perturbation of symmetric markov processes we present a path space integral representation of the semigroup associated with the quadratic form obtained by a lower order perturbation of the l 2 infinitesimal generator mathcal l of a general symmetric markov process an illuminating concrete example for mathcal l is delta d delta s d where d is a bounded euclidean domain in mathbb r d s in 0 1 delta d is the laplace operator in d with zero dirichlet boundary condition and delta s d is the fractional laplacian in d with zero exterior condition the strong markov process corresponding to mathcal l is a levy process that is the sum of brownian motion in mathbb r d and an independent symmetric 2s stable process in mathbb r d killed upon exiting the domain d this probabilistic representation is a combination of feynman kac and girsanov formulas crucial to the development is the use of an extension of nakao s stochastic integral for zero energy additive functionals and the associated ito formula both of which were recently developed in chen et al stochastic calculus for dirichlet processes preprint 2006

on the lp spectrum of laplacians on graphs abstract we study the p independence of spectra of laplace operators on graphs arising from regular dirichlet forms on discrete spaces here a sufficient criterion is given solely by a uniform subexponential growth condition moreover under a mild assumption on the measure we show a one sided spectral inclusion without any further assumptions we study applications to normalized laplacians including symmetries of the spectrum and a characterization for positivity of the cheeger constant furthermore we consider laplacians on planar tessellations for which we relate the spectral p independence to assumptions on the curvature

lp independence of spectral bounds of feynman kac semigroups by continuous additive functionals abstract we establish conditions for the l p independence of spectral bounds of feynman kac semigroup by continuous additive functionals whose revuz measures are smooth measures of kato class having non negative order green tightness our continuous additive functionals do not necessarily admit bounded variation in general examples of cauchy principal value and hilbert transform of brownian local time and for relativistic symmetric stable processes are presented

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

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

on dol power series abstract we study d0l power series we show how elementary morphisms introduced by ehrenfeucht and rozenberg can be used in connection with power series characterize the sequences of rational numbers and integers which can appear as coefficients in d0l power series and establish various decidability results

gaugeability and conditional gaugeability new kato classes are introduced for general transient borel right processes for which gauge and conditional gauge theorems hold these new classes are the genuine extensions of the green tight measures in the classical brownian motion case however the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability we show that gaugeability conditional gaugeability and the subcriticality for the associated schrodinger operators are equivalent for transient borel right processes with strong duals analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric markov processes these analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases connections with the positivity of the spectral radii of the associated schrodinger operators are also established

on transductions of formal power series over complete semirings abstract rational and pushdown transductions of formal languages are generalized to formal power series with coefficients in a complete semiring a characterization similar to nivat s theorem is given commutativity requirements for the coefficients are especially studied

equivalence and optimization of relational transactions a large class of relational database update transactions is investigated with respect to equivalence and optimization the transactions are straight line programs with inserts deletes and modifications using simple selection conditions several basic results are obtained it is shown that transaction equivalence can be decided in polynomial time a number of optimality criteria for transactions are then proposed as well as two normal forms polynomial time algorithms for transaction optimization and normalization are exhibited also an intuitively appealing system of axioms for proving transaction equivalence is introduced finally a simple natural subclass of transactions called strongly acyclic is shown to have particularly desirable properties

l p independence of spectral radius for generalized feynman kac semigroups under mild conditions on measures used in the perturbation we establish the l p independence of spectral radius for generalized feynman kac semigroups without assuming the irreducibility and the boundedness of the function appeared in the continuous additive functionals locally of zero energy in the framework of symmetric markov processes these results are obtained by using the gaugeability approach developed by the first named author as well as the recent progress on the irreducible decomposition for markov processes proved by the third author and on the analytic characterizations of gaugeability for generalized feynman kac functionals developed by the second and third authors

equational properties of kleene algebras of relations with conversion abstract we describe a set of equational axioms for the variety generated by all algebras of binary relations with operations of union composition conversion and reflexive transitive closure and neutral elements 0 the empty relation and 1 the identity relation

