excursions of dual processes there has been considerable interest in the excursions of a markov process in recent years perhaps the most important general result is that of maisonneuve 13 in which the existence of an exit system is established this general result was applied to the study of specific excursions by getoor in 5 then maisonneuve recast and generalized these results in 14 where he showed how to discuss the excursion straddling a certain class of stopping times t these included the excursion straddling a fixed time and the first excursion whose length exceeds a given value which were discussed in 5 the purpose of this paper is to study excursions for processes which satisfy duality conditions a start in this direction was made in section 10 of 5 under assumptions that were much too strong it turns out that the appropriate duality hypotheses are stronger than those of classical duality as described in i we assume the existence of dual transition densities rather than the weaker assumption of dual potential kernel densities our precise assumptions are described in section 2 and especially in section 3 in particular it is shown in these sections that a systematic use of space time processes obviates the need for any regularity assumptions on the density over and above the chapman kolmogorov equation section 4 summarizes the special properties of additive functionals under our hypotheses that are needed in later sections in theorem 4 5 we show that if m is a closed homogeneous optional set then under duality assumptions there exists a borel set f c e e such that me3 0 and t 0 xt xt f are indistinguishable in section 5 we begin the discussion of excursions from a closed homogeneous optional set m with r i n f t 0 t c m if f e e corresponds to m as above r inf t xt art f almost surely especially important is 5 17 which gives the joint distribution of r x r and x r this is obtained by applying a reversal argument to the excursion

stopping distributions for right processes letx be a transient right process for which semipolar sets are polar we characterize the measures which can arise as the distribution ofx t witht a non randomized stopping time

a complete characterization of the gap between convexity and sos convexity our first contribution in this paper is to prove that three natural sum of squares sos based sufficient conditions for convexity of polynomials via the definition of convexity its first order characterization and its second order characterization are equivalent these three equivalent algebraic conditions henceforth referred to as sos convexity can be checked by semidefinite programming whereas deciding convexity is np hard if we denote the set of convex and sos convex polynomials in n variables of degree d with tilde c n d and tilde sigma c n d respectively then our main contribution is to prove that tilde c n d tilde sigma c n d if and only if n 1 or d 2 or n d 2 4 we also present a complete characterization for forms homogeneous polynomials except for the case n d 3 4 which is joint work with blekherman and is to be published elsewhere our result states that the set c n d of convex forms in n variables of degree d equals the set sigm

representation theory of finite semigroups semigroup radicals and formal language theory in this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field generalizing results of rhodes for the field of complex numbers applications are given to obtain many new results as well as easier proofs of several results in the literature involving triangularizability of finite semigroups which semigroups have split basic semigroup algebras two sided semidirect product decompositions of finite monoids unambiguous products of rational languages products of rational languages with counter and cerny s conjecture for an important class of automata

on the quasi regularity of non sectorial dirichlet forms by processes having the same polar sets abstract we obtain a criterion for the quasi regularity of generalized non sectorial dirichlet forms which extends the result of p j fitzsimmons on the quasi regularity of sectorial semi dirichlet forms given the right markov process associated to a semi dirichlet form we present sufficient conditions for a second right process to be a standard one having the same state space the above mentioned quasi regularity criterion is then an application the conditions are expressed in terms of the associated capacities nests of compacts polar sets and quasi continuity the second application is on the quasi regularity of the generalized dirichlet forms obtained by perturbing a semi dirichlet form with kernels

excessive kernels and revuz measures we consider a proper submarkovian resolvent of kernels on a lusin measurable space and a given excessive measure with every quasi bounded excessive function we associate an excessive kernel and the corresponding revuz measure every finite measure charging no polar set is such a revuz measure provided the hypothesis b of hunt holds under a weak duality hypothesis we prove the revuz formula and characterize the quasi boundedness and the regularity in terms of revuz measures we improve results of azema 2 and getoor and sharpe 20 for the natural additive functionals of a borel right process

