A Classification of Trapezoidal Words

Trapezoidal words are finite words having at most n+1 distinct factors of length n, for every n>=0. They encompass finite Sturmian words. We distinguish trapezoidal words into two disjoint subsets: open and closed trapezoidal words. A trapezoidal word is closed if its longest repeated prefix has exactly two occurrences in the word, the second one being a suffix of the word. Otherwise it is open. We show that open trapezoidal words are all primitive and that closed trapezoidal words are all Sturmian. We then show that trapezoidal palindromes are closed (and therefore Sturmian). This allows us to characterize the special factors of Sturmian palindromes. We end with several open problems.Comment: In Proceedings WORDS 2011, arXiv:1108.341

On the Structure of Bispecial Sturmian Words

A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, that are the digital approximations of Euclidean segments in the plane. In 1997, J. Berstel and A. de Luca proved that \emph{palindromic} bispecial Sturmian words are precisely the maximal internal factors of \emph{primitive} Christoffel words. We extend this result by showing that bispecial Sturmian words are precisely the maximal internal factors of \emph{all} Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the language of Sturmian words.Comment: arXiv admin note: substantial text overlap with arXiv:1204.167

A parallelogram tile fills the plane by translation in at most two distinct ways

We consider the tilings by translation of a single polyomino or tile on the square grid Z2 (Z exposant 2). It is well-known that there are two regular tilings of the plane, namely, parallelogram and hexagonal tilings. Although there exist tiles admitting an arbitrary number of distinct hexagon tilings, it has been conjectured that no polyomino admits more than two distinct parallelogram tilings. In this paper, we prove this conjecture

On the restricted Hanoi Graphs

Consider the restricted Hanoi graphs which correspond to the variants of the famous Tower of Hanoi problem with multiple pegs where moves of the discs are restricted throughout the arcs of a movement digraph whose vertices represent the pegs of the puzzle and an arc from vertex $p$ to vertex $q$ exists if and only if moves from peg $p$ to peg $q$ are allowed. In this paper, we gave some notes on how to construct the restricted Hanoi graphs as well as some combinatorial results on the number of arcs in these graphs.Comment: 8 pages, 2 figure

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 &Aring;bo 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.&nbsp; International activities that have been characteristic to TUCS since its inception continue strong. TUCS&rsquo; participation in European collaboration through EIT ICT Labs Master&rsquo;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&nbsp; now running for their first year. The joint students will add to the already international athmosphere of the ICT House.&nbsp; 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&nbsp; new practices and structures will be initiated to support the tradition of close academic collaboration.&nbsp; The TUCS&rsquo; 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

A socio-technical framework to guide implementation and value realisation of distributed ledger technologies (dlt) in the construction sector

Construction is highly resistant to change. Its many challenges have persisted for decades rooted in a lack of trust, reluctance to collaborate and share information. New technologies offer increased transparency, efficiency, and collaboration. Building Information Modelling (BIM), while being the most successful to advance construction to date, has not done enough to combat the challenges. The aim of this research was to investigate the potential of distributed ledger technologies (DLT) and smart contracts (SCs) to provide solutions for the sector. Through empirical investigations (systematic literature review, interviews, focus groups, survey), a framework to guide implementation and value realisation of DLT and SCs in the construction sector was proposed. A socio-technical approach was taken resulting in a framework encompassing four dimensions of technology, process, policy and society. This approach recognises DLT and SCs are not a panacea in and of themselves and should be used in conjunction with advancements across the four dimensions to de-risk any potential failure of these systems. The framework is made up of several conceptual constructs for use at meso and macro scales to support evaluation of the as-is to achieve a desired state and offers progressive roadmaps to reach the point of implementation. The findings demonstrate the requirement for DLT and SCs to integrate with other systems (e.g., BIM, IoT, AI) to add value. Furthermore, technology alone is insufficient to solve the sector’s problems also requiring reform of outdated practices (e.g., procurement, payments, contract management). Contributions to knowledge include: the first known socio-technical framework for systematic and progressive implementation of DLT and SCs in construction. This places equal importance on society and technology for the implementation of these new technological systems and will facilitate their success to unlock benefits for the sector amid the myriad challenges it faces; through this socio-technical approach, the framework encourages active involvement of stakeholders placing importance on the realisation that engaging with users of the system is central to its success; the position of an organisation (or group) looking to develop DLT- or SC-based applications at the meso scale or the position of the sector with regard to how it wants to incorporate these technologies into its existing systems and processes at the macro scale can be evaluated using the framework’s progressive approach that considers every stage of developing and implementing an application; the constructs considering both meso and macro scales minimise any potential decoupling between policy and practice in terms of implementation; and the framework aims to provide a flexible set of tools to encourage the sector to create an ecosystem ready to support these applications as well as provide guidance in the development of applications