@article{19796,
  abstract     = {Motivation: Boolean networks are popular dynamical models of cellular processes in systems biology. Their attractors model phenotypes that arise from the interplay of key regulatory subcircuits. A succession diagram (SD) describes this interplay in a discrete analog of Waddington’s epigenetic attractor landscape that allows for fast identification of attractors and attractor control strategies. Efficient computational tools for studying SDs are essential for the understanding of Boolean attractor landscapes and connecting them to their biological functions.
Results: We present a new approach to SD construction for asynchronously updated Boolean networks, implemented in the biologist’s Boolean attractor landscape mapper, biobalm. We compare biobalm to similar tools and find a substantial performance increase in SD construction, attractor identification, and attractor control. We perform the most comprehensive comparative analysis to date of the SD structure in experimentally-validated Boolean models of cell processes and random ensembles. We find that random models (including critical Kauffman networks) have relatively small SDs, indicating simple decision structures. In contrast, nonrandom models from the literature are enriched in extremely large SDs, indicating an abundance of decision points and suggesting the presence of complex Waddington landscapes in nature.
Availability and implementation: The tool biobalm is available online at https://github.com/jcrozum/biobalm. Further data, scripts for testing, analysis, and figure generation are available online at https://github.com/jcrozum/biobalm-analysis and in the reproducibility artefact at https://doi.org/10.5281/zenodo.13854760.},
  author       = {Trinh, Van Giang and Park, Kyu Hyong and Pastva, Samuel and Rozum, Jordan C.},
  issn         = {1367-4811},
  journal      = {Bioinformatics},
  number       = {5},
  publisher    = {Oxford University Press},
  title        = {{Mapping the attractor landscape of Boolean networks with biobalm}},
  doi          = {10.1093/bioinformatics/btaf280},
  volume       = {41},
  year         = {2025},
}

@article{19854,
  abstract     = {Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular in systems biology due to their ability to model long-term biological phenotypes within a qualitative, predictive framework. Boolean networks model phenotypes as attractors, which are closely linked to minimal trap spaces (inescapable hypercubes in the system’s state space). In biological applications, attractors and minimal trap spaces are typically in one-to-one correspondence. However, this correspondence is not guaranteed: motif-avoidant attractors (MAAs) that lie outside minimal trap spaces are possible. MAAs are rare and poorly understood, despite recent efforts. In this contribution to the BMB & JMB Special Collection “Problems, Progress and Perspectives in Mathematical and Computational Biology”, we summarize the current state of knowledge regarding MAAs and present several novel observations regarding their response to node deletion reductions and linear extensions of edges. We conduct large-scale computational studies on an ensemble of 14 000 models derived from published Boolean models of biological systems, and more than 100 million Random Boolean Networks. Our findings quantify the rarity of MAAs; in particular, we only observed MAAs in biological models after applying standard simplification methods, highlighting the role of network reduction in introducing MAAs into the dynamics. We also show that MAAs are fragile to linear extensions: in sparse networks, even a single linear node can disrupt virtually all MAAs. Motivated by this observation, we improve the upper bound on the number of delays needed to disrupt a motif-avoidant attractor.},
  author       = {Pastva, Samuel and Park, Kyu Hyong and Huvar, Ondřej and Rozum, Jordan C. and Albert, Réka},
  issn         = {1432-1416},
  journal      = {Journal of Mathematical Biology},
  publisher    = {Springer Nature},
  title        = {{An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?}},
  doi          = {10.1007/s00285-025-02235-8},
  volume       = {91},
  year         = {2025},
}

