leaf languages and string compression tight connections between leaf languages and strings compressed by straight line programs slps are established it is shown that the compressed membership problem for a language l is complete for the leaf language class defined by l via logspace machines a more difficult variant of the compressed membership problem for l is shown to be complete for the leaf language class defined by l via polynomial time machines as a corollary it is shown that there exists a fixed linear visibly pushdown language for which the compressed membership problem is pspace complete for xml languages it is shown that the compressed membership problem is conp complete furthermore it is shown that the embedding problem for slp compressed strings is hard for pp probabilistic polynomial time

compression of low entropy strings with lempel ziv algorithms we compare the compression ratio of the lempel ziv algorithms with the empirical entropy of the input string this approach makes it possible to analyze the performance of these algorithms without any assumption on the input and to obtain worst case results we show that in this setting the standard definition of optimal compression algorithm is not satisfactory in fact although lempel ziv algorithms are optimal according to the standard definition there exist families of low entropy strings which are not compressed optimally more precisely the compression ratio achieved by lz78 resp lz77 can be much higher than the zeroth order entropy h0 resp the first order entropy h1 for this reason we introduce the concept of lambda optimal algorithm an algorithm is lambda optimal with respect to hk if loosely speaking its compression ratio is asymptotically bounded by lambda times the kth order empirical entropy hk we prove that lz78 cannot be lambda optimal with respect to any hk with k geq 0 then we describe a new algorithm which combines lz78 with run length encoding rle and is 3 optimal with respect to h0 finally we prove that lz77 is 8 optimal with respect to h0 and that it cannot be lambda optimal with respect to hk for any k geq 1

semi classical properties of berezin toeplitz operators with c k symbol we obtain the semi classical expansion of the kernels and traces of toeplitz operators with ck symbol on a symplectic manifold we also give a semi classical estimate of the distance of a toeplitz operator to the space of self adjoint and multiplication operators we obtain the semi classical expansion of the kernels and traces of toeplitz operators with ck symbol on a symplectic manifold we also give a semi classical estimate of the distance of a toeplitz operator to the space of self adjoint and multiplication operators

a really simple approximation of smallest grammar in this paper we present a really simple linear time algorithm constructing a context free grammar of size 4 g log 3 2 n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c algorithms with such an approximation guarantee and running time are known however all of them were non trivial and their analyses were involved the here presented algorithm computes the lz77 factorisation and transforms it in phases to a grammar in each phase it maintains an lz77 like factorisation of the word with at most factors as well as additional o letters where was the size of the original lz77 factorisation in one phase in a greedy way by a left to right sweep and a help of the factorisation we choose a set of pairs of consecutive letters to be replaced with new symbols i e nonterminals of the constructed grammar we choose at least 2 3 of the letters in the word and there are o many different pairs among them hence there are o log n phases each of them introduces o nonterminals to a grammar a more precise analysis yields a bound 4 log n as g this yields the desired bound g 4 g log n g

tree compression with top trees we introduce a new compression scheme for labeled trees based on top trees our compression scheme is the first to simultaneously take advantage of internal repeats in the tree as opposed to the classical dag compression that only exploits rooted subtree repeats while also supporting fast navigational queries directly on the compressed representation we show that the new compression scheme achieves close to optimal worst case compression can compress exponentially better than dag compression is never much worse than dag compression and supports navigational queries in logarithmic time

semiclassical spectral analysis of toeplitz operators on symplectic manifolds the case of discrete wells we consider toeplitz operators associated with the renormalized bochner laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold we study the asymptotic behavior in the semiclassical limit of low lying eigenvalues and the corresponding eigensections of a self adjoint toeplitz operator under assumption that its principal symbol has a non degenerate minimum with discrete wells as an application we prove upper bounds for low lying eigenvalues of the bochner laplacian in the semiclassical limit

