On the logical definability of certain graph and poset languages

We show that it is equivalent, for certain sets of finite graphs, to be definable in CMS (counting monadic second-order logic, a natural extension of monadic second-order logic), and to be recognizable in an algebraic framework induced by the notion of modular decomposition of a finite graph. More precisely, we consider the set $F\_\infty$ of composition operations on graphs which occur in the modular decomposition of finite graphs. If $F$ is a subset of $F\_{\infty}$, we say that a graph is an \calF-graph if it can be decomposed using only operations in $F$. A set of $F$-graphs is recognizable if it is a union of classes in a finite-index equivalence relation which is preserved by the operations in $F$. We show that if $F$ is finite and its elements enjoy only a limited amount of commutativity -- a property which we call weak rigidity, then recognizability is equivalent to CMS-definability. This requirement is weak enough to be satisfied whenever all $F$-graphs are posets, that is, transitive dags. In particular, our result generalizes Kuske's recent result on series-parallel poset languages

Extended Connectors: Structuring Glue Operators in BIP

Based on a variation of the BIP operational semantics using the offer predicate introduced in our previous work, we extend the algebras used to model glue operators in BIP to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T(P), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T(P), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints.Comment: In Proceedings ICE 2013, arXiv:1310.401

Linearity in the non-deterministic call-by-value setting

We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity present in such formalisms. After proving the subject reduction and the strong normalisation properties, we propose a translation of this calculus into the System F with pairs, which corresponds to a non linear fragment of linear logic. The translation provides a deeper understanding of the linearity in our setting.Comment: 15 pages. To appear in WoLLIC 201

An overview of recent distributed algorithms for learning fuzzy models in Big Data classification

AbstractNowadays, a huge amount of data are generated, often in very short time intervals and in various formats, by a number of different heterogeneous sources such as social networks and media, mobile devices, internet transactions, networked devices and sensors. These data, identified as Big Data in the literature, are characterized by the popular Vs features, such as Value, Veracity, Variety, Velocity and Volume. In particular, Value focuses on the useful knowledge that may be mined from data. Thus, in the last years, a number of data mining and machine learning algorithms have been proposed to extract knowledge from Big Data. These algorithms have been generally implemented by using ad-hoc programming paradigms, such as MapReduce, on specific distributed computing frameworks, such as Apache Hadoop and Apache Spark. In the context of Big Data, fuzzy models are currently playing a significant role, thanks to their capability of handling vague and imprecise data and their innate characteristic to be interpretable. In this work, we give an overview of the most recent distributed learning algorithms for generating fuzzy classification models for Big Data. In particular, we first show some design and implementation details of these learning algorithms. Thereafter, we compare them in terms of accuracy and interpretability. Finally, we argue about their scalability

On one-way cellular automata with a fixed number of cells

We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA