a very hard log space counting class abstract we consider the logarithmic space counting and optimization classes l span l and opt l which are defined analogously to their polynomial time counterparts we obtain complete functions for these three classes in terms of graphs and finite automata we show that l and opt l are both included in nc 2 but that surprisingly span l seems to be a much harder class than l and opt l we demonstrate that span l functions can be computed in polynomial time if and only if p p and all the classes of the polynomial time hierarchy are included in p this result follows from the fact that span l and p are very similar span l p and any function in p can be represented as the difference of a function in fl and a function in span l nevertheless the inclusion p span l would imply nl p np we furthermore investigate restrictions of the classes opt l and span l

derivation digraphs for dependencies in ordinal and similarity based data we present graph based method of reasoning with if then rules describing dependencies between attributes in ordinal and similarity based data the rules we consider have two basic interpretations as attribute implications in object attribute incidence data where objects are allowed to have attributes features to degrees and as similarity based functional dependencies in an extension of the codd model of data main results in this paper show that degrees to which if then rules are semantically entailed from sets or graded sets of other if then rules can be characterized by existence of particular directed acyclic graphs with vertices labeled by attributes and degrees coming from complete residuated lattices in addition we show that the construction of directed acyclic graphs can be used to compute closures of sets of attributes and normalized proofs

advances in residual vector quantization a review advances in residual vector quantization rvq are surveyed definitions of joint encoder optimality and joint decoder optimality are discussed design techniques for rvqs with large numbers of stages and generally different encoder and decoder codebooks are elaborated and extended fixed rate rvqs and variable rate rvqs that employ entropy coding are examined predictive and finite state rvqs designed and integrated into neural network based source coding structures are revisited successive approximation rvqs that achieve embedded and refinable coding are reviewed a new type of successive approximation rvq that varies the instantaneous block rate by using different numbers of stages on different blocks is introduced and applied to image waveforms and a scalar version of the new residual quantizer is applied to image subbands in an embedded wavelet transform coding system

computing logcfl certificates the complexity class logcfl consists of all languages or decision problems which are logspace reducible to a context free language since logcfl is included in ac1 the problems in logcfl are highly parallelizable by results of ruzzo jcss 21 1980 218 the complexity class logcfl can be characterized as the class of languages accepted by alternating turing machines atms which use logarithmic space and have polynomially sized accepting computation trees we show that for each such atm m recognizing a language a in logcfl it is possible to construct an llogcfl transducer tm such that tm on input w e a outputs an accepting tree for m on w it follows that computing single logcfl certificates is feasible in functional ac1 and is thus highly parallelizable wanke j algorithms 16 1994 470 has recently shown that for any fixed k deciding whether the treewidth of a graph is at most k is in the complexity class logcfl as an application of our general result we show that the task of computing a tree decomposition for a graph of constant treewidth is in functional logcfl and thus in ac1 we also show that the following tasks are all highly parallelizable computing a solution to an acyclic constraint satisfaction problem computing an m coloring for a graph of bounded treewidth computing the chromatic number and minimal colorings for graphs of bounded tree width

a new pebble game that characterizes parallel complexity classes a new two person pebble game that models parallel computations is defined this game extends the two person pebble game defined by dymond and tompa j comput system sci 30 1985 pp 149 161 and is used to characterize two natural parallel complexity classes namely logcfl and text ac 1 the characterizations show a fundamental way in which the computations in these two classes differ this game model also unifies the proofs of some well known results of complexity theory

two applications of inductive counting for complementation problems following the recent independent proofs of immerman siam j comput 17 1988 pp 935 938 and szelepcsenyi bull european assoc theoret comput sci 33 1987 pp 96 100 that nondeterministic space bounded complexity classes are closed under complementation two further applications of the inductive counting technique are developed first an errorless probabilistic algorithm for the undirected graph s t connectivity problem that runs in o log n space and polynomial expected time is given then it is shown that the class logcfl is closed under complementation the latter is a special case of a general result that shows closure under complementation of classes defined by semi unbounded fan in circuits or equivalently nondeterministic auxiliary pushdown automata or tree size bounded alternating turing machines as one consequence it is shown that small numbers of role switches in two person pebbling can be eliminated