the smallest grammar problem this paper addresses the smallest grammar problem what is the smallest context free grammar that generates exactly one given string spl sigma this is a natural question about a fundamental object connected to many fields such as data compression kolmogorov complexity pattern identification and addition chains due to the problem s inherent complexity our objective is to find an approximation algorithm which finds a small grammar for the input string we focus attention on the approximation ratio of the algorithm and implicitly the worst case behavior to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature our first results are concern the hardness of approximating the smallest grammar problem most notably we show that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569 8568 unless p np we then bound approximation ratios for several of the best known grammar based compression algorithms including lz78 b isection sequential longest match greedy and re pair among these the best upper bound we show is o n sup 1 2 we finish by presenting two novel algorithms with exponentially better ratios of o log sup 3 n and o log n m sup where m sup is the size of the smallest grammar for that input the latter algorithm highlights a connection between grammar based compression and lz77

the complexity of tree automata and xpath on grammar compressed trees the complexity of various membership problems for tree automata on compressed trees is analyzed two compressed representations are considered dags which allow to share identical subtrees in a tree and straight line context free tree grammars which moreover allow to share identical intermediate parts in a tree several completeness results for the classes nl p and pspace are obtained finally the complexity of the evaluation problem for structural xpath queries on trees that are compressed via straight line context free tree grammars is investigated

data compression of stereopairs two fundamentally different techniques for compressing stereopairs are discussed the first technique called disparity compensated transform domain predictive coding attempts to minimize the mean square error between the original stereopair and the compressed stereopair the second technique called mixed resolution coding is a psychophysically justified technique that exploits known facts about human stereovision to code stereopairs in a subjectively acceptable manner a method for assessing the quality of compressed stereopairs is also presented it involves measuring the ability of an observer to perceive depth in coded stereopairs it was found that observers generally perceived objects to be further away in compressed stereopairs than they did in originals it is proved that the rate distortion limit for coding stereopairs cannot in general be achieved by a coder that first codes and decodes the right picture sequence independently of the left picture sequence and then codes and decodes the left picture sequence given the decoded right picture sequence

the lot transform coding without blocking effects an exact derivation of an optimal lapped orthogonal transform lot is presented the optimal lot is related to the discrete cosine transform dct in such a way that a fast algorithm for a nearly optimal lot is derived compared to the dct the fast lot requires about 20 30 more computations mostly additions an image coding example demonstrates the effectiveness of the lot in reducing blocking effects the lot actually leads to slightly smaller signal reconstruction errors than does the dct

motion compensating prediction with fractional pel accuracy the effect of fractional pel accuracy on the efficiency of motion compensating predictors is studied using various spatial prediction interpolation filters in model calculations the power spectral density of the prediction error is related to the probability density function of the displacement error prediction can be improved both by higher accuracy of motion compensation and by spatial wiener filtering in the predictor beyond a critical accuracy the possibility of further improving prediction by more accurate motion compensation is small experiments with videophone signals and with broadcast tv signals confirm these model calculations sinc interpolation bilinear interpolation and wiener filtering are compared at integer pel 1 2 pel 1 4 pel and 1 8 pel accuracies a three state technique for reliable displacement estimation with fractional pel accuracy is introduced it is based on phase correlation for motion compensation with block size of 16 pels 16 pels 1 4 pel accuracy appears to be sufficient for broadcast tv signals whereas for videophone signals 1 2 pel accuracy is desirable

squeezed states and hermite polynomials in a complex variable following the lines of the recent paper of j p gazeau and f h szafraniec j phys a math theor 44 495201 2011 we construct here three types of coherent states related to the hermite polynomials in a complex variable which are orthogonal with respect to a non rotationally invariant measure we investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics we also obtain a second realization of the canonical coherent states in the bargmann space of analytic functions in terms of a squeezed basis all this is done in the flavor of the classical approach of v bargmann commun pure appl math 14 187 1961

