International Workshop on Boolean Networks (IWBN 2020)
January 07‑10, 2020 07‑10 de enero 2020
Universidad de Concepción

Universidad de Concepción
Depto. de Ing. Inf. y Cs. de la Computación
Depto. de Ingeniería Matemática

Contact information: Contacto:
iwbn2020 at

Boolean networks are a particular type of finite dynamic system that has been widely used in modeling complex systems such as: social networks, communication networks and, especially, biological systems such as gene regulation networks and neural networks. Las redes Booleanas son un tipo particular de sistema dinámicos finito que ha sido ampliamente usado en el modelamiento de sistemas complejos como: redes sociales, redes de comunicación y especialmente sistemas biológicos como redes de regulación génica y redes neuronales.

This workshop aims at the scientific exchange on problems of Boolean networks and related combinatorial objects, from the point of view of discrete mathematics and computer science. Este workshop apunta al intercambio científico sobre problemas de las redes booleanas y objetos combinatorios relacionados, desde el punto de vista de la matemática discreta y ciencias de la computación.

Participation in the workshop is free of charge but requires prior registration to the email: iwbn2020 at La participación en el workshop no tiene costo, pero requiere de una inscripción previa al correo: iwbn2020 at

Poster Afiche

Scientific Committee Comité Científico

  • Julio Aracena. Universidad de Concepción. Chile.
  • Eric Goles. Universidad Adolfo Ibáñez. Chile.
  • Adrien Richard. Université de Nice Sophia Antipolis. France.
  • Lilian Salinas. Universidad de Concepción. Chile.
  • Sylvain Sené. Université d'Aix Marseille. France.

Organizing Committee Comité Organizador

  • Julio Aracena. DIM, Universidad de Concepción.
  • Anahí Gajardo. DIM, Universidad de Concepción.
  • Lilian Salinas. DIICC, Universidad de Concepción.
  • Christopher Thraves. DIM, Universidad de Concepción.

Plenary Speakers Charlas Plenarias

  • Maximilien Gadouleau. Durham University, UK.
  • Boolean network classes[+]

    Many structural and algorithmic results in graph theory concern special classes of graphs (e.g. bipartite, chordal, cographs, etc.). In this talk, we shall investigate how we could define different classes of Boolean networks and review some old and some recent results about their dynamics. We could define Boolean network classes e.g. recursively, or based on their interaction graph, or based on their local functions.

  • Eric Goles. Universidad Adolfo Ibáñez, Chile.
  • Automata Networks: 40 years of problems and applications[+]

    I will present a kind of survey on different problems related to automata networks that I have developed and shared with several colleagues in the last 40 years. Some of them are now closed, other semi‑closed and several ones remain open.

  • Mathew Macauley. Clemson University, USA.
  • An introduction to algebraic biology: theory and applications[+]

    Since Boolean functions can be expressed as polynomials, computational algebraic tools can be useful in the analysis of Boolean networks. I will use two examples from biology: analyzing a model of the tryptophanase (tna) operon in E. coli, and reverse engineering a mammalian signaling network, to illustrate how computational algebra arises. Relevant tools will include Gröbner bases, primary decomposition of ideals, and Alexander duality. Even better: biological applications like these have inspired completely new areas of classical mathematics. I will give a few examples of these, from the theory of pseudomonomial ideals, to a signed version of Stanley-Reisner theory. I will assume no prior knowledge of algebra in this talk.

  • Reinhard Laubenbacher. University of Conneticut, USA.
  • Boolean networks and their dynamics[+]

    While Boolean networks have found a wide range of applications in the life sciences and elsewhere, their utility as models of dynamic processes has been limited by a relative lack of mathematical tools for their analysis, in comparison to continuous models. The size and complexity of published models is growing to the point where simulation and sampling methods for the determination of model dynamics are increasingly unsatisfactory. Also, much remains to be learned about the structural characteristics of Boolean network models in different application domains. Since the class of Boolean networks on n nodes is equivalent to the class of all set functions on binary strings of length n, such characteristics are needed in order to identify suitable structural restrictions on models that are sufficiently broad to cover applications, but sufficiently narrow to allow in depth mathematical analysis. This talk will outline approaches to a mathematical research program that can help address these issues and provide a foundation for the study of Boolean networks and their dynamics.