a fast mmse encoding technique for vector quantization the authors present a very efficient minimum mean squared error mmse encoding method useful for vector quantization using this method results in a considerable reduction in the number of multiplications and additions the increase in the number of comparisons is moderate and therefore the overall saving in the number of operations is still considerable very little precomputation and extra storage is required

minimax partial distortion competitive learning for optimal codebook design the design of the optimal codebook for a given codebook size and input source is a challenging puzzle that remains to be solved the key problem in optimal codebook design is how to construct a set of codevectors efficiently to minimize the average distortion a minimax criterion of minimizing the maximum partial distortion is introduced in this paper based on the partial distortion theorem it is shown that minimizing the maximum partial distortion and minimizing the average distortion will asymptotically have the same optimal solution corresponding to equal and minimal partial distortion motivated by the result we incorporate the alternative minimax criterion into the on line learning mechanism and develop a new algorithm called minimax partial distortion competitive learning mmpdcl for optimal codebook design a computation acceleration scheme for the mmpdcl algorithm is implemented using the partial distance search technique thus significantly increasing its computational efficiency extensive experiments have demonstrated that compared with some well known codebook design algorithms the mmpdcl algorithm consistently produces the best codebooks with the smallest average distortions as the codebook size increases the performance gain becomes more significant using the mmpdcl algorithm the robustness and computational efficiency of this new algorithm further highlight its advantages

fast full search block matching algorithm for motion compensated video compression this paper proposes a fast block matching algorithm that uses three fast matching error measures besides the conventional mean absolute error mae or mean square error mse an incoming reference block in the current frame is compared to candidate blocks within the search window using multiple matching criteria these three fast matching error measures are established on the integral projections having the advantages of being good block features and having simple complexity in measuring matching errors most of the candidate blocks can be rejected only by calculating one or more of the three fast matching error measures the time consuming computations of mse or mae are performed on only a few candidate blocks that first pass all three fast matching criteria simulation results show that a reduction of over 86 in computations is achieved after integrating the three fast matching criteria into the full search algorithm while ensuring optimal accuracy

two fast nearest neighbor searching algorithms for image vector quantization in this paper two efficient codebook searching algorithms for vector quantization vq are presented the first fast search algorithm utilizes the compactness property of signal energy on transform domain and the geometrical relations between the input vector and every codevector to eliminate those codevectors that have no chance to be the closest codeword of the input vector it achieves a full search equivalent performance as compared with other fast methods of the same kind this algorithm requires the fewest multiplications and the least total times of distortion measurements then a suboptimal searching method which sacrifices the reconstructed signal quality to speed up the search of nearest neighbor is presented this algorithm performs the search process on predefined small subcodebooks instead of the whole codebook for the closest codevector experimental results show that this method not only needs less cpu time to encode an image but also encounters less loss of reconstructed signal quality than tree structured vq does

undirected connectivity in log space we present a deterministic log space algorithm that solves st connectivity in undirected graphs the previous bound on the space complexity of undirected st connectivity was log4 3 obtained by armoni ta shma wigderson and zhou jacm 2000 as undirected st connectivity is complete for the class of problems solvable by symmetric nondeterministic log space computations the class sl this algorithm implies that sl e l where l is the class of problems solvable by deterministic log space computations independent of our work and using different techniques trifonov stoc 2005 has presented an o log n log log n space deterministic algorithm for undirected st connectivity our algorithm also implies a way to construct in log space a fixed sequence of directions that guides a deterministic walk through all of the vertices of any connected graph specifically we give log space constructible universal traversal sequences for graphs with restricted labeling and log space constructible universal exploration sequences for general graphs