@inproceedings{18177,
  abstract     = {Partially Specified Boolean Networks (PSBNs) represent a family of Boolean models resulting from possible interpretations of unknown update logics. Hybrid extension of CTL (HCTL) has the power to express complex dynamical phenomena, such as oscillations or stability. We present BNClassifier to classify Boolean Networks corresponding to a given PSBN according to criteria specified in HCTL. The implementation of the tool is fully symbolic (based on BDDs). The results are visualised using the machine-learning-based technology of decision trees.},
  author       = {Beneš, Nikola and Brim, Luboš and Huvar, Ondřej and Pastva, Samuel and Šafránek, David},
  booktitle    = {Computational Methods in Systems Biology},
  isbn         = {9783031716706},
  issn         = {1611-3349},
  pages        = {19--26},
  publisher    = {Springer Nature},
  title        = {{BNClassifier: Classifying boolean models by dynamic properties}},
  doi          = {10.1007/978-3-031-71671-3_2},
  volume       = {14971},
  year         = {2024},
}

@misc{19800,
  abstract     = {This archive contains all the code and data necessary to reproduce the results presented in the 
"Mapping the attractor landscape of Boolean networks" paper.},
  author       = {trinh, Van Giang and Park, Kyu Hyong and Pastva, Samuel and Rozum, Jordan},
  publisher    = {Zenodo},
  title        = {{Mapping the attractor landscape of Boolean networks}},
  doi          = {10.5281/ZENODO.13854759},
  year         = {2024},
}

@inproceedings{15321,
  abstract     = {Boolean Networks (BNs) are widely used as a modeling formalism in several domains, notably systems biology and computer science. A fundamental problem in BN analysis is the enumeration of trap spaces, which are hypercubes in the state space that cannot be escaped once entered. Several methods have been proposed for enumerating trap spaces, however they often suffer from scalability and efficiency issues, particularly for large and complex models. To our knowledge, the most efficient and recent methods for the trap space enumeration all rely on Answer Set Programming (ASP), which has been widely applied to the analysis of BNs. Motivated by these considerations, our work proposes a new method for enumerating trap spaces in BNs using ASP. We evaluate the method on a mix of 250+ real-world and 400+ randomly generated BNs, showing that it enables analysis of models beyond the capabilities of existing tools (namely pyboolnet, mpbn, trappist, and trapmvn).},
  author       = {Trinh, Giang and Benhamou, Belaid and Pastva, Samuel and Soliman, Sylvain},
  booktitle    = {Proceedings of the 38th AAAI Conference on Artificial Intelligence},
  isbn         = {1577358872},
  issn         = {2374-3468},
  number       = {9},
  pages        = {10714--10722},
  publisher    = {Association for the Advancement of Artificial Intelligence},
  title        = {{Scalable enumeration of trap spaces in boolean networks via answer set programming}},
  doi          = {10.1609/aaai.v38i9.28943},
  volume       = {38},
  year         = {2024},
}

@inproceedings{14411,
  abstract     = {Partially specified Boolean networks (PSBNs) represent a promising framework for the qualitative modelling of biological systems in which the logic of interactions is not completely known. Phenotype control aims to stabilise the network in states exhibiting specific traits.
In this paper, we define the phenotype control problem in the context of asynchronous PSBNs and propose a novel semi-symbolic algorithm for solving this problem with permanent variable perturbations.},
  author       = {Beneš, Nikola and Brim, Luboš and Pastva, Samuel and Šafránek, David and Šmijáková, Eva},
  booktitle    = {21st International Conference on Computational Methods in Systems Biology},
  isbn         = {9783031426964},
  issn         = {1611-3349},
  location     = {Luxembourg City, Luxembourg},
  pages        = {18--35},
  publisher    = {Springer Nature},
  title        = {{Phenotype control of partially specified boolean networks}},
  doi          = {10.1007/978-3-031-42697-1_2},
  volume       = {14137},
  year         = {2023},
}

