Preface to special issue: Developments In Computational Models 2010

Automata Games for Multiple-model Checking

The second Dagstuhl seminar on coalgebraic logics took place from October 7–12, 2012, in the Leibniz Forschungszentrum Schloss Dagstuhl, following a successful earlier one in December 2009. From the 44 researchers who attended and the 30 talks presented, this collection highlights some of the progress that has been made in the field. We are grateful to Giuseppe Longo and his interest in a special issue in Mathematical Structures in Computer Science.

Mathematical Structures in Computer Science bridges the gap between theoretical computer science and software design. By publishing original perspectives from all areas of computing, the journal stresses applications from logic, algebra, geometry, category theory and other areas of logic and mathematics. Through issues such as this special issue, the journal also plans to play an occasional, but important role in the fields of intelligent computation and automation.

This article has two purposes. The first is to present a final coalgebra construction for finitary endofunctors on Set that uses a certain subset L* of the limit L of the first ω terms in the final sequence. L* is the set of points in L which arise from all coalgebras using their canonical morphisms into L, and it was used earlier for different purposes in Kurz and Pattinson (2005, Mathematical Structures in Computer Science, 15, 543–473). Viglizzo (2005, PhD Dessertation, Indiana University) showed that the same set L* carried a final coalgebra structure for functors in a certain inductively defined family. Our first goal is to generalize this to all finitary endofunctors; the result is implicit in Worrell (2005, Theoritical Computer Science, 338, 184–199). The second goal is to use the final coalgebra construction to propose coalgebraic logics similar to those in Lawrence S. Moss (1999, Annals of Pure and Applied Logic, 96, 277–317) but for all finitary endofunctors F on Set. This time one can dispense with all conditions on F, construct a logical language LF directly from it, and prove that two points in a coalgebra satisfy the same sentences of LF iff they are identified by the final coalgebra morphism. The language LF is very spare, having no boolean connectives. This work on LF is thus a re-working of coalgebraic logic for finitary functors on sets.

This issue of Mathematical Structures in Computer Science (MSCS) contains a selection of papers presented at the 12th International Colloquium on Theoretical Aspects of Computing (ICTAC 2015), which took place in Cali, Colombia, on October 29–31, 2015.

This special issue of Mathematical Structures in Computer Science contains a selection of papers presented at three satellite events of CONCUR'09, which was held between 31 August and 5 September 2009 in Bologna (Italy). Specifically, it contains three papers from the 16th International Workshop on Expressiveness in Concurrency (EXPRESS'09), one paper from the 2nd Interaction and Concurrency Experience (ICE'09) and two papers from the 6th Workshop on Structural Operational Semantics (SOS'09).

This special issue of Mathematical Structures in Computer Science contains six papers from the Workshop on Domains IX held at the University of Sussex (Brighton), on 22–24 September 2008. This was the ninth event in the long tradition of Domains workshops, which started in Darmstadt in 1994. Since then, workshops have been organised in Braunschweig (1996), Munich (1997), Siegen (1998), Darmstadt again (1999, 2004), Birmingham (2002) and Novosibirsk (2007).

Yao et al. (A note on the feasibility of generalized universal composability.Theory and Applications of Models of Computationpp. 474–485, 2007; A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science,19(1), pp. 193–205) claimed a potential limitation on the class of protocols that could be securely implemented in the generalized universal composability (GUC) framework proposed by Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Specifically, Yao et al. presented a concrete attack on a GUC Zero Knowledge (GUCZK) protocol, a natural adaptation Blum's ZK proof for Directed Hamiltonicity using the general GUC feasibility of Canetti et al. (Universally composable security with global setup.Lecture Notes in Computer Science, pp. 61–85, 2007). Interestingly, the attack was not analysed in the GUC model in Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) but in theFUC model, a new UC-like framework proposed in the same work. Nonetheless, Yao et al. (A note on the feasibility of generalised universal composability.Mathematical Structures in Computer Science19(1), pp. 193–205, 2009) argued that, in light of this attack, GUC would lose its concurrent general composability and proof of knowledge properties. Concretely, they argue that GUC composability would now be with respect to some adversaries with limited access to external arbitrary protocols.In this work, we show that the claimed attack from Yao et al. is indeed harmless and does not contradict the security of the mentioned GUCZK protocol, thus restoring the general feasibility for GUC.

The aim of this paper is to give an introduction how to use categorical methods in a specific field of computer science: The field of high-level-replacement systems has its roots in the well-established theories of formal languages, term rewriting, Petri nets, and graph grammars playing a fundamental role in computer science. More precisely, it is a generalization of the algebraic approach to graph grammars which is based on gluing constructions for graphs defined as pushouts in the category of graphs. The categorical theory of high-level-replacement systems is suitable for the dynamic handling of a large variety of high-level structures in computer science including different kinds of graphs and algebraic specifications. In this paper we discuss the basic principles and techniques from category theory applied in the field of high-level-replacement systems and present some basic results together with the corresponding categorical proof techniques.