bases and ambiguity of number systems abstract the degree of ambiguity of a given number system can be effectively computed we show also that all degrees of ambiguity do exist both as regards number systems and the sets represented by them in contrast to language theory there are inherently unambiguous sets the paper contains also results concerning the possibility of changing the base of a number system

lp independence of spectral bounds of generalized non local feynman kac semigroups let x be a symmetric strong markov process on a luzin space in this paper we present criteria of the lp independence of spectral bounds for generalized non local feynman kac semigroups of x that involve continuous additive functionals of x having zero quadratic variations and discontinuous additive functionals of x

conditional gauge theorem for non local feynman kac transforms feynman kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of markov processes general gauge and conditional gauge theorems are established for such transforms furthermore the l 2 infinitesimal generator of the schrodinger semigroup given by a non local feynman kac transform is determined in terms of its associated bilinear form

time reversal and elliptic boundary value problems in this paper we prove that there exists a unique bounded continuous weak solution to the dirichlet boundary value problem for a general class of second order elliptic operators with singular coefficients which does not necessarily have the maximum principle our method is probabilistic the time reversal of symmetric markov processes and the theory of dirichlet forms play a crucial role in our approach

scott induction and closure under ω sups lcf is the logic of computable read continuous functionals where continuity means the preservation of sups ne xn of chains x ne in cpo s p with least element most important sups have the form xf x ne fn and are given continuously by the least fixed point operator y consequently scotts induction axiom f r f x r f x r f f x r f yf is valid for certain relations r p p p such as those satisfying the condition f x r f x is closed under sups given a relation r we ask whether the obviously sufficient condition is also necessary for r to satisfy scott s induction axiom our main result shows that is not a necessary condition even for sets x p where r f x x e x as a consequence of certain definability and effectiveness aspects of the main result we also show that some rather interesting classes of cpo s can be finitely axiomatized in the language of lcf

on kleene algebras abstract in this paper we prove that the class of inversion free kleene algebras is not finitely based the main idea is to use a result of redko and salomaa for regular languages we also prove unsolvability of the word problem for kleene algebras and some other varieties of algebras

l codes and number systems abstract the notion of an l code is introduced as a generalization of the customary notion of a code attention is focused on unary l codes where the target alphabet consists of one letter only unary l codes can be identified with such number systems where the representation is unique surprisingly many unary morphisms are l codes furthermore even for non l codes there is only one exceptional length we also give a complete classification for the binary case

dynamic functional dependencies and database aging a simple extension of the relational model is introduced to study the effects of dynamic constraints on database evolution both static and dynamic constraints are used in conjunction with the model the static constraints considered here are functional dependencies fds the dynamic constraints involve global updates and are restricted to certain analogs of fds called dynamic fds the results concern the effect of the dynamic constraints on the static constraints satisfied by the database in the course of time the effect of the past history of the database on the static constraints is investigated using the notions of age and age closure the connection between the static constraints and the potential future evolution of the database is briefly discussed using the notions of survivability and survivability closure

lp independence of spectral bounds of schrodinger type semigroups let l be an m symmetric markov generator and a signed measure in the kato class we consider a schrodinger type operator h l on lp m we prove that under certain conditions for the markov semigroup generated by l and the potential the lp spectral bound of h is independent of p if and only if the l2 spectral bound is non positive

dynamic constraints and object migration a role set is the set of classes in a class hierarchy where an object may reside simultaneously a migration pattern is a sequence of role sets that an object can migrate through we define a migration inventory which is a set of migration patterns as a dynamic integrity constraint on object migration we consider three update languages sl which has five operators csl which extends sl with positive conditionals and csl which allows both positive and negative conditionals three subclasses of migration patterns of transactions are studied which are immediate start proper and lazy patterns it is shown that the family of all immediatestart proper or lazy migration patterns of every set of sl transactions is a regular set and the converse also holds in particular testing satisfiability of an inventory by a set of transactions is decidable for the extended languages we give a weaker characterization the family of all immediate start proper or lazy migration patterns of every set of csl csl transactions is recursively enumerable r e however every r e inventory can be the family of all migration patterns of some set of csl csl transactions and be a left quotient of the family of immediate start migration patterns of another set of csl csl transactions by a regular set although the exact characterizations of immediate start proper lazy migration patterns of csl csl transactions are still open it is proved that every context free inventory can be the family of proper and immediate start migration patterns of some csl csl transactions testing satisfiability of an inventory by a set of csl csl transactions is unfortunately undecidable

