a direct branching algorithm for checking the equivalence of two deterministic pushdown transducers one of which is real time strict abstract a new direct branching algorithm is presented for checking the equivalence of deterministic pushdown transducers one of whose associated deterministic pushdown automata dpdas is real time strict it is a straightforward extension of the corresponding algorithm for dpdas tomita 1982 and then proves the general applicability of our approach

an extended direct branching algorithm for checking equivalence of deterministic pushdown automata abstract this paper extends the direct branching algorithm of 25 for checking equivalence of deterministic pushdown automata it does so by providing a technique called halting for dealing with nodes with unbounded degree in the comparison tree this may occur when a skipping step may be applied infinitely many times to a certain node as a result of infinite sequences of e moves this extension allows the algorithm to check equivalence of two deterministic pushdown automata when none of them is real time but in a certain condition that properly contains a case where one of them is real time strict

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

convergence of em image reconstruction algorithms with gibbs smoothing p j green has defined an osl one step late algorithm that retains the e step of the em algorithm for image reconstruction in emission tomography but provides an approximate solution to the m step further modifications of the osl algorithm guarantee convergence to the unique maximum of the log posterior function convergence is proved under a specific set of sufficient conditions several of these conditions concern the potential function of the gibb s prior and a number of candidate potential functions are identified generalization of the osl algorithm to transmission tomography is also considered

church rosser controlled rewriting systems and equivalence problems for deterministic context free languages we use a description of deterministic context free languages dcfl by a special type of church rosser rewriting systems to extend several procedures testing the equality of two languages in a subfamilyfof dcfl to procedures testing the equality of two languages one of which is inf the other beeing a general dcfl

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

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

restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound gauss markov random fields abstract over the last few years a growing number of researchers from varied disciplines have been utilizing markov random fields mrf models for developing optimal robust algorithms for various problems such as texture analysis image synthesis classification and segmentation surface reconstruction integration of several low level vision modules sensor fusion and image restoration however no much work has been reported on the use of simulated annealing sa and iterative conditional mode icm algorithms for maximum a posteriori estimation in image restoration problems when severe blurring is present in this paper we examine the use of compound gauss markov random fields cgmrf to restore severely blurred high range images for this deblurring problem the convergence of the sa and icm algorithms has not been established we propose two new iterative restoration algorithms which can be considered as extensions of the classical sa and icm approaches and whose convergence is established finally they are tested on real and synthetic images and the results compared with the restorations obtained by other iterative schemes

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

on some decision questions concerning pushdown machines abstract certain decision questions e g equivalence ambiguity single valuedness monotonicity etc concerning pushdown transducers and acceptors are investigated examples of results shown are the following 1 1 there is an algorithm to decide given two deterministic pushdown transducers one of which has a finite turn counter for a pushdown stack whether they are equivalent i e they define the same input output relation 2 2 there are subclasses of pushdown acceptors which have a decidable ambiguity problem but an undecidable inherent ambiguity problem it seems that these classes are the first known to exhibit this property 3 3 there is an algorithm to decide given a homomorphism h and a language l accepted by a finite turn nondeterministic counter automaton whether h is one to one on l in contrast there is no such algorithm if l is accepted by a 1 turn deterministic pushdown automaton or by an unrestricted deterministic counter automaton

a direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata a new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata dpda s after korenjak and hopcroft s branching algorithm it is not only powerful enough to be applicable to two dpda s accepting by empty stack one of which is real time but also simple even for dpda s in lower subclasses this is the first time the branching algorithm has been used to give such a general decision procedure without ever mixing the two languages in question in other words it deals with only the equivalence equation whose left hand side consists of a pure reachable configuration of one dpda and whose right hand side that of the other

n rational algebras i basic properties and free algebras a strict hierarchy of algebras in which only certain constructive chains have a least upper bound is studied such algebras called n rational are ideal interpretations for finite recursion schemes of higher types indeed the constructive chains that have least upper bounds in these algebras are obtained by unfolding rational recursion schemes of higher types part i of this paper deals with basic properties of these algebras the existence of free algebras in particular in part ii siam j comput 13 1984 pp 776 794 varieties and a logic of inequalities are studied a proof system with one infinitary inference rule is shown to be complete

bayesian restoration using a new nonstationary edge preserving image prior in this paper we propose a class of image restoration algorithms based on the bayesian approach and a new hierarchical spatially adaptive image prior the proposed prior has the following two desirable features first it models the local image discontinuities in different directions with a model which is continuous valued thus it preserves edges and generalizes the on off binary line process idea used in previous image priors within the context of markov random fields mrfs second it is gaussian in nature and provides estimates that are easy to compute using this new hierarchical prior two restoration algorithms are derived the first is based on the maximum a posteriori principle and the second on the bayesian methodology numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary mrf based with line process algorithms these experiments demonstrate the advantages of the proposed prior

pushdown machines for the macro tree transducer the macro tree transducer can be considered as a system of recursive function procedures with parameters where the recursion is on a tree e g the syntax tree of a program we investigate characterizations of the class of tree tree to string translations which is induced by macro tree transducers macro tree to string transducers respectively for this purpose we define several pushdown machines of which the control is recursive without parameters or even iterative and which work on a generalized pushdown as storage because of the relevance for semantics of programming languages we stress besides the nondeterministic case the study of machines for the total deterministic macro tree to string transducer which translates every input tree into exactly one output tree string respectively finally we characterize the n fold composition of total deterministic macro tree transducers by recursive pushdown machines with an iterated pushdown as storage which is a pushdown of pushdowns of of pushdowns

rational subsets of partially reversible monoids a class of monoids that can model partial reversibility allowing simultaneously instances of two sided reversibility one sided reversibility and no reversibility is considered some of the basic decidability problems involving their rational subsets syntactic congruences and characterization of recognizability are solved using purely automata theoretic techniques giving further insight into the structure of recognizable languages

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

a polynomial algorithm for deciding bisimilarity of normed context free processes the previous best upper bound on the complexity of deciding bisimilarity between normed context free processes due to huynh and tian is that the problem lies in the second level of the polynomial hierarchy their algorithm guesses a proof of equivalence and validates this proof in polynomial time using oracles freely answering questions which are in np in this paper we improve on this result by presenting a polynomial time algorithm which solves this problem as a corollary we have a polynomial algorithm for the equivalence problem for simple context free grammars

a polynomial time algorithm for deciding the equivalence problem for 2 tape deterministic finite state acceptors the equivalence problem for the class of one way deterministic 2 tape finite state acceptors is the problem of deciding l m 1 l m 2 where m 1 and m 2 are machines in this class a new algorithm for deciding equivalence is provided having time complexity proportional to p n where p is a polynomial and n is the size of the machines this improves upon the best previously known upper bound having order 2 cn 6 where c is a constant c beeri theoret comput sci 3 1976 pp 305 320

a generalized em algorithm for 3 d bayesian reconstruction from poisson data using gibbs priors a generalized expectation maximization gem algorithm is developed for bayesian reconstruction based on locally correlated markov random field priors in the form of gibbs functions and on the poisson data model for the m step of the algorithm a form of coordinate gradient ascent is derived the algorithm reduces to the em maximum likelihood algorithm as the markov random field prior tends towards a uniform distribution three different gibbs function priors are examined reconstructions of 3 d images obtained from the poisson model of single photon emission computed tomography are presented

l a l b decidability results from complete formal systems abstract the equivalence problem for deterministic pushdown automata is shown to be decidable we exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda m we then extend the result to deterministic pushdown transducers from a free monoid into an abelian group a general algebraic and logical framework inspired by harrison et al theoret comput sci 9 1979 173 205 conrcelle theoret comput sci 6 1978 255 279 and meitus kybernetika 5 1989 14 25 in russian is developed