a neural fuzzy system for image motion estimation many methods for computing optical flow image motion vector have been proposed while others continue to appear block matching methods are widely used because of their simplicity and easy implementation the motion vector is uniquely defined in block matching methods by the best fit of a small reference subblock from a previous image frame in a larger search region from the present image frame hence this method is very sensitive to the real environments involving occlusion specularity shadowing transparency etc in this paper a neural fuzzy system with robust characteristics and learning ability is incorporated with the block matching method to make a system adaptive for different circumstances in the neural fuzzy motion estimation system each subblock in the search region is assigned a similarity membership contributing different degrees to the motion vector this system is more reliable robust and accurate in motion estimation than many other methods including horn and schunck s optical flow fuzzy logic motion estimator fme best block matching nr and fast block matching since fast block matching algorithms can be used to reduce search time a three step fast search method is employed to find the motion vector in our system however the candidate motion vector is often trapped by the local minimum which makes the motion vector undesirable an improved three step fast search method is tested to reduce the effect from local minimum and some comparisons about fast search algorithms are made in addition a quarter compensation algorithm for compensating the interframe image to tackle the problem that the motion vector is not an integer but rather a floating point is proposed since our system can give the accurate motion vector we may use the motion information in many different applications such as motion compensation ccd camera auto focusing or zooming moving object extraction etc two application examples will be illustrated in this paper

quantized nambu poisson manifolds and n lie algebras we investigate the geometric interpretation of quantized nambu poisson structures in terms of noncommutative geometries we describe an extension of the usual axioms of quantization in which classical nambu poisson structures are translated to n lie algebras at quantum level we demonstrate that this generalized procedure matches an extension of berezin toeplitz quantization yielding quantized spheres hyperboloids and superspheres the extended berezin quantization of spheres is closely related to a deformation quantization of n lie algebras as well as the approach based on harmonic analysis we find an interpretation of nambu heisenberg n lie algebras in terms of foliations of rn by fuzzy spheres fuzzy hyperboloids and noncommutative hyperplanes some applications to the quantum geometry of branes in m theory are also briefly discussed

gl and geometric quantization an axiomatic approach to the approximation of infinite dimensional algebras is presented examples illustrating the need for a rigorous treatment of this subject geometric quantization is employed to construct systematicallysu n approximations of diffeomorphism algebras which first appeared in the theory of relativistic membranes

hermite polynomials and quasi classical asymptotics we study an unorthodox variant of the berezin toeplitz type of quantization scheme on a reproducing kernel hilbert space generated by the real hermite polynomials and work out the associated quasi classical asymptotics

orthogonal polynomials laguerre fock space and quasi classical asymptotics continuing our earlier investigation of the hermite case s t ali and m englis j math phys 55 042102 2014 we study an unorthodox variant of the berezin toeplitz quantization scheme associated with laguerre polynomials in particular we describe a laguerre analogue of the classical fock segal bargmann space and the relevant semi classical asymptotics of its toeplitz operators the former actually turns out to coincide with the hilbert space appearing in the construction of the well known barut girardello coherent states further extension to the case of legendre polynomials is likewise discussed

scene adaptive coder an efficient single pass adaptive bandwidth compression technique using the discrete cosine transform is described the coding process involves a simple thresholding and normalization operation on the transform coefficients adaptivity is achieved by using a rate buffer for channel rate equalization the buffer status and input rate are monitored to generate a feedback normalization factor excellent results are demonstrated for coding of color images at 0 4 bits pixel corresponding to real time color television transmission over a 1 5 mbit s channel

universal lossless compression via multilevel pattern matching a universal lossless data compression code called the multilevel pattern matching code mpm code is introduced in processing a finite alphabet data string of length n the mpm code operates at o log log n levels sequentially at each level the mpm code detects matching patterns in the input data string substrings of the data appearing in two or more nonoverlapping positions the matching patterns detected at each level are of a fixed length which decreases by a constant factor from level to level until this fixed length becomes one at the final level the mpm code represents information about the matching patterns at each level as a string of tokens with each token string encoded by an arithmetic encoder from the concatenated encoded token strings the decoder can reconstruct the data string via several rounds of parallel substitutions a o 1 log n maximal redundancy sample upper bound is established for the mpm code with respect to any class of finite state sources of uniformly bounded complexity we also show that the mpm code is of linear complexity in terms of time and space requirements the results of some mpm code compression experiments are reported