semidefinite programming relaxations for semialgebraic problems a hierarchy of convex relaxations for semialgebraic problems is introduced for questions reducible to a finite number of polynomial equalities and inequalities it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility the main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials and some results from real algebraic geometry the techniques provide a constructive approach for finding bounded degree solutions to the positivstellensatz and are illustrated with examples from diverse application fields

riesz decompositions in markov process theory riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions the decomposition of excessive measures is given for borel right processes the results for excessive functions are formulated within the framework of weak duality these results extend and generalize the pioneering work of hunt in this area

synchronizing automata with a letter of deficiency 2 we present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of cerny s construction

one point extensions of markov processes by darning this paper is a continuation of the works by fukushima tanaka ann inst henri poincare probab stat 41 419 459 2005 and chen fukushima ying stochastic analysis and application p 153 196 the abel symposium springer heidelberg on the study of one point extendability of a pair of standard markov processes in weak duality in this paper general conditions to ensure such an extension are given in the symmetric case characterizations of the one point extensions are given in terms of their dirichlet forms and in terms of their l2 infinitesimal generators in particular a generalized notion of flux is introduced and is used to characterize functions in the domain of the l2 infinitesimal generator of the extended process an important role in our investigation is played by the order approaching probability u

a convex polynomial that is not sos convex a multivariate polynomial p x p x 1 x n is sos convex if its hessian h x can be factored as h x m t x m x with a possibly nonsquare polynomial matrix m x it is easy to see that sos convexity is a sufficient condition for convexity of p x moreover the problem of deciding sos convexity of a polynomial can be cast as the feasibility of a semidefinite program which can be solved efficiently motivated by this computational tractability it is natural to study whether sos convexity is also a necessary condition for convexity of polynomials in this paper we give a negative answer to this question by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos convex

semidefinite representation of convex sets let s x in mathbb r n g 1 x geq 0 ldots g m x geq 0 be a semialgebraic set defined by multivariate polynomials g i x assume s is convex compact and has nonempty interior let s i x in mathbb r n g i x geq 0 and s resp s i be the boundary of s resp s i this paper as does the subject of semidefinite programming sdp concerns linear matrix inequalities lmis the set s is said to have an lmi representation if it equals the set of solutions to some lmi and it is known that some convex s may not be lmi representable helton and vinnikov in commun pure appl math 60 5 654 674 2007 a question arising from nesterov and nemirovski siam studies in applied mathematics society for industrial and applied mathematics siam philadelphia 1994 see helton and vinnikov in commun pure appl math 60 5 654 674 2007 and nemirovski in plenary lecture international congress of mathematicians icm madrid spain 2006 is given a subset s of mathbb r n does there exist an lmi representable set in some higher dimensional space mathbb r n n whose projection down onto mathbb r n equals s such s is called semidefinite representable or sdp representable this paper addresses the sdp representability problem the following are the main contributions of this paper i assume g i x are all concave on s if the positive definite lagrange hessian condition holds i e the hessian of the lagrange function for optimization problem of minimizing any nonzero linear function l t x on s is positive definite at the minimizer then s is sdp representable ii if each g i x is either sos concave 2 g i x w x t w x for some possibly nonsquare matrix polynomial w x or strictly quasi concave on s then s is sdp representable iii if each s i is either sos convex or poscurv convex s i is compact convex whose boundary has positive curvature and is nonsingular i e g i x 0 on s i s then s is sdp representable this also holds for s i for which s i s extends smoothly to the boundary of a poscurv convex set containing s iv we give the complexity of schmudgen and putinar s matrix positivstellensatz which are critical to the proofs of i iii

convergence and restart in branch and bound algorithms for global optimization application to concave minimization and d c optimization problems a general branch and bound conceptual scheme for global optimization is presented that includes along with previous branch and bound approaches also grid search techniques the corresponding convergence theory as well as the question of restart capability for branch and bound algorithms used in decomposition or outer approximation schemes are discussed as an illustration of this conceptual scheme a finite branch and bound algorithm for concave minimization is described and a convergent branch and bound algorithm based on the previous one is developed for the minimization of a difference of two convex functions

