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

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

robust stability of a class of polynomials with coefficients depending multilinearly on perturbations necessary and sufficient conditions are given for robust stability of a family of polynomials each polynomial is obtained by a multilinearity perturbation structure restrictions on the multilinearity are involved but in contrast to existing literature these restrictions are derived from physical considerations stemming from analysis of a closed loop interval feedback system the main result indicates that all polynomials in the family of polynomials have their zeros in the strict left half plane if and only if two requirements are satisfied at each frequency the first requirement is the zero exclusion condition involving four kharitonov rectangles the second requirement is that a specially constructed theta 0 parameterized set of 16 intervals must cover the positive reals for each theta epsilon 0 2 pi

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

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

rank two acm bundles on the del pezzo threefold with picard number 3 abstract a del pezzo threefold f with maximal picard number is isomorphic to p 1 p 1 p 1 in the present paper we completely classify locally free sheaves e of rank 2 such that h i f e t 0 for i 1 2 and t z such a classification extends similar results proved by e arrondo and l costa regarding del pezzo threefolds with picard number 1

regularity and cohomological splitting conditions for vector bundles on multiprojective spaces abstract we give a definition of regularity on multiprojective spaces which is different from the definitions of hoffman and wang and costa and miro roig using this notion we prove some splitting criteria for vector bundles

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

the geometry of ulrich bundles on del pezzo surfaces abstract given a smooth del pezzo surface x d p d of degree d we isolate the essential geometric obstruction to a vector bundle on x d being an ulrich bundle by showing that an irreducible curve d of degree dr on x d represents the first chern class of a rank r ulrich bundle on x d if and only if the kernel bundle of the general smooth element of d admits a generalized theta divisor moreover we show that any smooth arithmetically gorenstein surface whose ulrich bundles admit such a characterization is necessarily del pezzo this result is applied to produce new examples of complete intersection curves with semistable kernel bundle and also combined with work of farkas musta and popa to relate the existence of ulrich bundles on x d to the minimal resolution conjecture for curves lying on x d in particular we show that a smooth irreducible curve d of degree 3r lying on a smooth cubic surface x 3 represents the first chern class of an ulrich bundle on x 3 if and only if the minimal resolution conjecture holds for the general smooth element of d

the representation type of segre varieties abstract the goal of this work is to prove that all segre varieties n 1 n s p n n i 1 s n i 1 1 unless the quadric surface in p 3 support families of arbitrarily large dimension and rank of simple ulrich and hence acm vector bundles therefore they are of wild representation type

cohomological characterization of vector bundles on grassmannians of lines abstract we introduce a notion of regularity for coherent sheaves on grassmannians of lines we use this notion to prove some extension of evans griffith criterion to characterize direct sums of line bundles we also give in the line of previous results by costa and miro roig a cohomological characterization of exterior and symmetric powers of the universal bundles of the grassmannian

ribbons and their canonical embeddings we study double structures on the projective line and on certain other varieties with a view to having a nice family of degenerations of curves and k3 surfaces of given genus and clifford index our main interest is in the canonical embeddings of these objects with a view toward green s conjecture on the free resolutions of canonical curves we give the canonical embeddings explicitly and exhibit an approach to determining a minimal free resolution

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

robust stability of polynomials with multilinear parameter dependence abstract the problem is studied of testing for stability a class of real polynomials in which the coefficients depend on a number of variable parameters in a multilinear way we show that the testing for real unstable roots can be achieved by examining the stability of a finite number of corner polynomials obtained by setting parameters at their extreme values while checking for unstable complex roots normally involves examining the real solutions of up to m 1 simultaneous polynomial equations where m is the number of parameters when m 2 this is an especially simple task

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

node rewriting in graphs and hypergraphs a categorical framework vertex rewriting in graphs is a very powerful mechanism which has been studied for quite a long time in this paper we eventually provide a categorical theory of vertex rewriting and show how it can extend in a uniform way to node and pattern rewriting mechanisms in hypergraphs copyright 2001 elsevier science b v