  • Takeyuki Tamura. Kyoto University, Japan.
  • Algorithms for analyzing and controlling Boolean networks as biological networks[+]

    Boolean networks (BNs) can be considered as gene regulatory networks, where 1 (resp. 0) means that the gene is active (resp. inactive). Each singleton attractor (fixed point) corresponds to a cell type. We developed several rigorous exponential time algorithms that find singleton attractors for AND/OR BNs and nested canalyzing BNs. Furthermore, we developed integer linear programming (ILP)‑based methods for controlling BNs and singleton attractors.

    Metabolic networks represent relations between reactions and compounds in the metabolism of cells. In Boolean metabolic networks (BMN), either 0 or 1 is assigned to every node. “1” means that the corresponding reaction takes place or compound is producible, while “0” means that the corresponding reaction does not take place or compound is not producible. Reactions and compounds are represented by “AND” and “OR” nodes, respectively. The BMN is a bipartite graph and does not include negations. We developed ILP‑based methods of solving several optimization problems for controlling BMNs.

Invited Speakers Oradores Invitados

  • Florian Bridoux. Université d'Aix‑Marseille, France.
  • Complexity of limit cycle problems in conjunctive networks with different schedules[+]

    In this presentation, we will talk about conjunctive Boolean networks, namely, Boolean networks with conjunctive local functions. More precisely, we will show the complexity of the problem of determining if a conjunctive Boolean network has a limit cycle of a given length with different block sequential update schedules. We will first show this problem assuming a parallel (i.e. synchronous) update schedule.

    Next, we will allow for any block‑sequential update schedule and prove that this changes the problem complexity. Furthermore, we will prove that this problem is closely related to graph problems.

  • Luis Cabrera. Universidad de Concepción, Chile.
  • Inverse problems on the block‑sequential operator in Boolean networks[+]

    Motivated by the problem of the possible dynamics of a Boolean network with different update schedules, we study the block‑sequential operator that associates each Boolean network with block‑sequential schedule an equivalent Boolean network with a parallel scheme. In this presentation we focus on solving some inverse problems of this operator. In particular, on the complexity of finding the pre‑images of a given Boolean network.

  • Diego Maldonado. Universidad Adolfo Ibáñez, Chile.
  • A hard problem in a Boolean asynchronous freezing cellular automata[+]

    In this talk we will study a particularly complex boolean asynchronous freezing cellular automaton (BAFCA). A cellular automaton is called freezing if cells in state 1 remain always in that state. A cellular automaton is asynchronous if at each time‑step only one cell is updated following a fixed permutation, called updating scheme. Given configuration, we say that a cell in state 0 is unstable if there exists an updating scheme that changes the state of the cell. In this context, we define the problem AsyncUnstability, which consists in deciding if a cell is unstable or not. In general, AsyncUnstability is NP. In this talk, we show that there exists an BAFCA with only 2 states and von Neumann neighborhood where AsyncUnstability is NP‑complete. In other words, under the assumption that P ≠ NP, there is no polynomial‑time algorithm capable to decide if a cell is unstable for this rule.

  • Marco Montalva. Universidad Adolfo Ibáñez, Chile.
  • Combinatorics and dynamical classification of an Ising cellular automaton: the Q2R model[+]

    (joint work with Sergio Rica and Felipe Urbina)
    Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of configurations grows exponentially with the system size. As a consequence of the intrinsic reversibility of the model, the phase space is composed only by configurations that belong to a fixed point or a limit cycle. In this talk, we will show a classification of them in four types accordingly to well differentiated topological characteristics. Three of them –which we call of type S‑I, S‑II and S‑III– share a symmetry property, while the fourth, which we call of type AS, does not. Moreover, at a combinatorial level, we are able to determine the number of limit cycles for some small periods which are almost always present in the Q2R. Finally, we will discuss on some open problems.