markov processes on the lipschitz boundary for the neumann and robin problems abstract we investigate the markov process on the boundary of a bounded lipschitz domain associated to the neumann and robin boundary value problems we first construct l p semigroups of sub markovian contractions on the boundary generated by the boundary conditions and we show that they are induced by the transition functions of the forthcoming processes as in the smooth boundary case the process on the boundary is obtained by the time change with the inverse of a continuous additive functional of the reflected brownian motion the robin problem is treated with a kato type l p perturbation method using the revuz correspondence an exceptional polar set occurs on the boundary we make the link with the dirichlet forms approach

slowly synchronizing automata with fixed alphabet size abstract it was conjectured by cern in 1964 that a synchronizing dfa on n states always has a shortest synchronizing word of length at most n 1 2 and he gave a sequence of dfas reaching this bound in this paper we investigate the role of the alphabet size for each possible alphabet size we count dfas on n 6 states which synchronize in n 1 2 e steps for all e 2 n 2 furthermore we give constructions of automata with any number of states and 3 4 or 5 symbols which synchronize slowly namely in n 2 3 n o 1 steps in addition our results prove cern s conjecture for n 6 our computations lead to 31 dfas on 3 4 5 or 6 states which synchronize in n 1 2 steps of these dfa s 19 are new the remaining 12 which were already known are exactly the minimal ones the 19 new dfas are extensions of automata which were already known but for n 3 we prove that the cern automaton on n states does not admit non trivial extensions with the same smallest synchronizing word length n 1 2

killing a markov process under a stationary measure involves creation on construit la mesure de kuznetsov associee a une mesure excessive m et le semigroupe d un processus tue selon une fonctionnelle multiplicative m en termes de la mesure de kuznetsov correspondant a m

convexity in semialgebraic geometry and polynomial optimization we review several and provide new results on the theory of moments sums of squares and basic semialgebraic sets when convexity is present in particular we show that under convexity the hierarchy of semidefinite relaxations for polynomial optimization simplifies and has finite convergence a highly desirable feature as convex problems are in principle easier to solve in addition if a basic semialgebraic set mathbf k is convex but its defining polynomials are not we provide two algebraic certificates of convexity which can be checked numerically the second is simpler and holds if a sufficient and almost necessary condition is satisfied it also provides a new condition for mathbf k to have semidefinite representation for this we use and extend some of the recent results from the author and helton and nie math program to appear finally we show that when restricting to a certain class of convex polynomials the celebrated jensen s inequality in convex analysis can be extended to linear functionals that are not necessarily probability measures

absolute continuity of symmetric diffusions let x and y be symmetric diffusion processes with a common state space and let p m resp q be the law of x resp y with its symmetry measure m resp as initial distribution we study the consequences of the absolute continuity condition q t 1 t the density p also serves to link the dirichlet forms of x and y in a simple way our identification of l relies on notions of even and odd for additive functionals these notions complement fukushima s decomposition and the forward backward martingale decomposition of lyons and zheng

some zero one laws for additive functionals of markov processes let xt px be anm symmetric markov process with a strictly positive transition density consider the additive functionalat 0tf xs wheref e 0 is a universally measurable function on the state spacee among others we prove thatpx at 0 already impliespx at 0 the latter is also equivalent topx at 0 for quasi everyx e and allt 0 and to the analytic condition smallint f n fdm infty for a sequence of finely open borel setsfn such thate fn is polar in the special cases of brownian motion and bessel process these results were obtained earlier by h j engelbert w schmidt x x xue and the authors

a discontinuous time change for natural additive functionals which preserves duality continuous time changes of markov processes preserve duality but a discontinuous time change recently proposed by weidenfeld does not we modify his procedure to obtain a time change which preserves duality when the time changing functional is natural