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

bayesian modeling and classification of neural signals identifying and classifying action potential shapes in extracellular neural waveforms have long been the subject of research and although several algorithms for this purpose have been successfully applied their use has been limited by some outstanding problems the first is how to determine shapes of the action potentials in the waveform and second how to decide how many shapes are distinct a harder problem is that action potentials frequently overlap making difficult both the determination of the shapes and the classification of the spikes in this report a solution to each of these problems is obtained by applying bayesian probability theory by defining a probabilistic model of the waveform the probability of both the form and number of spike shapes can be quantified in addition this framework is used to obtain an efficient algorithm for the decomposition of arbitrarily complex overlap sequences this algorithm can extract many times more information than previous methods and facilitates the extracellular investigation of neuronal classes and of interactions within neuronal circuits

correlation coefficient based fast template matching through partial elimination partial computation elimination techniques are often used for fast template matching at a particular search location computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location due to the nonmonotonic growth pattern of the correlation based similarity measures partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures in this paper we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation and we propose basic mode and extended mode partial correlation elimination algorithms for fast template matching the basic mode algorithm is more efficient on small template sizes whereas the extended mode is faster on medium and larger templates we also propose a strategy to decide which algorithm to use for a given data set to achieve a high speedup elimination algorithms require an initial guess of the peak correlation value we propose two initialization schemes including a coarse to fine scheme for larger templates and a two stage technique for small and medium sized templates our proposed algorithms are exact i e having exhaustive equivalent accuracy and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes while the actual speedups are data dependent in most cases our proposed algorithms have been found to be significantly faster than the other algorithms

fast sequential implementation of neural gas network for vector quantization although the neural gas network proposed by martinetz et al in 1993 has been proven for its optimality in vector quantizer design and has been demonstrated to have good performance in time series prediction its high computational complexity nlogn makes it a slow sequential algorithm we suggest two ideas to speedup its sequential realization 1 using a truncated exponential function as its neighborhood function and 2 applying a new extension of the partial distance elimination method pde this fast realization is compared with the original version of the neural gas network for codebook design in image vector quantization the comparison indicates that a speedup of five times is possible while the quality of the resulting codebook is almost the same as that of the straightforward realization

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

a fast search algorithm for vector quantization using mean pyramids of codewords one of the most serious problems for vector quantization especially for high dimensional vectors is the high computational complexity of searching for the closest codeword in the codebook design and encoding phases although quantizing high dimensional vectors rather than low dimensional vectors results in better performance the computation time needed for vector quantization grows exponentially with the vector dimension this makes high dimensional vectors unsuitable for vector quantization to overcome this problem a fast search algorithm under the assumption that the distortion is measured by the squared euclidean distance is proposed using the mean pyramids of codewords the algorithm ran reject many codewords that are impossible matches and hence save a great deal of computation time the algorithm is efficient for high dimensional codeword searches experimental results confirm the effectiveness of the proposed method

on minimal sets of graded attribute implications we explore the structure of non redundant and minimal sets consisting of graded if then rules the rules serve as graded attribute implications in object attribute incidence data and as similarity based functional dependencies in a similarity based generalization of the relational model of data based on our observations we derive a polynomial time algorithm which transforms a given finite set of rules into an equivalent one which has the least size in terms of the number of rules

effect of ordering the codebook on the efficiency of the partial distance search algorithm for vector quantization recently c d bei and r m gray 1985 used a partial distance search algorithm that reduces the computational complexity of the minimum distortion encoding for vector quantization the effect of ordering the codevectors on the computational complexity of the algorithm is studied it is shown that the computational complexity of this algorithm can be reduced further by ordering the codevectors according to the sizes of their corresponding clusters

an improved fast adaptive search algorithm for vector quantization by progressive codebook arrangement abstract a simple and efficient search method for image coding vector quantization is suggested it exploits both the high correlation between contiguous frames and the source signal statistics by rearranging dynamically the codebook simulation results indicate a reduction over 90 of computational operations in comparison with the conventional full search method

fast search algorithms for vector quantization of images using multiple triangle inequalities and wavelet transform the encoding of vector quantization vq needs expensive computation for searching the closest codevector to the input vector this paper presents several fast encoding algorithms based on multiple triangle inequalities and wavelet transform to overcome this problem the multiple triangle inequalities confine a search range using the intersection of search areas generated from several control vectors a systematic way for designing the control vectors is also presented the wavelet transform combined with the partial distance elimination is used to reduce the computational complexity of the distance calculation of vectors the proposed algorithms provide the same coding quality as the full search method the experimental results indicate that the new algorithms perform more efficiently than existing algorithms