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

a direct branching algorithm for checking equivalence of strict deterministic vs ll k grammars abstract we present here an equivalence checking algorithm which operates directly on a pair of strict deterministic vs ll k grammars it is also straightforwardly applicable to a pair of ll k grammars though an ll k grammar is not necessarily strict deterministic the basic idea is from korenjak and hopcroft s branching algorithm for simple deterministic grammars but ours is so distinguished that it is throughout free from mixing the nonterminals of the respective grammars in question and then very simple

on the p adic local invariant cycle theorem for a proper flat generically smooth scheme x over a complete discrete valuation ring with finite residue field of characteristic p we construct a specialization morphism from the rigid cohomology of the geometric special fibre to d cris of the p adic etale cohomology of the geometric generic fibre and we make a conjecture p adic local invariant cycle theorem that describes the behavior of this map for regular x analogous to the situation in ell adic etale cohomology for ell ne p our main result is that if x has semistable reduction this specialization map induces an isomorphism on the slope 0 1 part

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

uber die lokale zetafunktion von shimuravarietaten monodromiefiltration und verschwindende zyklen in ungleicher charakteristik

the weil etale topology for number rings there should be a grothendieck topology for an arithmetic scheme x such that the euler characteristic of the cohomology groups of the constant sheaf z with compact support at infinity gives up to sign the leading term of the zeta function of x at s 0 we construct a topology the weil etale topology for the ring of integers in a number field whose cohomology groups hl z determine such an euler characterstic if we restrict to 3

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

some decision problems about controlled rewriting systems abstract a description of deterministic context free languages by some kind of finitely generated right congruences the sets of relations generating such right congruences are called controlled rewriting systems or c systems has been given previously in the first part of this paper we study several decision problems on c systems namely the confluence problem the equivalence problem the refinement problem the class equivalence problem and the class inclusion problem in the second part of the paper we deduce from the main theorem given previously a characterisation of dcfls by means of finitely generated congruences the sets of relations generating such congruences are now ordinary finite semi thue systems we study three decision problems on finite semi thue systems namely the class equivalence problem the word problem for the syntactic congruence of one class and the partial confluence problem all the problems are investigated in several classes of c systems or semi thue systems for every class we give an answer which may be yes the problem is decidable no the problem is undecidable or eq which means that the problem is recursively equivalent to the equivalence problem for dpda

dpda s in atomic normal form and applications to equivalence problems abstract in this paper we introduce a new normal form for dpda s the atomic normal form as an application using also the concept of address language due to gorn 19 20 we give alternate and more direct proofs of results of courcelle 3 4 relating recursion schemes and dpda s address languages enable us to encode trees even when they are not locally finite as a consequence the decidability of a new class of schemes corresponding to the stateless dpda s of 26 is obtained

decidability of dpda equivalence a proof of decidability of equivalence between deterministic pushdown automata is presented using a mixture of methods developed in concurrency and language theory the technique appeals to a tableau proof system for equivalence of configurations of strict deterministic grammars

tensor products of modules and the rigidity of tor let r be a hypersurface domain that is a ring of the form s f where s is a regular local ring and f is a prime element suppose m and n are finitely generated r modules we prove two rigidity theorems on the vanishing of tor in the first theorem we assume that the regular local ring s is unramified that m r n has finite length and that dim m dim n dim r with these assumptions if tor r m n 0 for some j 0 then tor r m n 0 for all i j the second rigidity theorem states that if m r n is reflexive then tor r m n 0 for all i 1 we use these theorems to prove the following theorem valid even if s is ramified if m r n is a maximal cohen macaulay r module then both m and n are maximal cohen macaulay modules and at least one of them is free

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

a segmentation based regularization term for image deconvolution this paper proposes a new and original inhomogeneous restoration deconvolution model under the bayesian framework for observed images degraded by space invariant blur and additive gaussian noise in this model regularization is achieved during the iterative restoration process with a segmentation based a priori term this adaptive edge preserving regularization term applies a local smoothness constraint to pre estimated constant valued regions of the target image these constant valued regions the segmentation map of the target image are obtained from a preliminary wiener deconvolution estimate in order to estimate reliable segmentation maps we have also adopted a bayesian markovian framework in which the regularized segmentations are estimated in the maximum a posteriori map sense with the joint use of local potts prior and appropriate gaussian conditional luminance distributions in order to make these segmentations unsupervised these likelihood distributions are estimated in the maximum likelihood sense to compute the map estimate associated to the restoration we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration the experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state of the art methods in benchmark tests

