Showing papers in "Acta Cybernetica in 2001"

The complexity of coloring graphs without long induced paths

Abstract: We discuss the computational complexity of determining the chromatic number of graphs without long induced paths. We prove NP-completeness of deciding whether a Ps-free graph is 5-colorable and of deciding whether a Pi2-free graph is 4-colorable. Moreover, we give a polynomial time algorithm for deciding whether a Ps-free graph is 3-colorable.

Regulated pushdown automata

Abstract: The present paper suggests a new investigation area of the formal language theory—regulated automata Specifically, it investigates pushdown automata that regulate the use of their rules by control languages It proves that this regulation has no effect on the power of pushdown automata if the control languages are regular However, the pushdown automata regulated by linear control languages characterize the family of recursively enumerable languages All these results are established in terms of (A) acceptance by final state, (B) acceptance by empty pushdown, and (C) acceptance by final state and empty pushdown In its conclusion, this paper formulates several open problems

Languages recognized by a class of finite automata

Abstract: We consider automata defined by left multiplications in graph algebras, and describe all languages recognized by these automata in terms of combinatorial properties of words which belong to these languages, regular expressions and linear grammars defining these languages. This description is applied to investigate closure properties of the obtained family of languages.

Equivalence of Mealy and Moore automata

Abstract: It is proved here that every Mealy automaton is a liomomorphic image of a Moore automaton, and among these Moore automata (up to isomorphism) there exists a unique one which is a homomorphic image of the others A unique simple Moore automaton M is constructed (up to isomorphism) in the set MO(A) of all Moore automata equivalent to a Mealy automaton A such that M is a homomorphic image of every Moore automaton belonging to MO{A) By the help of this construction, it can be decided in steps |X|k that automaton mappings inducing by states of a k-uniform finite Mealy [Moore] automaton are equal or not The structures of simple k-uniform Mealy [Moore] automata are described by the results of [1] It gives a possibility for us to get the k-uniform Mealy [Moore] automata from the simple k-uniform Mealy [Moore] automata Based on these results, we give a construction for finite Mealy [Moore] automata

The logic of knights, knaves, normals and mutes

Abstract: R. M. Smullyan wrote in his book about islands, knights and knaves. The knights always tell the truth and the knaves are always lying. Instead of say we shall examine the can say modal operator. We show the soundness and the completeness of this logic.

The debug slicing of logic programs

Abstract: This paper extends the scope and optimality of previous algorithmic debugging techniques of Prolog programs using slicing techniques. We provide a dynamic slicing algorithm (called Debug slice) which augments the data flow analysis with control-flow dependences in order to identify the source of a bug included in a program. We developed a tool for debugging Prolog programs which also handles the specific programming techniques (cut, if-then, OR). This approach combines the Debug slice with Shapiro's algorithmic debugging technique.

Logical definability of Y-tree and trellis systolic ω-languages

Abstract: In this paper we investigate the correspondence (in the style of the well known B uchi Theorem) between !-languages accepted by sys-tolic automata and suitable (proper) extensions of the Monadic Second Order theory of one successor (MSO<]). To this purpose we extend Y-tree and trellis systolic automata to deal with !-words and we study the expressiveness, closure and decidability properties of the two classes of !-languages accepted by Y-tree and trellis automata, respectively. We deene, then, two extensions of MSO<], MSO<; adj] and MSO<; 2x], which allow to express Y-tree !-languages and trellis !-languages, respectively .

Pseudo-Hamiltonian graphs

Abstract: A pseudo-h-hamiltonian cycle in a graph is a closed walk that visits every vertex exactly h times. We present a variety of combinatorial and algorithmic results on pseudo- h-hamiltonian cycles: First, we show that deciding whether a graph is pseudo-h-hamiltonian is NP-complete for any given h ≥ 1. Surprisingly, deciding whether there exists an h ≥ 1 such that the graph is pseudo-h-hamiltonian, can be done in polynomial time. We also present sufficient conditions for pseudo- h-hamiltonicity that are based on stable sets and on toughness. Moreover, we investigate the computational complexity of finding pseudo-h-hamiltonian cycles on special graph classes like bipartite graphs, split graphs, planar graphs, cocomparability graphs; in doing this, we establish a precise separating line between easy and difficult cases of this problem.

On isomorphic representations of generalized definite automata

Abstract: In this paper, the generalized definite automata are studied. In particular, systems which are isomorphically complete for this class with respect to the »¿-products are characterized.

Affine matching of two sets of points in arbitrary dimensions

Abstract: In many applications of computer vision, image processing, and remotely sensed data processing, an appropriate matching of two sets of points is required. Our approach assumes one-to-one correspondence between these sets and finds the optimal global affine transformation that matches them. The suggested method can be used in arbitrary dimensions. A sufficient existence condition for a unique transformation is given and proven.

Using decision trees to infer semantic functions of attribute grammars

Abstract: In this paper we present a learning method called LAG (Learning of Attribute Grammar) which infers semantic functions for simple classes of attribute grammars by means of examples and background knowledge. This method is an improvement on the AGLEARN approach as it generates the training examples on its own via the effective use of background knowledge. The background knowledge is given in the form of attribute grammars. In addition, the LAG method employs the decision tree learner C4.5 during the learning process. Treating the specification of an attribute grammar as a learning task gives rise to the application of attribute grammars to new sorts of problems such as the Part-of-Speech (PoS) tagging of Hungarian sentences. Here we inferred context rules for selecting the correct annotations for ambiguous words with the help of a background attribute grammar. This attribute grammar detects structural correspondences of the sentences. The rules induced this way were found to be more precise than those rules learned without this information.

Parallel simulation of spiral waves in reacting and diffusing media

Abstract: The propagation of the spiral waves in excitable media is governed by the non-linear reaction-diffusion equations. In order to solve these equations in the three-dimensional space, two methods have been implemented and parallelized on both shared- and distributed-memory computers. These implicit methods linearize the equations in time, following alternate directions in the first case (ADI), and using the Crank-Nicolson discretization in the second case. A linear system of algebraic equations has been obtained and it has been solved using direct methods in the ADI technique, while in the second case has been used the conjugated gradient (CG) method. An optimized version of the CG algorithm is presented here, in which the largest efficiency has been obtained.

Difference functions of dependence spaces

Abstract: Here the reduction problem is studied in an algebraic structure called dependence space. We characterize the reducts by the means of dense families of dependence spaces. Dependence spaces defined by indiscernibility relations are also considered. We show how we can determine dense families of dependence spaces induced by indiscernibility relations by applying indiscernibility matrices. We also study difference functions which connect the reduction problem to the general problem of identifying the set of all minimal Boolean vectors satisfying an isotone Boolean function.

Learning decision trees in continuous space

Abstract: Two problems of the ID3 and C4.5 decision tree building methods will be mentioned and solutions will be suggested on them. First, in both methods a Gain-type criteria is used to compare the applicability of possible tests, which derives from the entropy function. We are going to propose a new measure instead of the entropy function, which comes from the measure of fuzziness using a monotone fuzzy operator. It is more natural and much simpler to compute in case of concept learning (when elements belong to only two classes: positive and negative). Second, the well-known extension of the ID3 method for handling continuous attributes (C4.5) is based on discretization of attribute values and in it the decision space is separated with axis-parallel hyperplanes. In our proposed new method (CDT) continuous attributes are handled without discretization, and arbitrary geometric figures are used for separation of decision space, like hyperplanes in general position, spheres and ellipsoids. The power of our new method is going to be demonstrated oh a few examples.