quantum riemann surfaces i the unit disc we construct a non commutative algebra c mu bar u which is a quantum deformation of the algebra of continuous functions on the closed unit disc bar u c mu bar u is generated by the toeplitz operators on a suitable hilbert space of holomorphic functions onu

generalized bergman kernels and geometric quantization in geometric quantization it is well known that if f is an observable and f a polarization on a symplectic manifold m then the condition xf leaves f invariant where xf denotes the hamiltonian vector field associated to f is sufficient to guarantee that one does not have to compute the bks kernel explicitly in order to know the corresponding quantum operator it is shown in this paper that this condition on f can be weakened to xf leaves f f invariant and the corresponding quantum operator is then given implicitly by formula 4 8 in particular when f is a positive kahler polarization all observables can be quantized directly and moreover an explicit formula for the corresponding quantum operator is derived theorem 5 8 applying this to the phase space r2n one obtains a quantization prescription which ressembles the normal ordering of operators in quantum field theory when we translate this prescription to the usual position representation of quantum mechanics the result i

convergence of the wick star product we construct a frechet space as a subspace of c omega mathbb c n where the wick star product converges and is continuous the resulting frechet algebra mathcal a is studied in detail including a representation of mathcal a in the bargmann fock space and a discussion of star exponentials and coherent states

a class of generalized complex hermite polynomials a class of generalized complex polynomials of hermite type suggested by a special magnetic schrodinger operator is introduced and some related basic properties are discussed

fully functional suffix trees and optimal text searching in bwt runs bounded space indexing highly repetitive texts such as genomic databases software repositories and versioned text collections has become an important problem since the turn of the millennium a relevant compressibility measure for repetitive texts is r the number of runs in their burrows wheeler transforms bwts one of the earliest indexes for repetitive collections the run length fm index used o r space and was able to efficiently count the number of occurrences of a pattern of length m in a text of length n in o m log log n time with current techniques however it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r in this article we close this long standing problem showing how to extend the run length fm index so that it can locate the occ occurrences efficiently in o occ log log n time within o r space by raising the space to o r log log n our index counts the occurrences in optimal time o m and locates them in optimal time as well o m occ by further raising the space by an o w log factor where is the alphabet size and w e log n is the ram machine size in bits we support count and locate in o m log w and o m log w occ time which is optimal in the packed setting and had not been obtained before in compressed space we also describe a structure using o r log n r space that replaces the text and extracts any text substring of length e in the almost optimal time o log n r e log w within that space we similarly provide access to arbitrary suffix array inverse suffix array and longest common prefix array cells in time o log n r and extend these capabilities to full suffix tree functionality typically in o log n r time per operation our experiments show that our o r space index outperforms the space competitive alternatives by 1 2 orders of magnitude in time competitive implementations of the original fm index are outperformed by 1 2 orders of magnitude in space and or 2 3 in time

document listing on repetitive collections with guaranteed performance abstract we consider document listing on string collections that is finding in which strings a given pattern appears in particular we focus on repetitive collections a collection of size n over alphabet 1 is composed of d copies of a string of size n and s edits are applied on ranges of copies we introduce the first document listing index with size o n s precisely o n lg s lg 2 n lg d bits and with useful worst case time guarantees given a pattern of length m the index reports the ndoc 0 strings where it appears in time o m lg 1 n ndoc for any constant 0 and tells in time o m lg n if ndoc 0 our technique is to augment a range data structure that is commonly used on grammar based indexes so that instead of retrieving all the pattern occurrences it computes useful summaries on them we show that the idea has independent interest we introduce the first grammar based index that on a text t 1 n with a grammar of size r uses o r lg n bits and counts the number of occurrences of a pattern p 1 m in time o m 2 m lg 2 r for any constant 0 we also give the first index using o z lg n z lg n bits where t is parsed by lempel ziv into z phrases counting occurrences in time o m lg 2 n

new orthogonality relations for the hermite polynomials and related hilbert spaces the hermite polynomials give rise to orthonormal bases in bagmann like hilbert spaces xa 0 a 1 consisting of entire functions these hilbert spaces are related to the gelfand shilov space s1212 viz s1212 0 a 1 xa