finely harmonic functions of a markov process let x be a borel right process and m a fixed excessive measure given a finely open nearly borel set g we define an operator g which we regard as an extension of the restriction to g of the generator of x it maps functions on e to locally signed measures on g not charging m semipolars given a locally smooth signed measure we define h to be finely harmonic on g provided g h 0 on g and denote the class of such h by h f g under mild conditions on x we show that h h f g is equivalent to a local poisson representation of h we characterize h f g by an analog of the mean value property under secondary assumptions we obtain global poisson type representations and study the dirichlet problem for elements of h f g under suitable finiteness hypotheses the results take their nicest form when specialized to hunt processes

the cerný conjecture for one cluster automata with prime length cycle abstract we prove the cern conjecture for one cluster automata with prime length cycle consequences are given for the hybrid road coloring cern conjecture for strongly connected aperiodic digraphs with a proper cycle of prime length

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

dc decomposition of nonconvex polynomials with algebraic techniques we consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials we introduce algebraic techniques which reduce this task to linear second order cone and semidefinite programming this allows us to optimize over subsets of valid difference of convex decompositions dcds and find ones that speed up the convex concave procedure we prove however that optimizing over the entire set of dcds is np hard

on the equivalence of three potential principles for right markov processes we examine three of the principles of probabilistic potential theory in a nonclassical setting these are i the bounded maximum principle ii the positive definiteness of the energy of measures of bounded potential and iii the condition that each semipolar set is polar these principles are known to be equivalent in the context of two markov processes in strong duality when excessive functions are lower semicontinuous we show that when the principles are appropriately formulated their equivalence persists in the wider context of a borel right markov processx with distinguished excessive measurem we make no duality hypotheses andm need not be a reference measure our main tools are the stationary process y qm associated withx andm and a correspondence between potentials u and certain random measures over y qm

np hardness of deciding convexity of quartic polynomials and related problems we show that unless p np there exists no polynomial time or even pseudo polynomial time algorithm that can decide whether a multivariate polynomial of degree four or higher even degree is globally convex this solves a problem that has been open since 1992 when n z shor asked for the complexity of deciding convexity for quartic polynomials we also prove that deciding strict convexity strong convexity quasiconvexity and pseudoconvexity of polynomials of even degree four or higher is strongly np hard by contrast we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time

on the complexity of testing attainment of the optimal value in nonlinear optimization we prove that unless hbox p hbox np there exists no polynomial time or even pseudo polynomial time algorithm that can test whether the optimal value of a nonlinear optimization problem where the objective and constraints are given by low degree polynomials is attained if the degrees of these polynomials are fixed our results along with previously known frank wolfe type theorems imply that exactly one of two cases can occur either the optimal value is attained on every instance or it is strongly np hard to distinguish attainment from non attainment we also show that testing for some well known sufficient conditions for attainment of the optimal value such as coercivity of the objective function and closedness and boundedness of the feasible set is strongly np hard as a byproduct our proofs imply that testing the archimedean property of a quadratic module is strongly np hard a property that is of independent interest to the convergence of the lasserre hierarchy finally we give semidefinite programming sdp based sufficient conditions for attainment of the optimal value in particular a new characterization of coercive polynomials that lends itself to an sdp hierarchy

on the potential theory of symmetric markov processes on reprend des resultats de dynkin et on considere un processus de markov fort symetrique continu a droite on etudie la relation existant entre le cone de mesures positives d energie finie et la capacite

an application of flows to time shift and time reversal in stochastic processes a simple proposition theorem 1 on flows allows the investigation of random time shift and time reversal in markov processes without assuming any regularity of paths theorem 5 is a generalization of nagasawa s time reversal theorem and theorem 4 generalizes a recent result of getoor and glover 1 flows 1 1 we consider a flow in a measurable space 2 y that is a family of transformations at t e r such that oat 0s t for all s t e r and t c oto e a e r x 4 for all a e f r is the borel a algebra in r we put oty x y otw for every function y and pot a p 0t71a a e y p pot dt for every measure p we denote by the collection of all sets a e y such that t1a a for all t e r a function y is measurable with respect to the a algebra wif and only if it is measurable and invariant under all transformations ot obviously p a 0 or oo for all a e sl nevertheless we prove theorem 1 if p is a finite over y it determines uniquely the values p a for all a e 1 2 as a tool we use stationary times a stationary time t is a measurable mapping from 2 to the extended real line oo oo such that ott t t for all t e r suppose that y coincides with its completion with respect to the class of all probability measures then the first hitting time of a set a e y ta inf t ot e a and the last exit time from a ta sup t ot co a are stationary times2 the measurability follows from 5 chapter 3 1 received by the editors march 13 1984 1980 mathematics subject classification primary 60g 601 1 supported in part by national science foundation grant mcs 8202286 2we put inf oo sup oo c1985 american mathematical society 0002 9947 85 1 00 25 per page

