arxiv: 2604.27576 · v2 · submitted 2026-04-30 · 💻 cs.LO · cs.LG

Recognition: unknown

BAss: Symbolic Reasoning in Abstract Dialectical Frameworks

Samuel Pastva, Van-Giang Trinh

Pith reviewed 2026-05-07 08:09 UTC · model grok-4.3

classification 💻 cs.LO cs.LG

keywords Abstract Dialectical FrameworksBinary Decision DiagramsSymbolic ReasoningBoolean NetworksStable ModelsFixed PointsSystems BiologyFormal Argumentation

0 comments

The pith

BAss computes all admissible, complete, preferred and stable models of abstract dialectical frameworks using binary decision diagrams.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents BAss, a symbolic solver that uses binary decision diagrams to compute the full range of interpretations and models for abstract dialectical frameworks. It builds on the established link between ADFs and Boolean networks to extend earlier BDD tools and deliver results on large real-world instances. Experiments across collections of biological and argumentation models show BAss outperforms prior BDD solvers and matches or exceeds SAT and ASP methods when solution spaces grow large. The method succeeds in enumerating every fixed point or minimal trap space for certain biological networks that existing tools cannot finish. This capability opens concrete new case studies in systems biology that rely on exhaustive enumeration.

Core claim

BAss provides fully symbolic computation of all admissible, complete, and preferred interpretations together with two-valued and stable models of an ADF. By encoding the problem in BDDs and exploiting the ADF–Boolean-network equivalence, the solver scales to instances whose solution sets are too large for previous BDD implementations and competitive with SAT/ASP solvers on the same data.

What carries the argument

BAss, the BDD-based ADF symbolic solver that represents and manipulates the entire set of interpretations simultaneously via binary decision diagrams.

If this is right

Full enumeration of fixed points and minimal trap spaces becomes feasible for certain biological networks that previous tools could not finish.
Symbolic methods can replace or complement SAT/ASP solvers for ADF semantics when the number of solutions is large.
New systems-biology case studies that require exhaustive listing of all stable models or admissible interpretations are now tractable.
The same BDD encoding can be reused across both the ADF and Boolean-network communities without separate implementations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Hybrid solvers that switch between BDD and SAT representations depending on instance size could further extend the reachable model scale.
The approach may transfer to other formal-argumentation formalisms that share similar semantics definitions.
Automated parameter tuning of BDD variable orderings could reduce the remaining cases where performance lags behind SAT methods.

Load-bearing premise

The collection of real-world BN and ADF models used for testing is representative and that the BDD encoding stays compact without hidden exponential blow-up on those instances.

What would settle it

A publicly available ADF or Boolean-network model of realistic size on which BAss either times out or returns an incomplete set of interpretations while at least one SAT or ASP solver finishes and produces the complete set within the same time bound.

Figures

Figures reproduced from arXiv: 2604.27576 by Samuel Pastva, Van-Giang Trinh.

**Figure 1.** Figure 1: Cactus plots showing the runtime of individual tools across different ADF problem categories. view at source ↗

read the original abstract

We present BAss (BDD-based ADF symbolic solver), a novel analysis tool for Abstract Dialectical Frameworks (ADFs) based on Binary Decision Diagrams (BDDs). It supports the fully symbolic computation of all admissible, complete, and preferred interpretations, as well as two-valued and stable models of an ADFs. Our approach is inspired by the recently discovered equivalence between Boolean Networks (BNs) and ADFs by Heyninck et al. (2024) and Azpeitia et al. (2024), significantly extending current BDD-based tools bioLQM, AEON, and adf-bdd. We conducted experiments on a large-scale collection of real-world models from both the BN and ADF communities. Our results show that BAss dramatically outperforms previous BDD-based tools and is competitive (even significantly better in some cases) with state-of-the-art SAT/ASP-based methods, particularly in scenarios involving large solution spaces. Notably, BAss is able to enumerate all fixed points or minimal trap spaces of certain biological networks beyond the reach of existing tools, thereby enabling new analysis and case studies in systems biology. These results highlight the practical relevance of symbolic reasoning for complex real-world applications, particularly in systems biology and formal argumentation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

read the letter

BAss is a practical BDD solver that extends prior tools to full ADF semantics and handles some larger biological networks, but its performance edge lacks structural characterization of the test models. The paper takes the 2024 BN-ADFs equivalence and implements a uniform symbolic engine for admissible, complete, preferred, two-valued, and stable semantics. That is the concrete advance over bioLQM, AEON, and adf-bdd, which lacked full coverage. On the real-world collection the authors assembled, BAss finishes faster than those BDD baselines and stays competitive with SAT and ASP solvers, especially when solution spaces grow large. It also reaches some fixed-point and trap-space enumerations that timed out before. Those results are useful for systems-biology users who need exhaustive answers on networks that are still modest in size but already too big for earlier symbolic code. The experiments appear to rest on external, independently published models rather than synthetic cases tuned to the method, which is a plus. The soft spot is the missing analysis of why the diagrams stay compact. The paper reports runtimes and success rates but does not break out treewidth, cyclicity, or strongly connected components of the dependency graphs, nor does it test variable-ordering sensitivity. Without that, it is hard to know whether the speedups will transfer to other ADF instances or whether the benchmark set simply favors BDDs. The implementation itself looks grounded in the cited equivalence, and the claims do not appear circular. This paper is for researchers who build or use logic-based models of biological networks and want a ready tool for exhaustive symbolic queries. It is not a deep theoretical contribution, but the engineering and the empirical comparison are solid enough to merit referee time. I would send it to peer review and ask the authors to add a short section on the structural properties of the networks where the BDDs remain tractable.

