Tarski's influence on computer science

The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the method of elimination of quantifiers, the semantics of formal languages, modeltheoretic preservation theorems, and algebraic logic; various connections of each with computer science are taken up

Generation of cubic graphs

We describe a new algorithm for the efficient generation of all non-isomorphic connected cubic graphs. Our implementation of this algorithm is more than 4 times faster than previous generators. The generation can also be efficiently restricted to cubic graphs with girth at least 4 or 5

Generalized Vietoris Bisimulations

We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that bisimulation for a $\mathbf{Stone}$ coalgebra is the topological closure of bisimulation for the underlying $\mathbf{Set}$ coalgebra

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Brain enhancement through cognitive training: A new insight from brain connectome

Owing to the recent advances in neurotechnology and the progress in understanding of brain cognitive functions, improvements of cognitive performance or acceleration of learning process with brain enhancement systems is not out of our reach anymore, on the contrary, it is a tangible target of contemporary research. Although a variety of approaches have been proposed, we will mainly focus on cognitive training interventions, in which learners repeatedly perform cognitive tasks to improve their cognitive abilities. In this review article, we propose that the learning process during the cognitive training can be facilitated by an assistive system monitoring cognitive workloads using electroencephalography (EEG) biomarkers, and the brain connectome approach can provide additional valuable biomarkers for facilitating leaners' learning processes. For the purpose, we will introduce studies on the cognitive training interventions, EEG biomarkers for cognitive workload, and human brain connectome. As cognitive overload and mental fatigue would reduce or even eliminate gains of cognitive training interventions, a real-time monitoring of cognitive workload can facilitate the learning process by flexibly adjusting difficulty levels of the training task. Moreover, cognitive training interventions should have effects on brain sub-networks, not on a single brain region, and graph theoretical network metrics quantifying topological architecture of the brain network can differentiate with respect to individual cognitive states as well as to different individuals' cognitive abilities, suggesting that the connectome is a valuable approach for tracking the learning progress. Although only a few studies have exploited the connectome approach for studying alterations of the brain network induced by cognitive training interventions so far, we believe that it would be a useful technique for capturing improvements of cognitive function

Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist