Showing papers in "Acta Cybernetica in 2009"

Max/plus tree automata for termination of term rewriting

Abstract: We use weighted tree automata as certificates for termination of term rewriting systems. The weights are taken from the arctic semiring: natural numbers extended with -∞, with the operations "max" and "plus". In order to find and validate these certificates automatically, we restrict their transition functions to be representable by matrix operations in the semiring. The resulting class of weighted tree automata is called path-separated. This extends the matrix method for term rewriting and the arctic matrix method for string rewriting. In combination with the dependency pair method, this allows for some conceptually simple termination proofs in cases where only much more involved proofs were known before. We further generalize to arctic numbers "below zero": integers extended with -∞. This allows to treat some termination problems with symbols that require a predecessor semantics. Correctness of this approach has been formally verified in the Coq proof assistant and the formalization has been contributed to the CoLoR library of certified termination techniques. This allows formal verification of termination proofs using the arctic matrix method in combination with the dependency pair transformation. This contribution brought a substantial performance gain in the certified category of the 2008 edition of the termination competition. The method has been implemented by leading termination provers. We report on experiments with its implementation in one such tool, Matchbox, developed by the second author. We also show that our method can simulate a previous method of quasi-periodic interpretations, if restricted to interpretations of slope one on unary signatures.

Languages convex with respect to binary relations, and their closure properties

Abstract: A language is prefix-convex if it satisfies the condition that, if a word w and its prefix u are in the language, then so is every prefix of w that has u as a prefix. Prefix-convex languages include prefix-closed languages at one end of the spectrum, and prefix-free languages, which include prefix codes, at the other. In a similar way, we define suffix-, bifix-, factor-, and subword-convex languages and their closed and free counterparts. This provides a common framework for diverse languages such as codes, factorial languages and ideals. We examine the relationships among these languages. We generalize these notions to arbitrary binary relations on the set of all words over a given alphabet, and study the closure properties of such languages.

Counting distinct squares in partial words

Abstract: A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence start. In this paper, we investigate the problem of counting distinct squares in partial words, or sequences over a finite alphabet that may have some "do not know" symbols or "holes" (a (full) word is just a partial word without holes). A square in a partial word over a given alphabet has the form uu′ where u′ is compatible with u, and consequently, such square is compatible with a number of full words over the alphabet that are squares. We consider the number of distinct full squares compatible with factors in a partial word with h holes of length n over a k-letter alphabet, and show that this number increases polynomially with respect to k in contrast with full words, and give bounds in a number of cases. For partial words with one hole, it turns out that there may be more than two squares that have their last occurrence starting at the same position. We prove that if such is the case, then the hole is in the shortest square. We also construct a partial word with one hole over a k-letter alphabet that has more than k squares whose last occurrence start at position zero.

Complexity of problems concerning reset words for some partial cases of automata

Abstract: A word w is called a reset word for a deterministic finite automaton A if it maps all states of A to one state. A word w is called a compressing to M states for a deterministic finite automaton A if it maps all states of A to at most M states. We consider several subclasses of automata: aperiodic, D- trivial, monotonic, partially monotonic automata and automata with a zero state. For these subclasses we study the computational complexity of the following problems. Does there exist a reset word for a given automaton? Does there exist a reset word of given length for a given automaton? What is the length of the shortest reset word for a given automaton? Moreover, we consider complexity of the same problems for compressing words.

Recognizable tree series with discounting

Abstract: We consider weighted tree automata with discounting over commutative semirings. For their behaviors we establish a Kleene theorem and an MSOlogic characterization. We introduce also weighted Muller tree automata with discounting over the max-plus and the min-plus semirings, and we show their expressive equivalence with two fragments of weighted MSO-sentences.

Clouds, p-boxes, Fuzzy Sets, and Other Uncertainty Representations in Higher Dimensions

Abstract: Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data. In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which successfully copes with both higher dimensions and incomplete information.

A universal unification algorithm based on unification-driven leftmost outermost narrowing

Abstract: We formalize a universal uni cation algorithm for the class of equational theories which is induced by the class of canonical totally de ned not strictly subuni able term rewriting systems for short ctn trs For a ctn trs R and for two terms t and s the algorithm computes a ground complete set of ER uni ers of t and s where ER is the set of rewrite rules of R viewed as equations The algorithm is based on the uni cation driven leftmost outermost narrowing relation for short ulo narrowing relation which is introduced in this paper The ulo narrowing relation combines usual leftmost outermost narrowing steps and uni cation steps Since the uni cation steps are applied as early as possible some of the nonsuccessful derivations can be stopped earlier than in other approaches to ER uni cation Furthermore we formalize a deterministic version of our universal uni cation algorithm that is based on a depth rst left to right traversal through the narrowing trees The work of this author has been supported by the Deutsche Forschungsgemeinschaft DFG