hierarchy oriented searching algorithms using alternative duplicate codewords for vector quantization mechanism in this paper we will show those algorithms that speed up the search of a closest codeword over a given codebook the mechanism is based on a multilevel concept constructed as a hierarchical organization for a given codebook with size n existing n codewords there are only log email protected levels that need to be constructed in order to find the closest codeword where k is a parameter selection to optimize the comparisons in the course of the searching theoretically the comparisons required to find the closest codeword are on average email protected log email protected which is substantially faster than that of a full search job besides in order to approach the perfect match with the exact one among the codewords a duplicate mechanism is also applied to our algorithm so that the lowest possible distortion is achieved as is observed from the results of the experiments the estimation of comparisons in our execution without codeword duplicate is on average about email protected log email protected n times the full search method it is worth noting that the larger the size of the codebook the more the speed increases in particular there are two classifications non duplicate and duplicate method which are associated with the codewords distribution in the dominated set which were experimented on some tables the duplicate is manipulated by the training set containing six popular image data to demonstrate the efficiency of our scheme also the time requirement to find the closest codeword is effectively reduced especially in the case of a large sized codebook therefore our scheme offers a novel exploration and achieves a faster performance in the closest codeword searching for vector quantization of image data

vector quantization with variable precision classification we investigate variable precision classification vpc for speeding vector quantization vq vpc evaluates bit serially from the most significant bit when the magnitude of the error due to the unevaluated bits is less than the absolute magnitude of the discriminant we can classify without processing the remaining bits a proof shows that as the operand precision increases the average necessary precision becomes asymptotically independent of the operand precision vpc makes the complexity of the l sub 2 norm equivalent to the l sub 1 norm in vq of real images on average the codevector element s precision necessary for classification was under four bits we implemented binary classification circuitry using vpc and conventional approaches the key modules were designed and their performance estimated assuming 1 0 spl mu m gate array technology the implementations could search binary pruned trees at the television quality video rate when the overall execution time is important vpc more than halves the computational complexity

non cancellative boolean circuits a generalization of monotone boolean circuits cancellations are known to be helpful in efficient algebraic computation of polynomials over fields we define a notion of cancellation in boolean circuits and define boolean circuits that do not use cancellation to be non cancellative non cancellative boolean circuits are a natural generalization of monotone boolean circuits we show that in the absence of cancellation boolean circuits require super polynomial size to compute the determinant interpreted over gf 2 this non monotone boolean function is known to be in p in the spirit of monotone complexity classes we define complexity classes based on non cancellative boolean circuits we show that when the boolean circuit model is restricted by withholding cancellation p and popular classes within p are restricted as well but classes np and above remain unchanged

on the reducibility of sets inside np to sets with low information content this paper studies for various natural problems in np whether they can be reduced to sets with low information content such as branches p selective sets and membership comparable sets the problems that are studied include the satisfiability problem the graph automorphism problem the undirected graph accessibility problem the determinant function and all logspace self reducible languages some of these are complete for complexity classes within np but for others an exact complexity theoretic characterization is not known reducibility of these problems is studied in a general framework introduced in this paper prover verifier protocols with low complexity provers it is shown that all these natural problems indeed have such protocols this fact is used to show for certain reduction types that these problems are not reducible to sets with low information content unless their complexity is much less than what it is currently believed to be the general framework is also used to obtain a new characterization of the complexity class l l is the class of all logspace self reducible sets in ll sel

an improvement on codebook search for vector quantization presents a simple but effective algorithm to speed up the codebook search in a vector quantization scheme when a mse criterion is used a considerable reduction in the number of operations is achieved this algorithm was originally designed for image vector quantization in which the samples of the image signal pixels are positive although it can be used with any positive negative signal with only minor modifications

