Szilárd Zsolt Fazekas

THE POWER OF PROGRAMMED GRAMMARS WITH GRAPHS FROM VARIOUS CLASSES

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.

Bounds on Powers in Strings

We show a i¾?(nlogn) bound on the maximal number of occurrences of primitively-rooted k-th powers occurring in a string of length nfor any integer k, ki¾? 2. We also show a i¾?(n2) bound on the maximal number of primitively-rooted powers with fractional exponent e, 1 < e< 2, occurring in a string of length n. This result holds obviously for their maximal number of occurrences. The first result contrasts with the linear number of occurrences of maximal repetitions of exponent at least 2.

ON INEQUALITIES BETWEEN SUBWORD HISTORIES

In this paper we study subword inequalities, that is, inequalities between the number of occurrences of certain scattered subwords in a word. The problem of deciding whether a subword inequality holds for all words was proposed in [5]. We provide partial results describing a few cases in which the subword inequalities hold. Whether a subword inequality falls in these categories is decidable. However, the general question remains open.

One-Way Jumping Finite Automata

We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.

NUMBER OF OCCURRENCES OF POWERS IN STRINGS

We show a Θ(n log n) bound on the maximal number of occurrences of primitively-rooted k-th powers occurring in a string of length n for any integer k, k ≥ 2. We also show a Θ(n2) bound on the maximal number of primitively-rooted powers with fractional exponent e, 1 < e < 2, occurring in a string of length n. This result holds obviously for their maximal number of occurrences. The first result contrasts with the linear number of occurrences of maximal repetitions of exponent at least 2.

A NOTE ON THE DECIDABILITY OF SUBWORD INEQUALITIES

Extending the general undecidability result concerning the absoluteness of inequalities between subword histories, in this paper we show that the question whether such inequalities hold for all words is undecidable even over a binary alphabet and bounded number of blocks, i.e., unary factors of maximal length.

ON NON-PRIMITIVE PALINDROMIC CONTEXT-FREE LANGUAGES

This work continues investigations on avoidability of languages. We show that the language of primitive non-palindromes is strongly unavoidable for context-free languages that are not linear. This means that every language from this class contains infinitely many primitive non-palindromes. In the second part, we extend the defintion of palindromes. In the center of a word we admit a bounded factor that is not palindromic. For k-palindromes, the length of this factor can be up to k. For non-primitive words, k-palindromicity implies conventional palindromicity if these words are long enough. Therefore we can extend the unavoidability result to k-palindromes.