Adaptive Scheduling Solution for Grid Meta-Brokering

Abstract: The nearly optimal, interoperable utilization of various grid resources play an important role in the world of grids. Though well-designed, evaluated and widely used resource brokers have been developed, these existing solutions still cannot cope with the high uncertainty ruling current grid systems. To ease the simultaneous utilization of different middleware systems, researchers need to revise current solutions. In this paper we propose advanced scheduling techniques with a weighted fitness function for an adaptive Meta-Brokering Grid Service, which enables a higher level utilization of the existing grid brokers. We also set up a grid simulation environment to demonstrate the efficiency of the proposed meta-level scheduling solution. The presented evaluation results show that the proposed novel scheduling technique in the meta-brokering context delivers better performance.

MAT learners for recognizable tree languages and tree series

Abstract: We review a family of closely related query learning algorithms for unweighted and weighted tree automata, all of which are based on adaptations of the minimal adequate teacher (MAT) model by Angluin Rather than presenting new results, the goal is to discuss these algorithms in sufficient detail to make their similarities and differences transparent to the reader interested in grammatical inference of tree automata

Plagiarism Detection in Source Programs Using Structural Similarities

Abstract: The paper presents a plagiarism detection framework the goal of which is to determine whether two programs are similar to each other, and if so, to what extent. The issue of plagiarism detection has been considered earlier for written material, such as student essays. For these, text-based algorithms have been published. We argue that in case of program code comparison, structure based techniques may be much more suitable. The main idea is to transform the source code into mathematical objects, use appropriate reduction and comparison methods on these, and interpret the results appropriately. We have designed a generic program structure comparison framework and implemented it for the Prolog and SML programming languages. We have been using the implementation at BUTE to successfully detect plagiarism in homework assignments for years.

Complex independent process analysis

Abstract: We present a general framework for the search of hidden independent processes in the complex domain. The task is to estimate the hidden independent multidimensional complex-valued components observing only the mixture of the processes driven by them. In our model (i) the hidden independent processes can be multidimensional, they may be subject to (ii) moving averaging, or may evolve in an autoregressive manner, or (iii) they can be non-stationary. These assumptions are covered by integrated autoregressive moving average processes and thus our task is to solve their complex extensions. We show how to reduce the undercomplete version of complex integrated autoregressive moving average processes to real independent subspace analysis that we can solve. Simulations illustrate the working of the algorithm.

Statistical language models within the algebra of weighted rational languages

Abstract: Statistical language models are an important tool in natural language processing. They represent prior knowledge about a certain language which is usually gained from a set of samples called a corpus. In this paper, we present a novel way of creating N-gram language models using weighted finite automata. The construction of these models is formalised within the algebra underlying weighted finite automata and expressed in terms of weighted rational languages and transductions. Besides the algebra we make use of five special constant weighted transductions which rely only on the alphabet and the model parameter N. In addition, we discuss efficient implementations of these transductions in terms of virtual constructions.

Parameter Learning Online Algorithm for Multiprocessor Scheduling with Rejection

Abstract: In multiprocessor scheduling with rejection the jobs are characterized by a processing time and a penalty and it is possible to reject the jobs. The goal is to minimize the makespan of the schedule for the accepted jobs plus the sum of the penalties of the rejected jobs. In this paper we present a new online algorithm for the problem. Our algorithm is a parameter learning extension of the total reject penalty algorithm. The efficiency of the algorithm is investigated by an experimental analysis. In this paper we develop a new algorithm for the solution of the online scheduling with rejection problem on identical machines. The algorithm is based on the idea of learning the parameter of the Reject Total Penalty (RTP) algorithm. We measure the efficiency of the new algorithm by an experimental analysis. The problem of scheduling with rejection is defined in (2). In this model, it is possible to reject the jobs. The jobs are characterized by a processing time and a penalty. The goal is to minimize the makespan of the schedule for the accepted jobs plus the sum of the penalties of the rejected jobs. In the online case a 2.618- competitive algorithm is given for arbitrary number of machines. This algorithm is called Reject Total Penalty (RTP). One basic idea in scheduling with rejection is to compare the penalty and the load (processing time divided by the number of machines) of the job, and reject the job in the case when the penalty is smaller. This greedy algorithm can make a bad decision when the number of machines is large and this makes possible to appear large jobs with small loads. RTP handles these jobs more carefully. We give the detailed definition in the next section. In (2) a further, 1.618-competitive algorithm is presented in the case of 2 machines. Matching lower bounds are also given. In the offline case an FPTAS is presented for fixed number

Weighted tree-walking automata

Abstract: We define weighted tree-walking automata. We show that the class of tree series recognizable by weighted tree-walking automata over a commutative semiring K is a subclass of the class of regular tree series over K: If K is not a ring, then the inclusion is strict.

Improved Topic Identification for Similar Document Search on Mobile Devices

Abstract: This paper presents a novel, two level classifier ensemble designed to support document topic identification in mobile device environments. The proposed system aims at supporting mobile device users who search for documents located in other mobile devices which have similar topic to the documents on the users own device. Conforming to the environment of mobile devices, the algorithms are designed for slower processor, smaller memory capacity and they maintain small data traffic between the devices in order to keep low the cost of communication. We propose a keyword list based topic comparison, enhanced with a two level classifier ensemble to accelerate the topic identification process. The new technique enables document topic comparison using few communication traffic and it requires few calculations.

Weighted automata define a hierarchy of terminating string rewriting systems

Abstract: The "matrix method" (Hofbauer and Waldmann 2006) proves termination of string rewriting via linear monotone interpretation into the domain of vectors over suitable semirings. Equivalently, such an interpretation is given by a weighted finite automaton. This is a general method that has as parameters the choice of the semiring and the dimension of the matrices (equivalently, the number of states of the automaton). We consider the semirings of non-negative integers, rationals, algebraic numbers, and reals; with the standard operations and ordering. Monotone interpretations also allow to prove relative termination, which can be used for termination proofs that consist of several steps. The number of steps gives another hierarchy parameter. We formally define the hierarchy and we prove that it is infinite in both directions (dimension and steps).

On pure multi-pushdown automata that perform complete pushdown pops

Abstract: This paper introduces and discusses pure multi-pushdown automata that remove symbols from their pushdowns only by performing complete pushdown pops. This. means that during a pop operation, the entire pushdown is compared with a prefix of the input, and if they match, the whole contents of the pushdown is erased and the input is advanced by the prefix. The paper proves that these automata define an infinite hierarchy of language families identical with the infinite hierarchy of language families resulting from right linear simple matrix grammars. In addition, this paper discusses some other extensions of these automata with respect to operations they can perform with their pushdowns. More specifically, it discusses pure multi-pushdown automata that perform complete pushdown pops that are allowed to join two pushdowns and/or create a new pushdown.

Cohesion and Balance in a Human Resource Allocation Problem

Abstract: Collaborative work appears between intelligent agents of different types. The problem discussed occurred when many construction workers were taken to Germany from Romania to work in construction projects. Managers have to make independent groups of workers from some categories, like carpenters, brick layers, etc. To discover their collaborative attitudes they use the scoring method, where every worker scores the others from different trades. The objectives are to form groups of workers with high compatibility value and to have a high compatibility value for the worst group, too. The problem becomes more interesting if software collaborative groups or specialized intelligent agents are involved. One has to prospect also the level of knowledge overlap between the trade groups of agents. This paper resumes to the problem of construction workers so as there is no overlap between the trades and the level of knowledge is not in the universe of discourse. We propose a Greedy and a genetic algorithm approach and we compare these methods.

Weighted and unweighted trace automata

Abstract: We reprove Droste & Gastin's characterisation from [3] of the behaviors of weighted trace automata by certain rational expressions. This proof shows how to derive their result on weighted trace automata as a corollary to the unweighted counterpart shown by Ochmanski.

Kleene revisited by Suschkewitsch

Abstract: The aim of this paper is to generalize to nonassociative concatenation the well-known property that the family of left-linear languages is exactly the family of regular languages. For this purpose, we introduce a generalized Kleene star operation.

Homomorphisms preserving types of density

Abstract: The concept of density in a free monoid can be generalized from the infix relation to arbitrary relations. Many of the properties known for density can be established over these more general notions of densities. In this paper, we investigate homomorphisms which preserve different types of density. We demonstrate a strict hierarchy between families of homomorphisms which preserve density over different types of relations. However, as with the case of endomorphisms, a similar hierarchy for weak-coding homomorphisms collapses. We also present an algorithm to decide whether a homomorphism preserves density over any relation which satisfies some natural conditions.

3-level confidence voting strategy for dynamic fusion-selection of classifier ensembles

Abstract: There are two different stages to consider when constructing multiple classifier systems: The Meta-Classifier Stage that is responsible for the combination logic and basically treats the ensemble members as black boxes, and the Classifier Stage where the functionality of members is in focus. Furthermore, on the upper stage - also called voting strategy stage - the method of combining members can be done by fusion and selection of classifiers. In this paper, we propose a novel procedure for building the meta-classifier stage of MCSs, using an oracle of three-level voting strategy. This is a dynamic, half fusion-half selection type method for ensemble member combination, which is midway between the extremes of fusion and selection. The MCS members are weighted and combined with the help of the oracle, which is founded on a voting strategy of three levels: (1) The Local Implicit Confidence (LIC), (2) The Global Explicit Confidence (GEC), and (3) The Local Explicit Confidence (LEC). The first confidence segment is dependent of classifier construction, via the implicit knowledge gathered simultaneously with training. Since this strongly depends on the internal operation of the classifier, it can not always be obtained, for example, when using some particularly complex classification methods. We used several, known classifier algorithms (Decision Trees, Neural Networks, Logistic Regression, SVM) where it is possible to extract this information. The second goodness index is calculated on the validation partition of the labeled train data. It is used to obtain the general accuracy of a single classifier using a data set independent of the training partition. And finally, the third part of the confidence triplet depends also on the unlabeled objects yet to be classified. Due to this, it can only be calculated in classification time.

A Fixed Point Theorem for Stronger Association Rules and Its Computational Aspects

Abstract: Each relation induces a new closure operator, which is (in the sense of data mining) stronger than or equal to the Galois one. The goal is to give some evidence that the new closure operator is often properly stronger than the Galois one. An easy characterization of the new closure operator as a largest fixed point of an appropriate contraction map leads to a (modest) computer program. Finally, various experimental results obtained by this program give the desired evidence.

Determining initial bound by "Ray-method" in branch and bound procedure

Abstract: In this paper we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of this algorithm is based on the use of “ray” as introduced in the “ray-method” developed for solving integer linear programming problems [11], [12]. Instead of solving an integer programming problem we use the main idea of the ray-method to find an integer feasible solution of an integer linear programming problem along the ray as close to an optimal solution of the relaxation problem as possible. The objective value obtained in this manner may be used as an initial bound for the B&B method. It is well known that getting a “good bound” as soon as possible can often significantly increase the performance of the B&B method.

Backprojection Reconstruction Algorithm Using Order Statistic Filters In Breast Tomosynthesis

Abstract: Breast cancer is the most common cancer type and one of the leading cause of death among women. It has been recognized over the years that preventing the disease is the most powerful weapon, and the implementation of screening mammography has had significantly reduced the death rate. However, it is also proven that conventional mammography does not detect approximately 30% of breast cancers. Inventing new imaging technologies for the earlier detection of breast cancer is vital and is in the center of many ongoing studies. There are several new techniques using different imaging modalities that are under investigation. The most promising is the breast tomosynthesis, an advanced x-ray application that addresses the problem of structure superimposition, one of the major deficiencies of 2D mammography, by reconstructing a range of slices providing additional 3-dimensional information of the breasts. Our goal is to investigate and develop reconstruction algorithms that fit into the new mathematical model of tomosynthesis used in mammography. In this paper we show a backprojection reconstruction technique that is especially well-suited for the problem in question. This algorithm is capable to produce contrast-enhanced slices of the breast by taking only the projections that most probably hold the "important" information of the targeted lesions, ignoring part of the projections. This statistical approach also offers a good noise management performance, as a fortunate side-effect. After discussing the algorithm we publish the results of the comparison of this technique with other popular methods of the algorithm-family. We also look out the strict boundaries of the work done suggesting improvements of the reconstruction algorithm.

Limited Codes Associated with Petri Nets

Abstract: The purpose of this paper is to investigate the relationship between limited codes and Petri nets The set M of all positive firing sequences which start from the positive initial marking µ of a Petri net and reach µ itself forms a pure monoid M whose base is a bifix code Especially, the set of all elements in M which pass through only positive markings forms a submonoid N of M Also N has a remarkable property that N is pure Our main interest is in the base D of N The family of pure monoids contains the family of very pure monoids, and the base of a very pure monoid is a circular code Therefore, we can expect that D may be a limited code In this paper, we examine “small” Petri nets and discuss under what conditions D is limited

Alphabetical satisfiability problem for trace equations

Abstract: It is known that the satisfiability problem for equations over free partially commutative monoids is decidable but computationally hard. In this paper we consider the satisfiability problem for equations over free partially commutative monoids under the constraint that the solution is a subset of the alphabet. We prove that this problem is NP-complete for quadratic equations and that its uniform version is NP-complete for linear equations.

Filter Bank Design for Melody Recognition

Abstract: Recognizing different features of a waveform to later recompose the music that was originally present in the signal is a difficult task. There are numerous fields of application where these techniques are known to be useful including music authoring, digitizer design, automatic music transcription. There are many different methods that can be used for this purpose giving somehow inadequate quality regarding noise, polyphony or time- / frequency localization compared to the human auditory system. In this article, I will show a new filter design method specifically designed to be aware of human perception features. I will also show the way how a complete filter bank can be assembled and used for melody recognition in real time. Finally, I will point out the benefits of this filter design compared to other methods.