Kayoko Shikishima-Tsuji

Some Results on Directable Automata

In this paper, we provide some properties of classes of regular languages consisting of directing words of directable automata and some new results on the shortest directing words of nondeterministic directable automata.

Termination and derivational complexity of confluent one-rule string-rewriting systems

It is not known whether the termination problem is decidable for one-rule string-rewriting systems, though the confluence of such systems is decidable by Wrathall (in: Word Equations and Related Topics, Lecture Notes in Computer Science, vol. 572, 1992, pp. 237–246). In this paper we develop techniques to attack the termination and complexity problems of confluent one-rule string-rewriting systems. With given such a system we associate another rewriting system over another alphabet. The behaviour of the two systems is closely related and the termination problem for the new system is sometimes easier than for the original system. We apply our method to systems of the special type {apbq→t}, where t is an arbitrary word over {a,b}, and give a complete characterization for termination. We also give a complete analysis of the derivational complexity for the system {apbq→bnam}.

On termination of confluent one-rule string-rewriting systems

Abstract The termination of a confluent one-rule string-rewriting system R = { → t} is reduced to that of another one-rule system R′ = {′ → t′} such that s′ is self-overlap-free (sof). A necessary and sufficient condition is given for termination of a one-rule system R = { → t} such that s is sof and s overlaps t once on both sides.

Closure of language classes under bounded duplication

Duplication is an operation generating a language from a single word by iterated application of rewriting rules u →uu on factors. We extend this operation to entire languages and investigate, whether the classes of the Chomsky hierarchy are closed under duplication. Here we treat mainly bounded duplication, where the factors duplicated cannot exceed a given length. n nWhile over two letters the regular languages are closed under bounded duplication, over three or more letters they are not, if the length bound is 4 or greater. For 2 they are closed under duplication, the case of 3 remains open. Finally, the class of context-free languages is closed under duplication over alphabets of any size.

Hairpin completion with bounded stem-loop

Pseudopalindromes are words that are fixed points for some antimorphic involution. In this paper we discuss a newer word operation, that of pseudopalindromic completion, in which symbols are added to either side of the word such that the new obtained words are pseudopalindromes. This notion represents a particular type of hairpin completion, where the length of the hairpin is at most one. We give precise descriptions of regular languages that are closed under this operation and show that the regularity of the closure under the operation is decidable.

Regularity of Iterative Hairpin Completions of Crossing (2, 2)-Words

Hairpin completion is a formal operation inspired from DNA biochemistry. It is known that the (one step) hairpin completion of a regular language is linear context-free, but not regular in general. Further, it is decidable whether the (one step) hairpin completion of a regular language is regular. However, it is an open question whether the iterated hairpin completion of a regular language is regular, even if it is a singleton. If the word is a non-crossing α-word, there are results, but for crossing words there are no results. In this paper, we give necessary and sufficient conditions that the iterated hairpin completion of a given crossing (2, 2)-α-word in αΣ*α¯ is regular.

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.

Shortest directing words of nondeterministic directable automata

In this paper, we will survey several results on the shortest directing words of various types of nondeterministic directable automata.