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

simulated annealing in compound gaussian random fields image processing recently a stochastic relaxation technique called simulated annealing has been developed to search for a globally optimal solution in image estimation and restoration problems the convergence of simulated annealing has been proved only for random fields with a compact range space because of this images were modeled as random fields with bounded discrete or continuous values however in most image processing problems it is more natural to model the image as a random field with values in a noncompact space e g conditional gaussian models the proof of convergence of the stochastic relaxation method is extended to a class of compound gauss markov random fields simulation results are provided to show the power of these methods

single image defogging by multiscale depth fusion restoration of fog images is important for the deweathering issue in computer vision the problem is ill posed and can be regularized within a bayesian context using a probabilistic fusion model this paper presents a multiscale depth fusion mdf method for defog from a single image a linear model representing the stochastic residual of nonlinear filtering is first proposed multiscale filtering results are probabilistically blended into a fused depth map based on the model the fusion is formulated as an energy minimization problem that incorporates spatial markov dependence an inhomogeneous laplacian markov random field for the multiscale fusion regularized with smoothing and edge preserving constraints is developed a nonconvex potential adaptive truncated laplacian is devised to account for spatially variant characteristics such as edge and depth discontinuity defog is solved by an alternate optimization algorithm searching for solutions of depth map by minimizing the nonconvex potential in the random field the mdf method is experimentally verified by real world fog images including cluttered depth scene that is challenging for defogging at finer details the fog free images are restored with improving contrast and vivid colors but without over saturation quantitative assessment of image quality is applied to compare various defog methods experimental results demonstrate that the accurate estimation of depth map by the proposed edge preserved multiscale fusion should recover high quality images with sharp details

language equivalence of probabilistic pushdown automata we study the language equivalence problem for probabilistic pushdown automata ppda and their subclasses we show that the problem is interreducible with the multiplicity equivalence problem for context free grammars the decidability of which has been open for several decades interreducibility also holds for ppda with one control state in contrast for the case of a one letter input alphabet we show that ppda language equivalence and hence multiplicity equivalence of context free grammars is in pspace and at least as hard as the polynomial identity testing problem

a weaker sufficient condition for the equivalence of a pair of dpda s to be decidable abstract this short paper further extends the result of tomita 1984 to have a weaker sufficient condition for the equivalence of a pair of non real time deterministic pushdown automata to be decidable

rigid cohomology and invariant cycles for a semistable log scheme introduction let k be a perfect field of characteristic p 0 we indicate by w the ring of witt vectors of k and by k0 its quotient field the study of cohomological theories like rigid or crystalline cohomology encounters some problems when applied to singular k varieties in this paper we deal with the rigid cohomology of a particular type of singular k varieties recently a new theory log crystalline cohomology has provided a way to associate to a proper semistable k l log scheme y m the cohomology groups

l a l b a simplified decidability proof we give a proof of decidability of the equivalence problem for deterministic pushdown automata which simplifies that of senizergues theoret comput sci 251 2000 1

the io and oi hierarchies abstract an analysis of recursive procedures in algol 68 with finite modes shows that a denotational semantics of this language can be described on the level of program schemes using a typed calculus with fixed point operators in the first part of this paper we derive classical schematological theorems for the resulting class of level n schemes in part two we investigate the language families obtained by call by value and call by name interpretation of level n schemes over the algebra of formal languages it is proved that differentiating according to the functional level of recursion leads to two infinite hierarchies of recursive languages the io and oi hierarchies which can be characterized as canonical extensions of the regular context free and io and oi macro languages respectively sufficient conditions are derived to establish strictness of io like hierarchies finally we derive that recursion on higher types induces an infinite hierarchy of control structures by proving that level n schemes are strictly less powerful than level n 1 schemes

decidability of bisimulation equivalence for process generating context free languages a context free grammar cfg in greibach normal form coincides in another notation with a system of guarded recursion equations in basic process algebra hence to each cfg a process can be assigned as solution which has as its set of finite traces the context free language cfl determined by that cfg while the equality problem for cfl s is unsolvable the equality problem for the processes determined by cfg s turns out to be solvable here equality on processes is given by a model of process graphs modulo bisimulation equivalence the proof is given by displaying a periodic structure of the process graphs determined by cfg s as a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context free languages is given

