A Coalgebraic View on Reachability

Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra can be computed in that base category

Projected Power Iteration for Network Alignment

The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein interactions) and it is very closely related to the quadratic assignment problem which has graph isomorphism, traveling salesman and minimum bisection problems as particular cases. The graph matching problem is NP-hard in general. However, under some restrictive models for the graphs, algorithms can approximate the alignment efficiently. In that spirit the recent work by Feizi and collaborators introduce EigenAlign, a fast spectral method with convergence guarantees for Erd\H{o}s-Reny\'i graphs. In this work we propose the algorithm Projected Power Alignment, which is a projected power iteration version of EigenAlign. We numerically show it improves the recovery rates of EigenAlign and we describe the theory that may be used to provide performance guarantees for Projected Power Alignment.Comment: 8 page

Random Generation and Enumeration of Accessible Determinisitic Real-time Pushdown Automata

This papers presents a general framework for the uniform random generation of deterministic real-time accessible pushdown automata. A polynomial time algorithm to randomly generate a pushdown automaton having a fixed stack operations total size is proposed. The influence of the accepting condition (empty stack, final state) on the reachability of the generated automata is investigated.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223, pp.12, 2015, Implementation and Application of Automata - 20th International Conferenc

Grammatical inference of directed acyclic graph languages with polynomial time complexity

[EN] In this paper we study the learning of graph languages. We extend the well-known classes of k-testability and k-testability in the strict sense languages to directed graph languages. We propose a grammatical inference algorithm to learn the class of directed acyclic k- testable in the strict sense graph languages. The algorithm runs in polynomial time and identifies this class of languages from positive data. We study its efficiency under several criteria, and perform a comprehensive experimentation with four datasets to show the validity of the method. Many fields, from pattern recognition to data compression, can take advantage of these results.Gallego, A.; López Rodríguez, D.; Calera-Rubio, J. (2018). Grammatical inference of directed acyclic graph languages with polynomial time complexity. Journal of Computer and System Sciences. 95:19-34. https://doi.org/10.1016/j.jcss.2017.12.002S19349