Showing papers in "Acta Cybernetica in 1999"

The transducers and formal tree series

Abstract: W e introduce tree transducers over formal tree series as a generalization of a restricted type of root-to-frontier tree transducers and show that linear nondeleting recognizable tree transducers do preserve recognizability of tree series.

Trips on trees

Abstract: A \"trip\" is a triple (g,u,v) where g is, in general, a graph and u and v are nodes of that graph. The trip is from u to v on the graph g. For the special case that g is a tree (or even a string) we investigate ways of specifying and implementing sets of trips. The main result is that a regular set of trips, specified as a regular tree language, can be implemented by a tree-walking automaton that uses marbles and one pebble.

Directable nondeterministic automata

Abstract: An automaton is directable if it has a directing word which takes it from every state to the same state. For nondeterministic (n.d.) automata directability can be defined in several meaningful ways. We consider three such notions. An input word w of an n.d. automaton A is (1) Dl-directing if the set of states aw in which A may be after reading w consists of the same single state c for all initial states a; (2) D2-directing if the set aw is independent of the initial state a; (3) D3-directing if some state c appears in all of the sets aw. We consider the sets of D1-, D2and D3-directing words of a given n.d. automaton, and compare the classes of D1-, D2and D3-directable n.d. automata with each other. We also estimate the lengths of the longest possible minimum-length D1-, D2and D3-directing words of an n-state n.d. automaton. All questions are studied separately for n.d. automata which have at least one next state for every input-state pair.

Two simple algorithms for bin covering

Abstract: We define two simple algorithms for the bin covering problem and give their asymptotic performance.

Limiting distortion of a wavelet image codec

Abstract: A new image compression algorithm, Distortion Limited Wavelet Image Codec (DLWIC), is introduced. The codec is designed to be simple to implement, fast and have modest requirements for the working storage. It is shown, how the distortion of the result can be calculated while progressively coding a transformed image and thus how the mean square error of the result can be limited to a predefined value. The DLWIC uses zerotrees for ecient coding of the wavelet coecients. Correlations between dierent orientation components are also taken into account by binding together the coecients on the three dierent orientation components in the same spatial location. The maximum numbers of significant bits in the coecients of all subtrees are stored in two-dimensional heap structure that allows the coder to test the zerotree property of a subtree with only one comparison. The compression performance of the DLWIC is compared to the industry standard JPEG compression and to an advanced wavelet image compression algorithm, vqSPIHT. An estimation of execution speed and memory requirements for the algorithm is given. The compression performance of the algorithm seems to exceed the performance of the JPEG and to be comparable with the vqSPIHT.

Decompositions of automata and transition semigroups

Abstract: The purpose of this paper is to describe structural properties of automatawhose transition semigroups have a zero, left zero, right zero or bi-zero, orare nilpotent extensions of rectangular bands, left zero bands or right zerobands, or are nilpotent. To describe the structure of these automata we usevarious well-known decomposition methods of automata theory – direct sumdecompositions, subdirect and parallel decompositions, and extensions of au-tomata. Automata that appear as the components in these decompositionsbelong to some well-known classes of automata, such as directable, definite,reverse definite, generalized definite and nilpotent automata. But, we alsointroduce some new classes of automata: generalized directable, trapped, one-trapped, locally directable, locally one-trapped, locally nilpotent and locallydefinite automata. We explain relationships between the classes of all theseautomata.Keywords: automaton, transition semigroup, direct sum decomposition,directable automata, trapped automata, generalized directable automata, lo-cally directable automata, generalized varieties,

Minimizing the number of tardy jobs on a single machine with batch setup times

Abstract: This paper investigates a single-machine sequencing problem where the jobs are divided into families, and where a setup time is incurred whenever there is a switch from a job in one family to a job in another family. This setup only depends on the family of the job next to come and hence is sequence independent. The jobs are due-dated, and the objective is to nd a sequence of jobs that minimizes the number of tardy jobs. The special case of this problem where in every family the jobs have at most two di erent due dates is known to be NP-complete [Bruno & Downey, 1978]. The main result of this paper is a polynomial time algorithm for the remaining open case where in every family all the jobs have the same due date. This case may be formulated as a dual resource allocation problem with a tree-structured constraint system, which can be solved to optimality in polynomial time.

Test suite reduction in conformance testing

Abstract: Conformance testing is based on a test suite. Standardization committees release standard test suites, which consist of hundreds of test cases. The main problem of conformance testing is that we do not have enough time to execute them all. Therefore, test selection is required to maximize the test coverage. In our earlier papers [6,7] we outlined a new method of selecting an optimal test suite which can detect the errors with better probability' and réduce the • time of testing. In this paper we will expound the mathematical optimization method for test suite optimization based on cost and test coverage, and we will apply this method to an ISDN protocol.

On extended simple eco-grammar systems

Abstract: In this contribution extended simple eco-grammar systems are studied. A simple eco-grammar system is formed from an environment given by a set of OL rules and from some agents represented by sets of CF rules. In an extended simple eco-grammar system we distinguish a subset of the alphabet of the system and only strings over this subalphabet are in the generated language. The relations between language classes generated with different parameters and derivation modes are investigated.