approximation of grammar based compression via recompression in this paper we present a simple linear time algorithm constructing a context free grammar of size o g log n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c otherwise additional cost of o n log is needed algorithms with such an approximation guarantee and running time are known the novelty of this paper is a particular simplicity of the algorithm as well as the analysis of the algorithm which uses a general technique of recompression recently introduced by the author furthermore contrary to the previous results this work does not use the lz representation of the input string in the construction nor in the analysis

random access to grammar compressed strings and trees grammar based compression where one replaces a long string by a small context free grammar that generates the string is a simple and powerful paradigm that captures sometimes with slight reduction in efficiency many of the popular compression schemes including the lempel ziv family run length encoding byte pair encoding sequitur and re pair in this paper we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string let s be a string of length n compressed into a context free grammar mathcal s of size n we present two representations of mathcal s achieving o log n random access time and either o n cdot alpha k n construction time and space on the pointer machine model or o n construction time and space on the ram here alpha k n is the inverse of the k th row of ackermann s function our representations also efficiently support decompression of any substring in s we can decompres

compressed range minimum queries abstract given a string s of n integers in 0 a range minimum query rmq i j asks for the index of the smallest integer in s i j it is well known that the problem can be solved with a succinct data structure of size 2 n o n and constant query time in this paper we show how to preprocess s into a compressed representation that allows fast range minimum queries this allows for sublinear size data structures with logarithmic query time the most natural approach is to use string compression and construct a data structure for answering range minimum queries directly on the compressed string we investigate this approach in the context of grammar compression we then consider an alternative approach instead of compressing s using string compression we compress the cartesian tree of s using tree compression we show that this approach can be exponentially better than the former is never worse by more than an o factor i e for constant alphabets it is never asymptotically worse and can in fact be worse by an factor

berezin toeplitz quantization on kaehler manifolds we study the berezin toeplitz quantization on kaehler manifolds we explain first how to compute various associated asymptotic expansions then we compute explicitly the first terms of the expansion of the kernel of the berezin toeplitz operators and of the composition of two berezin toeplitz operators as application we estimate the norm of donaldson s q operator

toeplitz quantization of kahler manifolds ang gl n n limits for general compact kahler manifolds it is shown that both toeplitz quantization and geometric quantization lead to a well defined by operator norm estimates classical limit this generalizes earlier results of teh authors and klimek and lesniewski obtained for the tours and higher genus riemann surfaces respectively we thereby arrive at an approximation of the poisson algebra by a sequence of finitedimensional matrix algebrasgl n n

on the compressibility of finite languages and formal proofs abstract we consider the minimal number of productions needed for a grammar to cover a finite language l as the grammatical complexity of l we study this measure for several types of word and tree grammars and show that it is closely connected to well known measures for the complexity of formal proofs in first order predicate logic we construct an incompressible sequence of finite word languages and transfer this and several other results about the complexity of word and tree languages to formal proofs

repair and all irreducible grammars are upper bounded by high order empirical entropy irreducible grammars are a class of context free grammars with well known representatives such as repair with a few tweaks longest match greedy and sequential we show that a grammar based compression method described by kieffer and yang 2000 is upper bounded by the high order empirical entropy of the string when the underlying grammar is irreducible specifically given a string s over an alphabet of size sigma we prove that if the underlying grammar is irreducible then the length of the binary code output by this grammar based compression method is bounded by s h k s o s log sigma for any k in o log sigma s where h k s is the k order empirical entropy of s this is the first bound encompassing the whole class of irreducible grammars in terms of the high order empirical entropy with coefficient 1

approximation of smallest linear tree grammar a simple linear time algorithm for constructing a linear context free tree grammar of size o r g r g log n r g for a given input tree t of size n is presented where g is the size of a minimal linear context free tree grammar for t and r is the maximal rank of symbols in t which is a constant in many applications this is the first example of a grammar based tree compression algorithm with a good i e logarithmic in terms of the size of the input tree approximation ratio the analysis of the algorithm uses an extension of the recompression technique from strings to trees