  • Pedro Montealegre. Universidad Adolfo Ibáñez, Chile.
  • The impact of topology in the prediction of freezing automata networks[+]

    An Automata Network is a map F : Qn → Qn where Q is a finite alphabet. It can be viewed as a graph with n vertices, called interaction graph, where each vertex has a state in Q. The state of each vertex v evolves following a synchronous update rule fv, which only depends on the neighbors in the interaction graph. An automata network is called freezing if a partial order can be defined on Q, in such a way that the state of a vertex is only allowed to evolve to a bigger state according to this order.

    In this work we study the prediction problem, consisting in computing the state of a vertex after the evolution of the network. Naturally, every initial configuration of a q‑state Freezing Automata Network reaches a fixed point in at most qn time‑steps. Therefore, the prediction problem can be solved in polynomial‑time for every Freezing Automata Network.

    A major trend in automata network theory is to understand how the interaction graph affects dynamical properties of F. In this context, we study in which cases the prediction problem can be solved more efficiently than the simple simulation of the evolution of each cell.

    In this talk, we show that for every Freezing Automata Network defined over an interaction graph of bounded tree‑width the prediction problem is in NC. Conversely, we show that for every family of graphs of unbounded tree‑width, there exists a family of Freezing Automata Networks defined over it, for which the prediction problem is P‑Complete.

  • Andrés Moreira. Universidad Federico Santa María, Chile.
  • Multivariate information in random Boolean networks[+]

    We numerically apply the framework of O‑information, as recently developed by Rosas et al, to study the dynamics that govern Random Boolean Networks (RBNs). O‑information is a multivariate extension of mutual information, and is therefore expected to illuminate the high‑order interdependencies that underlie distributed information processing. The results recover the familiar picture of order, chaos and complex behaviours of RBNs, which O‑information reveals, respectively, as redundancy‑dominated, synergistical and as a balance thereof. This suggests a novel way to study the dynamics between and within the different phases, as well as its relation with topology, restrictions on local functions or other variants.

  • Henning S Mortveit. University of Virginia, USA.
  • Structure‑to‑Function theory for Boolean networks[+]

    A central goal in research on Boolean Networks is to relate properties of their constituents (graphs, functions, and update mechanism) to properties of their phase spaces. In the first part of the presentation I will give examples of such results for threshold Boolean Networks. In the second and main part of the talk I will present a new Lipschitz continuity result showing the close relationship between phase spaces of asynchronous Boolean networks (ABNs) under toric equivalence of update sequences. I will close by remarking on how the diversity of dynamics for permutation ABNs is closely governed by the cycle structure of the underlying graph.

  • Antonio Porreca. Université d'Aix‑Marseille, France.
  • Composing behaviours in the semiring of dynamical systems[+]

    By considering the operations of product and sum (co‑product) in the category of finite dynamical systems, we obtain a semiring structure, which allows us to analyse the composition of dynamics from an algebraic point of view. This semiring R appears to have a relatively complex structure, including multiple distinct decompositions into irreducible elements. We investigate the algorithmic solvability of equations in the associated semiring of polynomials R[X], which ranges from undecidable to tractable, as well as the related question of (in)decomposability of finite dynamical systems.