a time space tradeoff for undirected graph traversal by walking automata we prove a time space tradeoff for traversing undirected graphs using a structured model that is a nonjumping variant of cook and rackoff s jumping automata for graphs

fast nearest neighbor search algorithms based on approximation elimination search abstract in this paper we provide an overview of fast nearest neighbor search algorithms based on an approximation elimination framework under a class of elimination rules namely partial distance elimination hypercube elimination and absolute error inequality elimination derived from approximations of euclidean distance previous algorithms based on these elimination rules are reviewed in the context of approximation elimination search the main emphasis in this paper is a comparative study of these elimination constraints with reference to their approximation elimination efficiency set within different approximation schemes

an efficient data structure for lattice operations in this paper we consider the representation and management of an element set on which a lattice partial order relation is defined in particular let n be the element set size we present an nradn space implicit data structure for performing the following set of basic operations 1 test the presence of an order relation between two given elements in constant time 2 find a path between two elements whenever one exists in o l steps where l is the path length 3 compute the successors and or predecessors set of a given element in o h steps where h is the size of the returned set 4 given two elements find all elements between them in time o k log d where k is the size of the returned set and d is the maximum in degree or out degree in the transitive reduction of the order relation 5 given two elements find the least common ancestor and or the greatest common successor in o sqrt n time 6 given k elements find the least common ancestor and or the greatest common successor in o sqrt n k log n time unless stated otherwise all logarithms are to the base 2 the preprocessing time is o n2 focusing on the first operation representing the building box for all the others we derive an overall nradn space times time bound which beats the order n2 bottleneck representing the present complexity for this problem moreover we will show that the complexity bounds for the first three operations are optimal with respect to the worst case additionally a stronger result can be derived in particular it is possible to represent a lattice in space o n sqrt t where t is the minimum number of disjoint chains which partition the element set

inductive counting for width restricted branching programs as an application of the inductive counting technique to a circuit like model we prove that complementation on nondeterministic branching programs can be done without increasing the width excessively a consequence of this result is that the class of languages recognized by a generalization of nonuniform finite automata to nonconstant space is closed under complement

in search of the optimal searching sequence for vq encoding the codeword searching sequence is sometimes very vital to the efficiency of a vector quantization vq encoding algorithm in this paper we evaluate some necessary criteria for the derivation of an optimal searching sequence and derive the optimal searching sequence based on such criteria

canonical dichotomous direct bases closure systems are usually characterized in terms of implications the directness property of implicational systems is a key issue in their computational usability in this work we focus on this property studying its connection with the structure of implicational systems and the design of methods for transforming any implicational system into an equivalent direct implicational system we introduce a new paradigm based on the bipartition of the implicational sets into two components according to their behavior wrt the closure in addition we present the notions of two new direct bases named dd basis and canonical dd basis also providing two methods to compute each of them the advantages of the dichotomous approach will be shown both from the theoretical and empirical points of view

fast vector quantization algorithms based on nearest partition set search a fast search method for vector quantization is proposed in this paper it makes use of the fact that in the generalized lloyd algorithm gla a vector in a training sequence is either placed in the same minimum distance partition mdp as in the previous iteration or in a partition within a very small subset of partitions the proposed method searches for the mdp for a training vector only in this subset of partitions plus the single previous mdp as the size of this subset is much smaller than the total number of codevectors the search process is speeded up significantly the creation of the subset is essential as it has a direct effect on the improvement in computation time of the proposed method the schemes that create the subset efficiently have been proposed the proposed method generates a codebook identical to that generated using the gla it is simple and requires only minor modification of the gla and a modest amount of additional memory the experimental results show that the computation time of codebook training was improved by factors from 6 6 to 50 7 and from 5 8 to 70 4 for two test data sets when codebooks of sizes from n 16 to 2048 were trained the proposed method was also combined with an earlier published method to further improve the computation time