sequential codes lossless compression of individual sequences and kolmogorov complexity a general class of sequential codes for lossless compression of individual sequences on a finite alphabet is defined including many types of codes that one would want to implement the principal requirement for membership in the class is that the encoding and decoding operations be performable on a computer the opta function for the class of codes is then considered which is the function that assigns to each individual sequence the infimum of the rates at which the sequence can be compressed over this class of sequential codes two results about the opta function are obtained 1 it is shown that any sequential code in the class compresses some individual sequence at a rate strictly greater than the rate for that sequence given by the opta function and 2 it is shown that the opta function takes a value strictly greater than that of the kolmogorov 1965 complexity rate function for some individual sequences

quantization towards a comparison between methods in this paper it is shown that the procedure of geometric quantiztion applied to kahler manifolds gives the following result the hilbert space h consists roughly speaking of holomorphic functions on the phase space m and to each classical observable f i e a real function on m is associated an operator f on h as follows first multiply by f 1 4 drf dr being the laplace de rham operator on the kahler manifold m and then take the holomorphic part see g m tuynman j math phys 27 573 1987 this result is correct on compact kahler manifolds and correct modulo a boundary term md on noncompact kahler manifolds in this way these results can be compared with the quantization procedure of berezin math ussr izv 8 1109 1974 9 341 1975 commun math phys 40 153 1975 which is strongly related to quantization by products e g see c moreno and p ortega navarro amn inst h poincare sec a 38 215 1983 lett math phys 7 181 1983 c moreno lett math phys 11 3

weighted bergman kernels and quantization let be a bounded pseudoconvex domain in c n two positive functions on such that log log are plurisubharmonic and z a point at which log is smooth and strictly plurisubharmonic we show that as k the bergman kernels with respect to the weights k have an asymptotic expansion for x y near z where x y is an almost analytic extension of phi x x x and similarly for further if in addition is of finite type behave reasonably at the boundary and log log are strictly plurisubharmonic on we obtain also an analogous asymptotic expansion for the berezin transform and give applications to the berezin quantization finally for smoothly bounded and strictly pseudoconvex and a smooth strictly plurisubharmonic defining function for we also obtain results on the berezin toeplitz quantization

berezin transform of two arguments abstract we describe the asymptotic behavior of the berezin transform of two arguments which generalizes the standard notion of the berezin transform the asymptotic analysis we give is in the setting of the holomorphic and the harmonic fock spaces respectively

identification of berezin toeplitz deformation quantization we give a complete identification of the deformation quantization which was obtained from the berezin toeplitz quantization on an arbitrary compact kahler manifold the deformation quantization with the opposite star product proves to be a differential deformation quantization with separation of variables whose dassifying form is explicitly calculated its characteristic dass which dassifies star products up to equivalence is obtained the proof is based on the microlocal description of the szego kernel of a strictly pseudoconvex domain given by boutet de monvel and sjostrand

two variable extensions of the laguerre and disc polynomials abstract this work contains a detailed study of a one parameter generalization of the 2 d hermite polynomials and a two parameter extension of zernike s disc polynomials we derive linear and bilinear generating functions and explicit formulas for our generalizations and study integrals of products of some of these 2 d orthogonal polynomials we also establish a combinatorial inequality involving elementary symmetric functions and solve the connection coefficient problem for our polynomials

on the vocabulary of grammar based codes and the logical consistency of texts this paper presents a new interpretation for zipf mandelbrot s law in natural language which rests on two areas of information theory firstly we construct a new class of grammar based codes and secondly we investigate properties of strongly nonergodic stationary processes the motivation for the joint discussion is to prove a proposition with a simple informal statement if a text of length n describes n independent facts in a repetitive way then the text contains at least n log n different words under suitable conditions on n in the formal statement two modeling postulates are adopted firstly the words are understood as nonterminal symbols of the shortest grammar based encoding of the text secondly the text is assumed to be emitted by a finite energy strongly nonergodic source whereas the facts are binary iid variables predictable in a shift invariant way