  • Adrien Richard. Université de Nice Sophia Antipolis. France.
  • Synchronizing Boolean networks asynchronously[+]

    The asynchronous automaton associated with a Boolean network f : {0,1}n → {0,1}n is the finite deterministic automaton with set of states {0,1}n, alphabet {1,…, n}, and where the action of letter i on a state x consists in either switching the i‑th component if f(x) ≠ xi or doing nothing otherwise. This action is extended to words in the natural way. We then say that the Boolean network is synchronizing if there is a word w whose action is constant, that is, for some state x, the result of action of w on any state is x. In this talk, we present some works in progress concerning synchronizing Boolean networks. Our main result is that a Boolean network is synchronizing if its signed interaction graph is strong, has no positive cycle, and maximum in‑degree two (and the result is false if one the three hypotheses is dropped).

  • Gonzalo Ruz. Universidad Adolfo Ibáñez, Chile.
  • On the use of computational intelligence for threshold Boolean network inference with applications[+]

    In this talk we will present several applications of computational intelligence (genetic algorithms, differential evolution, swarm intelligence, neural networks, etc.) to the problem of inferring threshold Boolean networks that contain a desired Boolean trajectory or specific attractors. Applications to several biological models will be analyzed.

  • Lilian Salinas. Universidad de Concepción, Chile.
  • Enumerating the fixed points of a Boolean network from a positive feedback vertex set[+]

    Abstract Lilian Salinas

Otros Participantes Other Participants

  • Julio Aracena. Universidad de Concepción, Chile.
  • Anahí Gajardo. Universidad de Concepción, Chile.
  • Christopher Thraves. Universidad de Concepción, Chile
  • Rodrigo Torres. Universidad del Bío‑Bío, Chile.
  • Darshana Jayadharan Pillai. Pontificia Universidad Católica de Chile, Chile.
  • Katherinne Tabilo. Universidad de Concepción, Chile.
  • José Abey. Pontificia Universidad Católica de Chile, Chile.
  • Raúl Astete. Universidad de Concepción, Chile.
  • Rolando Kindelan. Universidad de Chile, Chile.
  • Mónica Caniupan. Universidad del Bío‑Bío, Chile.
  • Tatiana Gutierrez. Universidad del Bío‑Bío, Chile.
  • Patricio Asenjo. Universidad de Concepción, Chile.
  • Jaime Luckmann. Universidad de Concepción, Chile.
  • Catalina Opazo. Universidad de Concepción, Chile.
  • Pablo Concha. Universidad del Bío‑Bío, Chile.
  • Katherine de la Hoz. Universidad de Concepción, Chile.
  • Sebastián Orellana. Universidad Federico Santa María, Chile

Program Programa

Martes, 07 de eneroTuesday, January 07
14:30−15:00Inauguración. Opening
15:00−16:00Eric Goles Automata Networks: 40 years of problems and applicationsslides
16:00−16:30Pausa CaféCoffee Break
16:30−17:20Lilian Salinas Enumerating the fixed points of a Boolean network from a positive feedback vertex setslides
18:00−19:30Cóctel de bienvenidaCocktail
Miércoles, 08 de eneroWednesday, January 08
09:00−10:00Reinhard Laubenbacher Boolean networks and their dynamicsslides
10:00−10:50Adrien RichardSynchronizing Boolean networks asynchronouslyslides
10:50−11:20Pausa CaféCoffee Break
11:20−12:10Henning S MortveitStructure‑to‑Function theory for Boolean networksslides
12:10−13:00Pedro MontealegreThe impact of topology in the prediction of freezing automata networksslides
14:30−15:30Maximilien GadouleauBoolean network classesslides
15:30−16:00Pausa CaféCoffee Break
16:00−16:50Florian BridouxComplexity of limit cycle problems in conjunctive networks with different schedulesslides
Jueves, 09 de eneroThursday, January 09
09:00−10:00Takeyuki TamuraAlgorithms for analyzing and controlling Boolean networks as biological networksslides
10:00−10:50Gonzalo RuzOn the use of computational intelligence for threshold Boolean network inference with applicationsslides
10:50−11:20Pausa CaféCoffee Break
11:20−12:10Luis CabreraInverse problems on the block‑sequential operator in Boolean networksslides
12:10−13:00Diego Maldonado A hard problem in a Boolean asynchronous freezing cellular automataslides
Viernes, 10 de eneroFriday, January 10
09:00−10:00Mathew MacauleyAn introduction to algebraic biology: theory and applicationsslides
10:00−10:50Andrés MoreiraMultivariate information in random Boolean networksslides
10:50−11:20Pausa CaféCoffee Break
11:20−12:10Marco MontalvaCombinatorics and dynamical classification of an Ising cellular automaton: the Q2R modelslides
12:10−13:00Antonio Porreca Composing behaviours in the semiring of dynamical systemsslides
14:30−16:00Discusión FinalFinal Discussion