On minimal and maximal clones II

Abstract: Two minimal clones which generate all operations, and two maximal clones with trivial intersection are given on 2p-element sets where p > 5 is a prime number.

Optimal parameters of a sinusoidal representation of signals

Abstract: In the spectral analysis of digital signals, one of the most useful parametric models is the representation by a sum of phase-shifted sinusoids in form of ∑ N−1 n=0 An sin(ωnt + φn), where An, ωn, and φn are the component’s amplitude, frequency and phase, respectively. This model generally fits well speech and most musical signals due to the shape of the representation functions. If using all of the above parameters, a quite difficult optimization problem arises. The applied methods are generally based on eigenvalue decomposition [3]. However this procedure is computationally expensive and works only if the sinusoids and the residual signal are statistically uncorrelated. To speed up the representation process also rather ad hoc methods occur [4]. The presented algorithm applies the newly established Homogeneous Sinus Representation Function (HSRF) to find the best representing subspace of fixed dimension N by a BFGS optimization. The optimum parameters {A,ω, φ} ensure the mean square error of approximation to be below a preset threshold.

Grammars working on layered strings

Abstract: We consider first an operation with strings and languages suggested by superposed windows on the computer screen (as well as by cryptographic systems of Richelieu type): we assume that the strings contain usual symbols as well as a transparent symbol. Superposing two strings (justified to left), we produce a new string consisting of the symbols observable from above. This operation is investigated as an abstract operation on strings, then it is used in building a variant of grammar systems with the component grammars working on the layers of an array of strings. Each grammar can rewrite only symbols in its layer which are observable from above. The language generated in this way consists of strings of the observable symbols, produced at the end of a derivation. The power of several variants of these generative mechanisms is investigated for the case of two layered strings. When a matrix-like control on the work of the component grammars is considered, then a characterization of recursively enumerable languages is obtained.

Descriptional complexity of multi-continuous grammars

Abstract: The present paper discusses multi-continuous grammars and their descriptional complexity with respect to the number of nonterminals. It proves that six-nonterminal multi-continuous grammars characterize the family of recursively enumerable languages. In addition, this paper formulates an open problem area closely related to this characterization.

Object-oriented model for partially separable functions in parameter estimation

Abstract: In parameter estimation, a model function depending on adjustable parameters is fitted to a set of observed data. The parameter estimation task is an optimisation problem, which needs a computational kernel for evaluating the model function values and derivatives. This article presents an object-oriented framework for representing model functions, which are partially separable, or structural. Such functions are commonly encountered, e.g., in spectroscopy. The model is general, being able to cover a range of varying model functions. It offers flexibility at runtime allowing the construction of the model functions from predefined component functions. The mathematical expressions are encapsulated and a close mapping between mathematics and program code is preserved. Also, all interfacing code can be written independently of the particular mathematical formula. These properties together make it easy to adapt the model to different problem domains: only tightly controlled changes to the program code are required. The paper shows how derivatives of the model function can be computed using automatic differentiation relieving the programmer from writing explicit analytical derivative codes. The persistence of the objects involved is discussed and finally the computational efficiency of the function and derivative evaluation is addressed. It is shown that the benefits of the object-oriented model, namely the higher abstraction level and increased.flexibility, are achieved with a very moderate loss of performance. This is demonstrated by comparing the performance with low-level tailored C-code.

Analysis of the completion time of Markov reward models and its application

Abstract: Analysis of Markov Reward Models (MRM) with preemptive resume (prs) policy usually results in a double transform expression, whose solution is based on the inverse transformations both in time and reward variable domain. This paper discusses the case when the reward rates can be either 0 or positive, and analyses the completion time of MRMs. We present a symbolic expression of moments of the completion time, from which a computationally eeective recursive numerical method can be obtained. As a numerical example the mean and the standard deviation of the completion time of a Carnegie-Mellon multiprocessor system are evaluated by the proposed method.

Construction of recursive algorithms for polarity matrices calculation in polynomial logical function representation

Abstract: There is no algorithm for the calculation of optimal fixed polarity expansion. Therefore, the efficient calculation of polarity matrix consisting of all fixed polarity expansion coefficients is very important task. We show that polarity matrix can be generated as convolution of function f with rows of relates transform matrix. The recursive properties of the convolution matrix affect to properties of polarity matrix. In literature are known some recursive algorithms for the calculation of polarity matrix of some expressions for Multiple-valued (MV) functions [3,6]. We give a unique method to construct recursive procedures for the polarity matrices calculation for any Kronecker product based expression of MV functions. As a particular cases we derive • two recursive algorithms for calculation of fixed polarity Reed-Muller-Fourier expressions for four-valued functions.

Testing Internet applications — terminology and applicability

Abstract: This paper examines the applicability of OSI conformance test methodology to Internet protocols. It summarizes the differences between them and introduces the Internet Reference Model along with a new abstract test method, which was designed for the practical purposes of conformance testing of TCP/IP protocols. Some interesting test cases and points, that were chosen from RIP, demonstrate the facilities of the model and give impression of testing Internet protocols.