time space trade offs for lempel ziv compressed indexing abstract given a string s the compressed indexing problem is to preprocess s into a compressed representation that supports fast substring queries the goal is to use little space relative to the compressed size of s while supporting fast queries we present a compressed index based on the lempel ziv 1977 compression scheme we obtain the following time space trade offs for constant sized alphabets i o m occ lg lg n time using o z lg n z lg lg z space or ii o m 1 lg z lg n z occ lg lg n lg z time using o z lg n z space for integer alphabets polynomially bounded by n iii o m 1 lg z lg n z occ lg lg n lg z time using o z lg n z lg lg z space or iv o m occ lg lg n lg z time using o z lg n z lg z space where n and m are the length of the input string and query string respectively z is the number of phrases in the lz77 parse of the input string occ is the number of occurrences of the query in the input and 0 is an arbitrarily small constant in particular i improves the leading term in the query time of the previous best solution from o m lg m to o m at the cost of increasing the space by a factor lg lg z alternatively ii matches the previous best space bound but has a leading term in the query time of o m 1 lg z lg n z however for any polynomial compression ratio i e z o n 1 for constant 0 this becomes o m our index also supports extraction of any substring of length l in o l lg n z time technically our results are obtained by novel extensions and combinations of existing data structures of independent interest including a new batched variant of weak prefix search

fixed and adaptive predictors for hybrid predictive transform coding hybrid predictive transform coding is studied the usual formulation is to first apply a unitary transform and then code the transform coefficients with independent dpcm coders i e the prediction is performed in the transform domain this structure is compared to spatial domain prediction where a difference signal is formed in the spatial domain and then coded by a transform coder a linear spatial domain predictor which minimizes the mean square prediction error also minimizes the mean square of each transform coefficient the two structures are equivalent if the transform domain prediction scheme is extended to a more general predictor hence the structure that gives the easiest implementation can be chosen the spatial domain structure is preferred for motion compensation and for line interlaced video signals interframe hybrid coding experiments are performed on interlaced videophone scenes using an adaptive transform coder motion compensation gives a rate reduction of 25 35 percent compared to frame difference prediction with the same mean square error the subjective advantage is even greater since the dirty window effect is not present with motion compensation it is important to perform the motion estimation with fractional pel accuracy field coding with a switched predictor using previous field in moving areas is an interesting alternative to frame coding with frame difference prediction

compact q gram profiling of compressed strings we consider the problem of computing the q gram profile of a string t of size n compressed by a context free grammar with n production rules we present an algorithm that runs in o email protected expected time and uses o n q k t q space where email protected qn is the exact number of characters decompressed by the algorithm and k t email protected email protected is the number of distinct q grams in t this simultaneously matches the current best known time bound and improves the best known space bound our space bound is asymptotically optimal in the sense that any algorithm storing the grammar and the q gram profile must use w n q k t q space to achieve this we introduce the q gram graph that space efficiently captures the structure of a string with respect to its q grams and show how to construct it from a grammar

computing sequences with addition chains given a sequence n 1 cdots n m of positive integers what is the smallest number of additions needed to compute all m integers starting with 1 this generalization of the addition chain m 1 problem will be called the addition sequence problem we show that the sequence 2 0 2 1 cdots 2 n 1 2 n 1 can be computed with n 2 13 sqrt n log n additions and that n sqrt n 2 is a lower bound this lower bound result is applied to show that the addition sequence problem is np complete

efficient generation of minimal length addition chains an addition chain for a positive integer n is a set 1 a0 a1 ar n of integers such that for each i ge 1 a i a j a k for some k le j i this paper is concerned with some of the computational aspects of generating minimal length addition chains for an integer n particular attention is paid to various pruning techniques that cut down the search time for such chains certain of these techniques are influenced by the multiplicative structure of n later sections of the paper present some results that have been uncovered by searching for minimal length addition chains

circular symmetry and the trace formula let m be a compact n dimensional manifold without boundary and let p be a positive first order elliptic self adjoint classical pseudodifferential operator on lz m the hilbert space of half densities on m the spectrum of p is discrete and accumulates only at we denote the eigenvalues with multiplicities by 2o 21 2 recall that the singularities of the inverse fourier transform of the spectral measure