce an ltl like logic with atomic formulae built over a constraint language interpreting variables in z the constraint language includes periodicity constraints and comparison constraints of the form x y and x

the bisimulation problem for equational graphs of finite out degree the bisimulation problem for equational graphs of finite out degree is shown to be decidable we reduce this problem to the eta bisimulation problem for deterministic rational vectors of boolean series on the alphabet of a deterministic pushdown automaton cal m we then exhibit a complete formal system for deducing equivalent pairs of such vectors

on the differential equations satisfied by weighted orbital integrals weighted orbital integrals are distributions on reductive groups over local fields appearing both in the local and global trace formulas there are associated invariant distributions which play the same role in the invariant trace formulas in the case of real groups the fourier transforms of these distributions satisfy a system of differential equations as a step towards determining those fourier transforms we show that this system is holonomic and has a simple singularity at infinity we deduce that any solution has a series expansion and is a linear combination of certain canonical solutions for some groups of small rank we solve the recursion formula for the coefficients explicitly

the theory of ends pushdown automata and second order logic abstract a class of edge labeled graphs called context free are defined according to their behavior at infinity such graphs are generalizations of cayley graphs of context free groups they are also shown to be definable in a very natural way in terms of push down automata using rabin s theorem on the monadic second order theory of the finite binary tree these graphs are also shown to have a decidable monadic second order theory questions about tiling systems and cellular automata operating on these graphs are decidable even when the analogous questions are not when the systems operate on a two dimensional grid

growth and ergodicity of context free languages a language l over a finite alphabet e is called growth sensitive if forbidding any set of subwords f yields a sublanguage l f whose exponential growth rate is smaller than that of l it is shown that every ergodic unambiguous nonlinear context free language is growth sensitive ergodic means for a context free grammar and language that its dependency di graph is strongly connected the same result as above holds for the larger class of essentially ergodic context free languages and if growth is considered with respect to the ambiguity degrees then the assumption of unambiguity may be dropped the methods combine a construction of grammars for 2 block languages with a generating function technique regarding systems of algebraic equations

on complexity functions of infinite words associated with generalized dyck languages in this article we construct a family of infinite words generated by countable automata and also generated by substitutions over infinite alphabets closely related to parenthesis languages and we study their complexity functions we obtain a family of binary infinite words m b indexed on the number b 1 of parenthesis types such that the growth order of the complexity function of m b is n logn 2 if b 1 and n 1 l o g 2 b b if b 2

stable viscosity matrices for systems of conservation laws abstract a natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension u 1 f u x 0 u r m is studied these matrices are admissible in the sense that small amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system u t f u x v du x x as ifv 0 if d is in this class the class is determined by a linearized stability requirement the cauchy problem for the equation u 1 f u 0 u x vdu xx should be well posed in l 2 uniformly in v as v 0 previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion

word problems of groups formal languages characterizations and decidability abstract let g be a group and let g be a monoid homomorphism from the set of all strings over some finite alphabet onto the group g the set is then called a generating set for g and the language 1 1 is called the word problem of g with respect to the generating set via the homomorphism and is denoted by w g we consider nine conditions that hold in each such language of the form w g and determine which combinations of these conditions are equivalent to the property of the language in question being the word problem of a group we show that each of these nine conditions is decidable for the family of regular languages but that each is undecidable for the family of one counter languages the languages accepted by one counter pushdown automata we also show that the property of a language being the word problem of a group is undecidable for the family of one counter languages but is decidable for the family of deterministic context free languages the languages accepted by deterministic pushdown automata

deciding bisimulation like equivalences with finite state processes we show that characteristic formulae for finite state systems up to bisimulation like equivalences e g strong and weak bisimilarity can be given in the simple branching time temporal logic ef since ef is a very weak fragment of the modal mu calculus model checking with ef is decidable for many more classes of infinite state systems this yields a general method for proving decidability of bisimulation like equivalences between infinite state processes and finite state ones we apply this method to the class of pad processes which strictly subsumes pa and pushdown pda processes showing that a large class of bisimulation like equivalences including e g strong and weak bisimilarity is decidable between pad and finite state processes on the other hand we also demonstrate that no reasonable bisimulation like equivalence is decidable between state extended pa processes and finite state ones furthermore weak bisimilarity with finite state processes is shown to be undecidable even for state extended bpp which are also known as parallel pushdown processes

the large scale geometry of strongly aperiodic subshifts of finite type abstract a subshift on a group g is a closed g invariant subset of a g for some finite set a it is said to be a subshift of finite type sft if it is defined by a finite collection of forbidden patterns to be strongly aperiodic if all point stabilizers are trivial and weakly aperiodic if all point stabilizers are infinite index in g we show that groups with at least 2 ends have a strongly aperiodic sft and that having such an sft is a qi invariant for finitely presented groups we show that a finitely presented torsion free group with no weakly aperiodic sft must be qi rigid the domino problem on g asks whether the sft specified by a given set of forbidden patterns is empty we show that decidability of the domino problem is a qi invariant

a stable trace formula iii proof of the main theorems this paper is the last of three articles designed to stabilize the trace formula our goal is to stabilize the global trace formula for a general connected group subject to a condition on the fundamental lemma that has been established in some special cases in the first article i we laid out the foundations of the process we also stated a series of local and global theorems which together amount to a stabilization of each of the terms in the trace formula in the second paper ii we established a key reduction in the proof of one of the global theorems in this paper we shall complete the proof of the theorems we shall combine the global reduction of ii with the expansions that were established in section 10 of i we refer the reader to the introduction of i for a general discussion of the problem of stabilization the introduction of ii contains further discussion of the trace formula with emphasis on the elliptic coefficients agll s these objects are basic ingredients of the geometric side of the trace formula

on the complexity of a family of k context free sequences we introduce a large family of k context free sequences for which we give a polynomial upper bound on their complexity functions