the equivalence problem for real time dpdas the equivalence problem for deterministic real time pushdown automata is shown to be decidable this result is obtained by showing that valiant s parallel stacking technique using a replacement function introduced in this paper succeeds for deterministic real time pushdown automata equivalence is also decidable for two deterministic pushdown automata one of which is real time

stochastic modeling and estimation of multispectral image data multispectral images consist of multiple channels each containing data acquired from a different band within the frequency spectrum since most objects emit or reflect energy over a large spectral bandwidth there usually exists a significant correlation between channels due to often harsh imaging environments the acquired data may be degraded by both blur and noise simply applying a monochromatic restoration algorithm to each frequency band ignores the cross channel correlation present within a multispectral image a gibbs prior is proposed for multispectral data modeled as a markov random field containing both spatial and spectral cliques spatial components of the model use a nonlinear operator to preserve discontinuities within each frequency band while spectral components incorporate nonstationary cross channel correlations the multispectral model is used in a bayesian algorithm for the restoration of color images in which the resulting nonlinear estimates are shown to be quantitatively and visually superior to linear estimates generated by multichannel wiener and least squares restoration

formal languages over gf 2 abstract variants of the union and concatenation operations on formal languages are investigated in which boolean logic in the definitions that is conjunction and disjunction is replaced with the operations in the two element field gf 2 conjunction and exclusive or union is thus replaced with symmetric difference whereas concatenation gives rise to a new gf 2 concatenation operation which is notable for being invertible all operations preserve regularity and for a pair of languages recognized by an m state and an n state dfa their gf 2 concatenation is recognized by a dfa with m 2 n states and this number of states is in the worst case necessary similarly the state complexity of gf 2 inverse is 2 n 1 next a new class of formal grammars based on gf 2 operations is defined and it is shown to have the same computational complexity as ordinary grammars with union and concatenation in particular simple parsing in time o n 3 fast parsing in the time of matrix multiplication and parsing in nc2

nivat s theorem for pushdown transducers abstract the notions of an extended pushdown automaton pda and a pushdown transducer pdt are formalized in matrix notation by generalizing the concept of a pushdown transition matrix the resulting matrices form a semiring the equivalence to nonextended pdas and pdts is shown the semiring structure gives a new proof that the types reset pushdown and one counter are real time types moreover it allows the construction of the functional composition of a pushdown transduction and a finite transducer mapping as an important application nivat s theorem is generalized to rational and polynomial pdts over arbitrary semirings examples include the mirror image of the input and the dyck reduction

on the finite valuedness problem for sequential machines abstract for a set a a 1 a m of n x n matrices with nonnegative integer entries let p a be the set of all finite products of matrices in a we show that there is a square space algorithm to decide given a whether or not p a is finite as a corollary we show that there is an exponential space algorithm to decide given a nondeterministic mealy sequential machine m with accepting states whether there exists an integer d 0 such that on every input the number of accepting computations of m producing distinct outputs is at most d if d exists the smallest such d can be computed in space exponential in size m log d the space bound reduces to polynomial for the analogous problem of ambiguity of nondeterministic finite acceptors

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

bayesian multichannel image restoration using compound gauss markov random fields we develop a multichannel image restoration algorithm using compound gauss markov random fields cgmrf models the line process in the cgmrf allows the channels to share important information regarding the objects present in the scene in order to estimate the underlying multichannel image two new iterative algorithms are presented and their convergence is established they can be considered as extensions of the classical simulated annealing and iterative conditional methods experimental results with color images demonstrate the effectiveness of the proposed approaches

rational points over finite fields for regular models of algebraic varieties of hodge type geq 1 let r be a discrete valuation ring of mixed characteristics 0 p with finite residue field k and fraction field k let k be a finite extension of k and let x be a regular proper and flat r scheme with generic fibre x k and special fibre x k assume that x k is geometrically connected and of hodge type geq 1 in positive degrees then we show that the number of k rational points of x satisfies the congruence x k equiv 1 mod k thanks to cite bbe07 we deduce such congruences from a vanishing theorem for the witt cohomology groups h q x k w so x k q for q 0 in our proof of this last result a key step is the construction of a trace morphism between the witt cohomologies of the special fibres of two flat regular r schemes x and y of the same dimension defined by a surjective projective morphism f y to x