an efficient encoding algorithm for vector quantization based on subvector technique in this paper a new and fast encoding algorithm for vector quantization is presented this algorithm makes full use of two characteristics of a vector the sum and the variance a vector is separated into two subvectors one is composed of the first half of vector components and the other consists of the remaining vector components three inequalities based on the sums and variances of a vector and its two subvectors components are introduced to reject those codewords that are impossible to be the nearest codeword thereby saving a great deal of computational time while introducing no extra distortion compared to the conventional full search algorithm the simulation results show that the proposed algorithm is faster than the equal average nearest neighbor search enns the improved enns the equal average equal variance nearest neighbor search eenns and the improved eenns algorithms comparing with the improved eenns algorithm the proposed algorithm reduces the computational time and the number of distortion calculations by 2 4 to 6 and 20 5 to 26 8 respectively the average improvements of the computational time and the number of distortion calculations are 4 and 24 6 for the codebook sizes of 128 to 1024 respectively

an efficient nearest neighbor search method a simple but efficient nearest neighbor search algorithm is proposed and simulation results demonstrating its effectiveness in the case of vector quantization for a given source are presented the simulation results indicate that use of this approach reduces the number of multiplications and additions to as low as 9 percent of those required for the conventional full search method the reduction in the number of subtractions is also considerable the increase in the number of comparisons is moderate and therefore the total number of operations can be as low as 28 percent of those required by the full search method an additional advantage of the described algorithm is the fact that it requires no precomputations and or extra memory

a fast search algorithm for vector quantization using l sub 2 norm pyramid of codewords vector quantization for image compression requires expensive encoding time to find the closest codeword to the input vector this paper presents a fast algorithm to speed up the closest codeword search process in vector quantization encoding by using an appropriate topological structure of the codebook we first derive a condition to eliminate unnecessary matching operations from the search procedure then based on this elimination condition a fast search algorithm is suggested simulation results show that with little preprocessing and memory cost the proposed search algorithm significantly reduces the encoding complexity while maintaining the same encoding quality as that of the full search algorithm it is also found that the proposed algorithm outperforms the existing search algorithms

on finite block length quantization distortion we investigate the upper and lower bounds on the quantization distortions for independent and identically distributed continuous sources in the finite block length regime we derive a lower bound on the quantization distortion as well as an upper bound on the quantization distortion based on random quantization codebooks moreover we apply the obtained bounds to the continuous gaussian source for the gaussian source we propose a computationally tractable method to numerically compute the upper and lower bounds for both bounded and unbounded quantization codebooks numerical results show that the gap between the upper and lower bounds is small for the block length of several hundreds and the upper and lower bounds are tighter than those proposed in the existing works

symmetric space bounded computation abstract a symmetric turing machine is one such that the yields relation between configurations is symmetric the space complexity classes for such machines are found to be intermediate between the corresponding deterministic and nondeterministic space complexity classes certain natural problems are shown to be complete for symmetric space complexity classes and the relationship of symmetry to determinism and nondeterminism is investigated

the complexity of acyclic conjunctive queries this paper deals with the evaluation of acyclic booleanconjunctive queries in relational databases by well known resultsof yannakakis 1981 this problem is solvable in polynomial time its precise complexity however has not been pinpointed so far weshow that the problem of evaluating acyclic boolean conjunctivequeries is complete for logcfl the class of decision problems thatare logspace reducible to a context free language since logcfl iscontained in ac1 and nc2 the evaluation problem of acyclic booleanconjunctive queries is highly parallelizable we present a paralleldatabase algorithm solving this problem with alogarithmic number ofparallel join operations the algorithm is generalized to computingthe output of relevant classes of non boolean queries we also showthat the acyclic versions of the following well known database andai problems are all logcfl complete the query output tuple problemfor conjunctive queries conjunctive query containment clausesubsumption and constraint satisfaction the logcfl completenessresult is extended to the class of queries of bounded tree widthand to other relevant query classes which are more general than theacyclic queries