biquadratic optimization over unit spheres and semidefinite programming relaxations this paper studies the so called biquadratic optimization over unit spheres min x in mathbb r n y in mathbb r m sum 1 leq i k leq n 1 leq j l leq m b ijkl x i y j x k y l subject to x 1 y 1 we show that this problem is np hard and there is no polynomial time algorithm returning a positive relative approximation bound then we present various approximation methods based on semidefinite programming sdp relaxations our theoretical results are as follows for general biquadratic forms we develop a frac 1 2 max m n 2 approximation algorithm under a slightly weaker approximation notion for biquadratic forms that are square free we give a relative approximation bound frac 1 nm when min n m is a constant we present two polynomial time approximation schemes ptass which are based on sum of squares sos relaxation hierarchy and grid sampling of the standard simplex for practical computational purposes we propose the first order sos relaxation a convex quadratic sdp relaxation and a simple minimum eigenvalue method and show their error bounds some illustrative numerical examples are also included

sub markovian resolvents under weak duality hypothesis we study the weak duality between two sub markovian resolvents of kernels on a lusin topological space with respect to a given measure m our frame covers the probabilistic context of two borel markov processes in weak duality the main results are related to the coincidence of the m semipolar and m cosemipolar sets the revuz correspondence between the measures charging no cofinely open m polar set and the potential kernels associated with the homogeneous random measures of the process the equivalence between smoothness and cosmoothness a smooth measure is the revuz measure of a continuous additive functional we extend and improve results of r m blumenthal r k getoor j azema d revuz j b walsh r k getoor m j sharpe

on the lasserre hierarchy of semidefinite programming relaxations of convex polynomial optimization problems the lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions j b lasserre convexity in semialgebraic geometry and polynomial optimization siam j optim 19 1995 2014 2009 we give a new proof of the finite convergence property that does not require the assumption that the hessian of the objective be positive definite on the entire feasible set but only at the optimal solution in addition we show that the number of steps needed for convergence depends on more than the input size of the problem in particular the size of the semidefinite program that gives the exact reformulation of the convex polynomial optimization problem may be exponential in the input size

green s and dirichlet spaces associated with fine markov processes this is the second paper in a series devoted to green s and dirichlet spaces in the first paper we have investigated green s space k and the dirichlet space h associated with a symmetric markov transition function pt x b now we assume that p is a transition function of a fine markov process x and we prove that a the space h can be built from functions which are right continuous along almost all paths b the positive cone k in k can be identified with a cone m of measures on the state space c the positive cone h in h can be interpreted as the cone of green s potentials of measures m to every measurable set b in the state space e there correspond a subspace k b of k and a subspace h b of h the orthogonal projections of k onto k and of h onto h b can be expressed in terms of the hitting probabilities of b by the markov process x as the main tool we use additive functionals of x corresponding to measures m

markov processes and nonsymmetric dirichlet forms without regularity we study right markov processes in weak duality satisfying the sector condition of silverstein dirichlet space techniques are employed but without the customary c0 regularity hypothesis nonetheless the potential theory of such processes is quite amenable in particular it is proved that semipolar sets are quasi polar this extends results of silverstein and lejan