Satellite School on Boolean Networks Escuela Satélite en Redes Booleanas

This school will be held on January 6 and 7, it is aimed at graduate and advanced undergraduate students as well as researchers looking for a quick introduction to the main theoretical results about Boolean networks. Esta escuela se desarrollará los días 6 y 7 de enero de 2020, está dirigida a estudiantes de pre y postgrado e investigadores que desean una rápida introducción a los principales resultados teóricos en redes Booleanas.

The aim of this school is to introduce the Boolean network and the state of the art of the subject, so that undergraduate and graduate students can participate in the workshop that will take place between January 7 and 10. El objetivo de la escuela es presentar las redes Booleanas y el estado del arte en el tema, de modo que los estudiantes puedan participar en el Workshop que tomará lugar inmediatamente después.

The number of participants is limited, so those interested should apply before November 30 December 06, sending an email to iwbn2020 at with the subject “Application to School in Boolenan Networks” where they express their motivation to participate in the school and attach their CV. El número de participantes es limitado, por lo que los interesados deben presentar su solicitud antes del 30 de noviembre 06 de diciembre, enviando un correo electrónico a iwbn2020 at con el encabezado “Postulación a la escuela en redes Booleanas”, donde expresan su motivación para participar en la escuela y adjuntar su CV.

There are a limited number of accommodation and food scholarships for students outside of Concepción. For those who require it, they must include the request in their motivation email. Hay un número limitado de becas de alojamiento y alimentación para estudiantes fuera de Concepción. Para quienes lo requieran deben incluir la solicitud en su correo de motivación.

Tutorials Tutoriales

  • Julio Aracena, Universidad de Concepción, Chile.
  • Introducción a las redes Booleanas: motivación y conceptos básicos.

  • Maximilien Gadouleau, Durham University, United Kingdom.
  • Influence of the interaction graph on the dynamics of Boolean networks.

  • Adrien Richard, Université de Nice Sophia Antipolis, France.
  • Fixed points and feedback cycles in Boolean networks.

  • Lilian Salinas, Universidad de Concepción, Chile.
  • Dinámica de redes Booleanas con diferentes esquemas de actualización.

Programa Program

Las clases se realizarán en la Sala IS 3-1 de la Facultad de Ingeniería, Universidad de Concepción. Classes are held in classroom IS 3-1 of the Faculty of Engineering, Universidad de Concepción.

Lunes, 06 de eneroMonday, January 06
09:00−10:30 Julio Aracena Introducción a las redes Booleanas: motivación y conceptos básicos slides
11:00−12:30 Adrien Richard Fixed points and feedback cycles in Boolean networks slides
13:45−15:15 Luis Cabrera Taller práctico
15:30−17:00 Maximilien Gadouleau Influence of the interaction graph on the dynamics of Boolean networks slides
Martes, 07 de eneroTuesday, January 07
09:00−10:30 Lilian Salinas Dinámica de redes Booleanas con diferentes esquemas de actualización slides
11:00−12:30 Luis Cabrera Taller práctico

Facultad de Ciencias Físicas y Matemáticas Universidad de Concepción, Auditorio Alamiro Robledo.

Pictures Fotos