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

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 the genus and hartshorne rao module of projective curves in this paper optimal upper bounds for the genus and the dimension of the graded components of the hartshorne rao module of curves in projective n space are established this generalizes earlier work by hartshorne h and martin deschamps and perrin mdp special emphasis is put on curves in bf p 4 the first main result is a so called restriction theorem it says that a non degenerate curve of degree d geq 4 in bf p 4 over a field of characteristic zero has a non degenerate general hyperplane section if and only if it does not contain a planar curve of degree d 1 see th 1 3 then using methods of brodmann and nagel bounds for the genus and hartshorne rao module of curves in bf p n with non degenerate general hyperplane section are derived it is shown that these bounds are best possible in a very strict sense coupling these bounds with the restriction theorem gives the second main result for curves in bf p 4 then curves of maximal genus are investigated the betti numbers of their minimal free resolutions are computed and a description of all reduced curves of maximal genus in bf p n of degree geq n 2 is given finally all pairs d g of integers which really occur as the degree d and genus g of a non degenerate curve in bf p 4 are described

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

on the pseudoboundary of unstable polytopes of polynomials the pseudoboundary of a polytope is defined to be the set of all polynomials in the polytope each of which has at least one zero on the imaginary axis it is proven that a section of the pseudoboundary corresponding to any frequency spl omega sub 0 is itself a polytope whose vertices lie in the exposed two dimensional faces of the given polytope a simple algorithm is proposed to generate all the vertex polynomials of any section of the pseudoboundary of a polytope an illustrative example is given

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

robust hurwitz stability via sign definite decomposition abstract in this paper we first consider the problem of determining the robust positivity of a real function f x as the real vector x varies over a box x r l we show that it is sufficient to check a finite number of specially constructed points this is accomplished by using some results on sign definite decomposition we then apply this result to determine the robust hurwitz stability of a family of complex polynomials whose coefficients are polynomial functions of the parameters of interest we develop an eight polynomial vertex stability test that is a sufficient condition of hurwitz stability of the family this test reduces to kharitonov s well known result for the special case where the parameters are just the polynomial coefficients in this case the result is tight this test can be recursively and modularly used to construct an approximation of arbitrary accuracy to the actual stabilizing set the result is illustrated by examples

globally generated vector bundles on p1 p1 p1 with low first chern classes abstract we classify globally generated vector bundles on p 1 p 1 p 1 with small first chern class i e c 1 a 1 a 2 a 3 a i 2 our main method is to investigate the associated smooth curves to globally generated vector bundles via the hartshorne serre correspondence

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

resultants and chow forms via exterior syzygies let w be a vector space of dimension n 1 over a field k the chow divisor of a k dimensional variety x in p p w is the hypersurface in the grassmannian gk 1 of planes of codimension k 1 in p whose points over the algebraic closure of k are the planes that meet x the chow form of x is the defining equation of the chow divisor for example the resultant of k 1 forms of degree e in k 1 variables is the chow form of p embedded by the e th veronese mapping in p with n k e k 1 more generally the chow divisor of a k cycle i ni vi on projective space is defined to be i nidi where di is the chow divisor of vi the chow divisor of a sheaf f with k dimensional support is the chow divisor of the associated k cycle of f in this paper we will give a new expression for the chow divisor and apply it to give explicit formulas in many new cases starting with a sheaf f on p we use exterior algebra methods to define a canonical and effectively computable chow complex of f on each grassmannian of planes in p if f has k dimensional support we show that the chow form of f is the determinant of the chow complex of f on the grassmannian of planes of codimension k 1 the beilinson monad of f beilinson 1978 is the chow complex of f on the grassmannian of 0 planes that is on p itself in particular we are able to give explicit determinantal and pfaffian formulas for resultants in some cases where no polynomial formulas were known for example the horrocks mumford bundle gives rise to polynomial formulas for the resultant of five homogeneous forms of degrees 4 6 or 8 in five variables the easiest of our new formulas to write down is for the resultant of 3 quadratic forms in three variables the chow form of the veronese surface in p using the tangent bundle of p conclude that it can be written in bezout form described below as the pfaffian of the matrix 0 245 345 135 045 035 145 235

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

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

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

some stability theorems for polygons of polynomials some necessary and sufficient conditions for a polynomial in a polygon of polynomials to vanish on the imaginary axis are obtained these theorems generalize the segment lemma of h chapellat and s p bhattachartta see ibid vol 34 p 448 50 1989 to a polygon of polynomials