a polynomial algorithm testing partial confluence of basic semi thue systems we give a polynomial algorithm solving the problem is s partially confluent on the rational set r for finite basic noetherian semi thue systems the algorithm is obtained by a polynomial reduction of this problem to the equivalence problem for deterministic 2 tape finite automata which has been shown to be polynomially decidable in fri gre82

a characterization of regular expressions under bisimulation we solve an open question of milner 1984 we define a set of so called well behaved finite automata that modulo bisimulation equivalence corresponds exactly to the set of regular expressions and we show how to determine whether a given finite automaton is in this set as an application we consider the star height problem

markovian reconstruction using a gnc approach this paper is concerned with the reconstruction of images or signals from incomplete noisy data obtained at the output of an observation system the solution is defined in maximum a posteriori map sense and it appears as the global minimum of an energy function joining a convex data fidelity term and a markovian prior energy the sought images are composed of nearly homogeneous zones separated by edges and the prior term accounts for this knowledge this term combines general nonconvex potential functions pfs which are applied to the differences between neighboring pixels the resultant map energy generally exhibits numerous local minima calculating its local minimum placed in the vicinity of the maximum likelihood estimate is inexpensive but the resultant estimate is usually disappointing optimization using simulated annealing is practical only in restricted situations several deterministic suboptimal techniques approach the global minimum of special map energies employed in the field of image denoising at a reasonable numerical cost the latter techniques are not directly applicable to general observation systems nor to general markovian prior energies this work is devoted to the generalization of one of them the graduated nonconvexity gnc algorithm in order to calculate nearly optimal map solutions in a wide range of situations in fact gnc provides a solution by tracking a set of minima along a sequence of approximate energies starting from a convex energy and progressing toward the original energy in this paper we develop a common method to derive efficient gnc algorithms for the minimization of map energies which arise in the context of any observation system giving rise to a convex data fidelity term and of markov random field mrf energies involving any nonconvex and or nonsmooth pfs as a side result we propose how to construct pertinent initializations which allow us to obtain meaningful solutions using local minimization of these map energies two numerical experiments an image deblurring and an emission tomography reconstruction illustrate the performance of the proposed technique

the picard lefschetz formula for p adic cohomology in this paper we discuss a p adic analogue of the picard lefschetz formula for a family with ordinary double points over a complete discrete valuation ring of mixed characteristic 0 p we construct vanishing cycle modules which measure the difference between the rigid cohomology groups of the special fiber and the de rham cohomology groups of the generic fiber furthermore the monodromy operators on the de rham cohomology groups of the generic fiber are described by the canonical generators of the vanishing cycle modules in the same way as in the case of the l adic or classical picard lefschetz formula for the construction and the proof we use the logarithmic de rham witt complexes and those weight filtrations investigated by mokrane

undecidability of bisimilarity by defender s forcing stirling l1996 1998r proved the decidability of bisimilarity on so called normed pushdown processes this result was substantially extended by senizergues l1998 2005r who showed the decidability of bisimilarity for regular or equational graphs of finite out degree this essentially coincides with weak bisimilarity of processes generated by unnormed pushdown automata where the e transitions can only deterministically pop the stack the question of decidability of bisimilarity for the more general class of so called type 1 systems which is equivalent to weak bisimilarity on unrestricted e popping pushdown processes was left open this was repeatedly indicated by both stirling and senizergues here we answer the question negatively that is we show the undecidability of bisimilarity on type 1 systems even in the normed case we achieve the result by applying a technique we call defender s forcing referring to the bisimulation games the idea is simple yet powerful we demonstrate its versatility by deriving further results in a uniform way first we classify several versions of the undecidable problems for prefix rewrite systems or pushdown automata as 01 complete or 11 complete second we solve the decidability question for weak bisimilarity on pa process algebra processes showing that the problem is undecidable and even 11 complete third we show 11 completeness of weak bisimilarity for so called parallel pushdown or multiset automata a subclass of labeled place transition petri nets