76 research outputs found
A Proof of the Factorization Forest Theorem
We show that for every homomorphism where is a finite
semigroup there exists a factorization forest of height \leq 3 \abs{S}. The
proof is based on Green's relations.Comment: 4 page
A Characterization of Infinite LSP Words
G. Fici proved that a finite word has a minimal suffix automaton if and only
if all its left special factors occur as prefixes. He called LSP all finite and
infinite words having this latter property. We characterize here infinite LSP
words in terms of -adicity. More precisely we provide a finite set of
morphisms and an automaton such that an infinite word is LSP if
and only if it is -adic and all its directive words are recognizable by
A proof of the factorization forest theorem
We show that for every homomorphism where is a finite semigroup there exists a factorization forest of height \leq 3 \abs{S}. The proof is based on Green's relations
Turku Centre for Computer Science – Annual Report 2013
Due to a major reform of organization and responsibilities of TUCS, its role, activities, and even structures have been under reconsideration in 2013. The traditional pillar of collaboration at TUCS, doctoral training, was reorganized due to changes at both universities according to the renewed national system for doctoral education. Computer Science and Engineering and Information Systems Science are now accompanied by Mathematics and Statistics in newly established doctoral programs at both University of Turku and Åbo Akademi University. Moreover, both universities granted sufficient resources to their respective programmes for doctoral training in these fields, so that joint activities at TUCS can continue. The outcome of this reorganization has the potential of proving out to be a success in terms of scientific profile as well as the quality and quantity of scientific and educational results.
International activities that have been characteristic to TUCS since its inception continue strong. TUCS’ participation in European collaboration through EIT ICT Labs Master’s and Doctoral School is now more active than ever. The new double degree programs at MSc and PhD level between University of Turku and Fudan University in Shaghai, P.R.China were succesfully set up and are
now running for their first year. The joint students will add to the already international athmosphere of the ICT House.
The four new thematic reseach programmes set up acccording to the decision by the TUCS Board have now established themselves, and a number of events and other activities saw the light in 2013. The TUCS Distinguished Lecture Series managed to gather a large audience with its several prominent speakers. The development of these and other research centre activities continue, and
new practices and structures will be initiated to support the tradition of close academic collaboration.
The TUCS’ slogan Where Academic Tradition Meets the Exciting Future has proven true throughout these changes. Despite of the dark clouds on the national and European economic sky, science and higher education in the field have managed to retain all the key ingredients for success. Indeed, the future of ICT and Mathematics in Turku seems exciting.</p
Characterization of infinite LSP words and endomorphisms preserving the LSP property
Answering a question of G. Fici, we give an -adic characterization of
thefamily of infinite LSP words, that is, the family of infinite words having
all their left special factors as prefixes.More precisely we provide a finite
set of morphisms and an automaton such that an infinite word is
LSP if and only if it is -adic and one of its directive words is
recognizable by .Then we characterize the endomorphisms that preserve
the property of being LSP for infinite words.This allows us to prove that there
exists no set of endomorphisms for which the set of infinite LSP words
corresponds to the set of -adic words. This implies that an automaton is
required no matter which set of morphisms is used.Comment: arXiv admin note: text overlap with arXiv:1705.0578
The palindromization map
The palindromization map has been defined initially by Aldo de Luca in the
context of Sturmian words. It was extended to the free group of rank by
Kassel and the second autho We extend their construction to arbitrary
alphabets. We also
investigate the suffix automaton and compact suffix automaton of the words
obtained by palindromization
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