@inproceedings{14718,
  abstract     = {Binary decision diagrams (BDDs) are one of the fundamental data structures in formal methods and computer science in general. However, the performance of BDD-based algorithms greatly depends on memory latency due to the reliance on large hash tables and thus, by extension, on the speed of random memory access. This hinders the full utilisation of resources available on modern CPUs, since the absolute memory latency has not improved significantly for at least a decade. In this paper, we explore several implementation techniques that improve the performance of BDD manipulation either through enhanced memory locality or by partially eliminating random memory access. On a benchmark suite of 600+ BDDs derived from real-world applications, we demonstrate runtime that is comparable or better than parallelising the same operations on eight CPU cores. },
  author       = {Pastva, Samuel and Henzinger, Thomas A},
  booktitle    = {Proceedings of the 23rd Conference on Formal Methods in Computer-Aided Design},
  isbn         = {9783854480600},
  location     = {Ames, IA, United States},
  pages        = {122--131},
  publisher    = {TU Vienna Academic Press},
  title        = {{Binary decision diagrams on modern hardware}},
  doi          = {10.34727/2023/isbn.978-3-85448-060-0_20},
  year         = {2023},
}

@article{12876,
  abstract     = {Motivation: The problem of model inference is of fundamental importance to systems biology. Logical models (e.g. Boolean networks; BNs) represent a computationally attractive approach capable of handling large biological networks. The models are typically inferred from experimental data. However, even with a substantial amount of experimental data supported by some prior knowledge, existing inference methods often focus on a small sample of admissible candidate models only.

Results: We propose Boolean network sketches as a new formal instrument for the inference of Boolean networks. A sketch integrates (typically partial) knowledge about the network’s topology and the update logic (obtained through, e.g. a biological knowledge base or a literature search), as well as further assumptions about the properties of the network’s transitions (e.g. the form of its attractor landscape), and additional restrictions on the model dynamics given by the measured experimental data. Our new BNs inference algorithm starts with an ‘initial’ sketch, which is extended by adding restrictions representing experimental data to a ‘data-informed’ sketch and subsequently computes all BNs consistent with the data-informed sketch. Our algorithm is based on a symbolic representation and coloured model-checking. Our approach is unique in its ability to cover a broad spectrum of knowledge and efficiently produce a compact representation of all inferred BNs. We evaluate the method on a non-trivial collection of real-world and simulated data.},
  author       = {Beneš, Nikola and Brim, Luboš and Huvar, Ondřej and Pastva, Samuel and Šafránek, David},
  issn         = {1367-4811},
  journal      = {Bioinformatics},
  number       = {4},
  publisher    = {Oxford University Press},
  title        = {{Boolean network sketches: A unifying framework for logical model inference}},
  doi          = {10.1093/bioinformatics/btad158},
  volume       = {39},
  year         = {2023},
}

@article{13263,
  abstract     = {Motivation: Boolean networks are simple but efficient mathematical formalism for modelling complex biological systems. However, having only two levels of activation is sometimes not enough to fully capture the dynamics of real-world biological systems. Hence, the need for multi-valued networks (MVNs), a generalization of Boolean networks. Despite the importance of MVNs for modelling biological systems, only limited progress has been made on developing theories, analysis methods, and tools that can support them. In particular, the recent use of trap spaces in Boolean networks made a great impact on the field of systems biology, but there has been no similar concept defined and studied for MVNs to date.

Results: In this work, we generalize the concept of trap spaces in Boolean networks to that in MVNs. We then develop the theory and the analysis methods for trap spaces in MVNs. In particular, we implement all proposed methods in a Python package called trapmvn. Not only showing the applicability of our approach via a realistic case study, we also evaluate the time efficiency of the method on a large collection of real-world models. The experimental results confirm the time efficiency, which we believe enables more accurate analysis on larger and more complex multi-valued models.},
  author       = {Trinh, Van Giang and Benhamou, Belaid and Henzinger, Thomas A and Pastva, Samuel},
  issn         = {1367-4811},
  journal      = {Bioinformatics},
  number       = {Supplement_1},
  pages        = {i513--i522},
  publisher    = {Oxford University Press},
  title        = {{Trap spaces of multi-valued networks: Definition, computation, and applications}},
  doi          = {10.1093/bioinformatics/btad262},
  volume       = {39},
  year         = {2023},
}