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

generalized satisfiability for the description logic alc the standard reasoning problem concept satisfiability in the basic description logic alc is pspace complete and it is exptime complete in the presence of general concept inclusions several fragments of alc notably logics in the fl el and dl lite families have an easier satisfiability problem for some of these logics satisfiability can be decided in polynomial time we classify the complexity of the standard variants of the satisfiability problem for all possible boolean and quantifier fragments of alc with and without general concept inclusions

an improvement of the minimum distortion encoding algorithm for vector quantization in this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords and about 25 40 percent for a tree search vector quantizer similar improvement can be achieved in other vector quantization systems

a logical approach to fuzzy truth hedges the starting point of this paper are the works of hajek and vychodil on the axiomatization of truth stressing and depressing hedges as expansions of hajek s bl logic by new unary connectives they showed that their logics are chain complete but standard completeness was only proved for the expansions over godel logic we propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages i they preserve the standard completeness properties of the original logic and ii any subdiagonal resp superdiagonal non decreasing function on 0 1 preserving 0 and 1 is a sound interpretation of the truth stresser resp depresser connectives hence these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense

a fast encoding algorithm for vector quantization using difference pyramid structure this paper proposed a fast vector quantization encoding algorithm called difference pyramid search dps according to the formation of the difference pyramid and partial distortion elimination a rejection test inequality is derived to progressively reject a lot of nonclosest code words as early as possible experimental results show that the proposed dps algorithm outperforms other pyramid based fast search algorithms including mean pyramid search l2 norm pyramid search and mean variance pyramid search

fast k dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding fast search algorithms are proposed and studied for vector quantization encoding using the k dimensional k d tree structure here the emphasis is on the optimal design of the k d tree for efficient nearest neighbor search in multidimensional space under a bucket voronoi intersection search framework efficient optimization criteria and procedures are proposed for designing the k d tree for the case when the test data distribution is available as in vector quantization application in the form of training data as well as for the case when the test data distribution is not available and only the voronoi intersection information is to be used the criteria and bucket voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform they are empirically observed to achieve constant search complexity for o log n tree depths and are found to be more efficient in reducing the search complexity a geometric interpretation is given for the maximum product criterion explaining reasons for its inefficiency with respect to the optimization criteria

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

fast clustering algorithms for vector quantization abstract some fast clustering algorithms for vector quantization vq based on the lbg recursive algorithm are presented and compared experimental results in comparison to the conventional vector quantization vq clustering algorithm with speech data demonstrate that the best approach will save more than 99 in the number of multiplications as well as considerable saving in the number of additions the increase in the number of comparisons is moderate an improve absolute error inequality aei criterion for euclidean distortion measure is also proposed and utilized in the vq clustering algorithm

a new vector quantization clustering algorithm the pairwise nearest neighbor pnn algorithm is presented as an alternative to the linde buzo gray 1980 lbg generalized lloyd 1982 algorithm for vector quantization clustering the pnn algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required without sacrificing performance in addition the time needed to generate a codebook grows only o n log n in training set size and is independent of the number of code words desired using this method one can either minimize the number of code words needed subject to a maximum rate the pnn algorithm can be used with squared error and weighted squared error distortion measure simulations on a variety of images encoded at 1 2 b pixel indicate that pnn codebooks can be developed in roughly 5 of the time required by the lbg algorithm

fast tree structured nearest neighbor encoding for vector quantization this work examines the nearest neighbor encoding problem with an unstructured codebook of arbitrary size and vector dimension we propose a new tree structured nearest neighbor encoding method that significantly reduces the complexity of the full search method without any performance degradation in terms of distortion our method consists of efficient algorithms for constructing a binary tree for the codebook and nearest neighbor encoding by using this tree numerical experiments are given to demonstrate the performance of the proposed method

computing sets of graded attribute implications with witnessed non redundancy in this paper we extend our previous results on sets of graded attribute implications with witnessed non redundancy we assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth stressing linguistic hedges as parameters which influence the semantics of graded attribute implications in this setting we introduce algorithm which transforms any set of graded attribute implications into an equivalent non redundant set of graded attribute implications with saturated consequents whose non redundancy is witnessed by antecedents of the formulas as a consequence we solve the open problem regarding the existence of general systems of pseudo intents which appear in formal concept analysis of object attribute data with graded attributes and linguistic hedges furthermore we show a polynomial time procedure for determining bases given by general systems of pseudo intents from sets of graded attribute implications which are complete in data