on lindenmayerian algebraic sequences abstract we define and study lindenmayerian algebraic sequences these sequences are a generalization of algebraic sequences k regular sequences and automatic sequences

finitely specifiable implicational dependency families une famille de dependance d implication id est une famille d exemples de base de donnees relationnelles composee de tous les cas qui satisfont un ensemble donne d ids dans cet article on montre que la collection de familles de dependances d implication specifiable de maniere finie n est pas bloquee sous les dependances de jointure ou de projection

the ring of k regular sequences ii in this paper we continue our study of k regular sequences begun in 1992 we prove some new results give many new examples from the literature and state some open problems

ambiguity and decision problems concerning number systems the representation of integers in arbitrary number systems is considered the main emphasis is on problems concerning ambiguity completeness and equivalence a rather general automata theoretic method for solving such in essence purely number theoretic problems is developed the method seems to be applicable in a variety of different situations

iteration theories of synchronization trees synchronization trees are shown to form an iteration theory in a natural way the class of grove iteration theories is introduced the regular synchronization trees are shown to be the free theories in the subclass of synchronization theories moreover the bisimulation equivalence classes of regular synchronization trees are shown to be the free synchronization theories satisfying an infinite idempotency law

analytic characterization of conditional gaugeability for non local feynman kac transforms abstract an analytic characterization of gaugeability and conditional gaugeability is given for non local or discontinuous feynman kac transforms of general symmetric markov processes this analytic characterization is very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases

characterizations for functional dependency and boyce codd normal form families abstract a functional dependency fd family was recently defined 20 as the set of all instances satisfying some set of functional dependencies a boyce codd normal form abbreviated bcnf family is defined here as an fd family specified by some bcnf set of functional dependencies the purpose of this paper is to present set theoretic algebraic characterizations relating to both types of families two characterizations of f i the smallest fd family containing the family i of instances are established the first involves the notion of agreement a concept related to that of a closed set of attributes the second describes f i as the smallest family of instances containing i and closed under four specific operations on instances companion results are also given for bcnf families the remaining results concern characterizations involving the well known operations of projection join and union two characterizations for when the projection of an fd family is again an fd family are given several corollaries are obtained including the effective decidability of whether a projection of an fd family is an fd family the problem for bcnf families disappears since it is shown that the projection of a bcnf family is always a bcnf family analogous to results for fd families presented in 20 characterizations of when the join and union of bcnf families are bcnf families are given finally the collections of all fd families and all bcnf families are characterized in terms of inverse projection operations and intersection

on lindenmayerian algebraic power series abstract we define lindenmayerian algebraic power series and study their properties these series generalize both algebraic series and etol languages

on the structure of armstrong relations for functional dependencies an armstrong relation for a set of functional dependencies fds is a relation that satisfies each fd implied by the set but no fd that is not implied by it the structure and size number of tuples of armstrong relatsons are investigated upper and lower bounds on the size of minimal sized armstrong relations are derived and upper and lower bounds on the number of distinct entries that must appear m an armstrong relation are given it is shown that the time complexity of finding an armstrong relation gwen a set of functional dependencies is precisely exponential in the number of attributes also shown s the falsity of a natural conjecture which says that almost all relations obeying a given set of fds are armstrong relations for that set of fds finally armstrong relations are used to generahze a result obtained by demetrovics using quite complicated methods about the possible sets of keys for a relauon

automata and languages generalized to ω continuous semirings abstract we generalize the following two language and automata theoretic results to continuous semirings i the family of languages accepted by finite automata is the smallest class containing all finite languages and closed under union product and star kleene s theorem ii the family of languages accepted by pushdown automata is the family ofcontext free languages