Bořivoj Melichar

Finding common motifs with gaps using finite automata

We present an algorithm that uses finite automata to find the common motifs with gaps occurring in all strings belonging to a finite set S = {S1,S2,...,Sr}. In order to find these common motifs we must first identify the factors that exist in each string. Therefore the algorithm begins by constructing a factor automaton for each string Si. To find the common factors of all the strings, the algorithm needs to gather all the factors from the strings together in one data structure and this is achieved by computing an automaton that accepts the union of the above-mentioned automata. Using this automaton we are able to create a new factor alphabet. Based on this factor alphabet a finite automaton is created for each string Si that accepts sequences of all non overlapping factors residing in each string. The intersection of the latter automata produces the finite automaton which accepts all the common subsequences with gaps over the factor alphabet that are present in all the strings of the set S = {S1,S2,...,Sr}. These common subsequences are the common motifs of the strings.

The hierarchy of LR-attributed grammars

The problem of attribute evaluation during LR parsing is considered. Several definitions of LR-attributed grammars are presented. Relations of corresponding attribute grammar classes are analysed. Also the relations between LR-attributed grammars and LL-attributed grammars and between LR-attributed grammars and a class of one-pass attributed grammars based on left-corner grammars are considered.

On regular tree languages and deterministic pushdown automata

The theory of formal string languages and of formal tree languages are both important parts of the theory of formal languages. Regular tree languages are recognized by finite tree automata. Trees in their postfix notation can be seen as strings. This paper presents a simple transformation from any given (bottom-up) finite tree automaton recognizing a regular tree language to a deterministic pushdown automaton accepting the same tree language in postfix notation. The resulting deterministic pushdown automaton can be implemented easily by an existing parser generator because it is constructed for an LR(0) grammar, and its size directly corresponds to the size of the deterministic finite tree automaton. The class of regular tree languages in postfix notation is a proper subclass of deterministic context-free string languages. Moreover, the class of tree languages which are in their postfix notation deterministic context-free string languages is a proper superclass of the class of regular tree languages.

Arbology: trees and pushdown automata

Trees are (data) structures used in many areas of human activity. Tree as the formal notion has been introduced in the theory of graphs. Nevertheless, trees have been used a long time before the foundation of the graph theory. An example is the notion of a genealogical tree. The area of family relationships was an origin of some terminology in the area of the tree theory (parent, child, sibling, ...) in addition to the terms originating from the area of the dendrology (root, branch, leaf, ...).

Computing all subtree repeats in ordered trees

We consider the problem of computing all subtree repeats in a given labeled ordered tree. We first transform the tree to a string representing its postfix notation, and then present an algorithm based on the bottom-up technique to solve it. The proposed algorithm consists of two phases: the preprocessing phase and the phase where all subtree repeats are computed. The linear time and space complexity of the proposed algorithm are important parts of its quality.

Computing all subtree repeats in ordered ranked trees

We consider the problem of finding all subtree repeats in a given ordered ranked tree. Specifically, we transform the given tree to a string representing its postfix notation, and then propose an algorithm based on the bottom-up technique. The proposed algorithm is divided into two phases: the preprocessing phase, and the phase where all subtree repeats are computed. The linear runtime of the algorithm, as well as the use of linear auxiliary space, are important aspects of its quality.

The longest common subsequence problem a finite automata approach

A new algorithm that creates a common subsequence automaton for a set of strings is presented. Moreover, it is shown that a longest common subsequence of two strings over a constant alphabet can be found in O (|A| (|S1 + |S2| + Σa∈A|S1|a|S2|a)) time, where |A| is the size of the alphabet, |Si| is the length of the input string i, and |Si|a is the number of occurrences of a ∈ A in Si.

ARITHMETIC CODING IN PARALLEL

We present an EREW PRAM cost optimal parallel algorithm for arithmetic coding computation. We solve the problem in time using n/log n processors. Each part of the algorithm as well as a well-known parallel prefix computation forming a basis of the algorithm are clarified on simple examples.

On two-dimensional pattern matching by finite automata

This paper presents a general concept of two-dimensional pattern matching using conventional (one-dimensional) finite automata. Then two particular models and methods, implementations of the general principle, are presented. The first of these two models presents an automata based version of the Bird and Baker approach with lower space complexity than the original algorithm. The second introduces a new model for two-dimensional approximate pattern matching using the two-dimensional Hamming distance.

Efficient determinization of visibly and height-deterministic pushdown automata

New algorithms for the determinization of nondeterministic visibly and nondeterministic real-time height-deterministic pushdown automata are presented. The algorithms improve the results of existing algorithms. They construct only accessible states and necessary pushdown symbols of the resulting deterministic pushdown automata. HighlightsTracking pushdown symbols which can appear on top of pushdown store for each state.Generating pop (return) transition only for possible top pushdown symbols for each state.Overall generating only accessible states and necessary pushdown store symbols.Visibly pushdown automata determinization algorithm.Height-deterministic (real-time) automata determinization algorithm.