Graph based data mining has become quite popular in the last few years. One of the best studied data structures in computer science and discrete mathematics are graphs. The use of social media has grown significantly in recent years. With the growth in its use, there has also been a substantial growth in the amount of information generated by users of social media. This paper discusses the metrics which are used in mining of social graphs. Keywords: Data Mining, Graphs, Social Graphs

Neural network-based machine learning is capable of approximating functions\nin very high dimension with unprecedented efficiency and accuracy. This has\nopened up many exciting new possibilities, not just in traditional areas of\nartificial intelligence, but also in scientific computing and computational\nscience. At the same time, machine learning has also acquired the reputation of\nbeing a set of "black box" type of tricks, without fundamental principles. This\nhas been a real obstacle for making further progress in machine learning. In\nthis article, we try to address the following two very important questions: (1)\nHow machine learning has already impacted and will further impact computational\nmathematics, scientific computing and computational science? (2) How\ncomputational mathematics, particularly numerical analysis, {can} impact\nmachine learning? We describe some of the most important progress that has been\nmade on these issues. Our hope is to put things into a perspective that will\nhelp to integrate machine learning with computational mathematics.\n

On knot-free vertex deletion: Fine-grained parameterized complexity analysis of a deadlock resolution graph problem

Grammars are fundamental structures in computer science that also have many applications in procedural content generation. This chapter starts by describing a classic type of grammar, the L-system, and its application to generating plants of various types. It then describes how rules and axioms for L-systems can be created through search-based methods. But grammars are not only useful for plants. Two longer examples discuss the generation of action-adventure levels through graph grammars, and the generation of Super Mario Bros. levels through grammatical evolution.

Matrisler bilgisayar bilimlerinde sıklıkla kullanılan veri yapılarıdır. Üçgensel matris gibi özel matris türleri için programlama dillerinde hazır yapılar bulunmamaktadır. Bir veri yapısı olarak üçgensel matris kullanmak gerekiyorsa programlama dilinden kaynaklanan bu eksiklik nedeniyle bellek ve zaman karmaşıklığı yönünden etkin olmayan yazılımlar kodlanmaktadır. Bu çalışmada üçgensel matris tipindeki yapıların bir boyutlu dizi olarak temsil edilmesinde kullanılan dönüşüm ve ters dönüşüm formülleri elde edilerek programların yer ve zaman karmaşıklığı açısından etkinliğinin arttırılması amaçlanmaktadır.

The linear-probing hash table is one of the oldest and most widely used data structures in computer science. However, linear probing famously comes with a major draw-back: as soon as the hash table reaches a high memory utilization, elements within the hash table begin to cluster together, causing insertions to become slow. This phenomenon, now known as primary clustering, was first captured by Donald Knuth in 1963; at a load factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 -1/x$</tex> , the expected time per insertion is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta(x^{2})$</tex> , rather than the more desirable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta(x)$</tex> . We show that there is more to the story than the classic analysis would seem to suggest. It turns out that small design decisions in how deletions are implemented have dramatic effects on the asymptotic performance of insertions. If these design decisions are made correctly, then even a hash table that is continuously at a load factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-\Theta(1/x)$</tex> can achieve average insertion time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\tilde{O}(x)$</tex> . A key insight is that the tombstones left behind by deletions cause a surprisingly strong “anti-clustering” effect, and that when insertions and deletions are one-for-one, the anti-clustering effects of deletions actually overpower the clustering effects of insertions. We also present a new variant of linear probing, which we call graveyard hashing, that completely eliminates primary clustering on any sequence of operations. If, when an operation is performed, the current load factor is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 -1/x$</tex> for some <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x$</tex> , then the expected cost of the operation is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(x)$</tex> . One corollary is that, in the external-memory model with a data block size of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$B$</tex> , graveyard hashing offers the following remarkable guarantee: at any load factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 -1/x$</tex> satisfying <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x=o(B)$</tex> , graveyard hashing achieves <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 +o(1)$</tex> expected block transfers per operation. Past external-memory hash tables have only been able to offer a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 +o(1)$</tex> guarantee when the block size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$B$</tex> is at least <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Omega(x^{2})$</tex> . Our results come with actionable lessons for both theoreticians and practitioners, in particular, that well-designed use of tombstones can completely change the asymptotic landscape of how the linear probing behaves (and if there are no deletions).