bounded and lp weak solutions for nonlinear equations of measure valued branching processes abstract we study the nonlinear schrodinger type equation c u c k 1 q k u k f where c is a bounded positive function we may replace the laplace operator with the generator of a borel right markov process with state space e and consider a nonlinear term induced by a perturbing kernel we solve this type of equation in an l p weak sense involving positive definite extensions of the solution from e to the set of all finite positive measures on e the extensions to the set of measures are related to the classical connection from the works of m nagasawa n ikeda s watanabe and m l silverstein between this nonlinear equation and the discrete branching markov processes we also investigate the existence of the bounded solutions for the dirichlet problem associated to the above equation with bounded boundary data our approach is based on probabilistic and analytic potential theoretical methods used on both spaces e and the set of all finite configurations of e like the revuz formula for the continuous additive functionals and the perturbation with kernels of the transition functions and resolvents

continuum sites stepping stone models coalescing exchangeable partitions and random trees analogues of stepping stone models are considered where the sitespace is continuous the migration process is a general markov process and the type space is infinite such processes were defined in previous work of the second author by specifying a feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing markov processes an alternative representation is obtained here in terms of a limit of interacting particle systems it is shown that under a mild condition on the migration process the continuum sites stepping stone process has continuous sample paths the case when the migration process is brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating brownian motion this duality relation is also used to show that a tree like random compact metric space that is naturally associated to an in nite family of coalescing brownian motions on the circle has hausdorff and packing dimension both almost surely equal to 1 2 and moreover this space is capacity equivalent to the middle 1 2 cantor set and hence also to the brownian zero set

a new decomposition method for multiuser dc programming and its applications we propose a novel decomposition framework for the distributed optimization of difference convex dc type nonseparable sum utility functions subject to coupling convex constraints a major contribution of the paper is to develop for the first time a class of inexact best response like algorithms with provable convergence where a suitably convexified version of the original dc program is iteratively solved the main feature of the proposed successive convex approximation method is its decomposability structure across the users which leads naturally to distributed algorithms in the primal and or dual domain the proposed framework is applicable to a variety of multiuser dc problems in different areas ranging from signal processing to communications and networking as a case study in the second part of the paper we focus on two examples namely i a novel resource allocation problem in the emerging area of cooperative physical layer security and ii and the renowned sum rate maximization of mimo cognitive radio networks our contribution in this context is to devise a class of easy to implement distributed algorithms with provable convergence to stationary solution of such problems numerical results show that the proposed distributed schemes reach performance close to and sometimes better than that of centralized methods

reset sequences for monotonic automata natarajan reduced the problem of designing a certain type of mechanical parts orienter to that of finding reset sequences for monotonic deterministic finite automata he gave algorithms that in polynomial time either find such sequences or prove that no such sequence exists in this paper a new algorithm based on breadth first search is presented that runs in faster asymptotic time than natarajan s algorithms and in addition finds the shortest possible reset sequence if such a sequence exists tight bounds on the length of the minimum reset sequence are given the time and space bounds of another algorithm given by natarajan are further improved that algorithm finds reset sequences for arbitrary deterministicfinite automata when all states are initially possible

homogeneous random measures and a weak order for the excessive measures of a markov process let x xt px be a right markov process and let m be an excessive measure for x associated with the pair x m is a stationary strong markov process yt qm with random times of birth and death with the same transition function as x and with m as one dimensional di stribution we use yt qm to study the cone of excessive measures for x a weak order is defined on this cone an excessive measure is weakly dominated by m if and only if there is a suitable homogeneous random measure tt such that yt q6 is obtained by birthing yt qm birth in t t dt occurring at rate s dt random measures such as s are studied through the use of palm measures we also develop aspects of the general theory of processes over yt qm including the moderate markov property of yt qm when the arrow of time is reversed applications to balayage and capacity are suggested

strongly supermedian kernels and revuz measures in the frame of borel right markov processes we investigate following an analytical point of view the revuz correspondence between classes of potential kernels and their associated measures improving upon the results of revuz azema getoor and sharpe fitzsimmons fitzsimmons and getoor and dellacherie maisonneuve and meyer in the probabilistic approach of the problem the kernels that occur are the potential operators of different types of homogeneous random measures we completely characterize the hypothesis b of hunt in terms of revuz measures