Referee Report

2 major / 3 minor

Summary. The paper introduces BAss, a BDD-based symbolic solver for Abstract Dialectical Frameworks (ADFs) that computes all admissible, complete, and preferred interpretations as well as two-valued and stable models. It builds on the recently established equivalence between Boolean Networks (BNs) and ADFs (Heyninck et al. 2024; Azpeitia et al. 2024), extends prior BDD tools (bioLQM, AEON, adf-bdd), and reports experimental results on real-world BN/ADF models showing dramatic outperformance over previous BDD solvers and competitiveness (sometimes superiority) with SAT/ASP solvers, especially on instances with large solution spaces. The work claims to enable enumeration of fixed points and minimal trap spaces for certain biological networks previously beyond reach.

Significance. If the performance and correctness claims hold, the work would be significant for bridging symbolic reasoning techniques with practical analysis in formal argumentation and systems biology. The BDD approach offers a promising alternative to SAT/ASP for exhaustive enumeration in large solution spaces, and the ability to handle previously intractable biological models could open new case studies. The paper correctly credits the foundational BN-ADF equivalence and positions the tool as an extension rather than a reinvention.

major comments (2)

[§4 (Experimental Evaluation)] §4 (Experimental Evaluation): The central performance claim—that BAss enumerates all fixed points/minimal trap spaces on certain biological networks beyond prior tools—rests on the assumption that the BDD encoding (via the BN equivalence) produces diagrams whose size remains tractable. However, the manuscript provides no analysis of dependency-graph properties (treewidth, cyclicity, number of SCCs) or variable-ordering heuristic behavior that would predict when compactness holds. This leaves open whether the observed speed-ups are intrinsic to the symbolic method or an artifact of the particular benchmark distribution.
[§3 (The BAss Approach) and §4] §3 (The BAss Approach) and §4: The abstract and experimental claims assert correct implementation of the ADF semantics via the BN equivalence, yet the paper supplies no verification details (e.g., cross-checks against known small ADF instances, data-exclusion rules, or timeout handling). Without these, it is impossible to confirm that the reported equivalence is faithfully realized in the BDD encoding.

minor comments (3)

[Abstract] The abstract refers to a 'large-scale collection' of real-world models but provides no quantitative summary (number of instances, variable counts, or solution-space sizes). Adding a table or paragraph with these statistics would improve clarity.
[§4 (Experimental Evaluation)] Ensure that all baseline tools (bioLQM, AEON, adf-bdd, and the SAT/ASP solvers) are cited with precise version numbers and that the experimental setup (hardware, timeout limits, memory bounds) is stated explicitly in §4.
[§2 (Preliminaries)] Notation for interpretations and models is introduced without a dedicated preliminary section; a short table summarizing the supported semantics (admissible, complete, preferred, stable, etc.) would aid readers unfamiliar with ADFs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We appreciate the recognition of BAss's potential significance in bridging symbolic methods with argumentation and systems biology. We address each major comment point by point below, describing the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: §4 (Experimental Evaluation): The central performance claim—that BAss enumerates all fixed points/minimal trap spaces on certain biological networks beyond prior tools—rests on the assumption that the BDD encoding (via the BN equivalence) produces diagrams whose size remains tractable. However, the manuscript provides no analysis of dependency-graph properties (treewidth, cyclicity, number of SCCs) or variable-ordering heuristic behavior that would predict when compactness holds. This leaves open whether the observed speed-ups are intrinsic to the symbolic method or an artifact of the particular benchmark distribution.

Authors: We agree that additional structural analysis of the benchmarks would help readers assess the generality of the performance results. In the revised manuscript, we will add a dedicated paragraph in §4 that reports, for each benchmark family: the number of SCCs, approximate treewidth (computed via standard heuristics such as min-fill), and a cyclicity measure (e.g., feedback arc set size relative to nodes). We will also describe the variable-ordering heuristic (the topological order induced by the BN/ADF dependency graph, with ties broken by variable appearance frequency) and show that BDD sizes remain modest precisely when the networks exhibit the sparse, modular structure typical of biological models. These additions will demonstrate that the observed speed-ups are tied to the symbolic method's exploitation of real-world structure rather than an artifact of the chosen distribution. revision: yes
Referee: §3 (The BAss Approach) and §4: The abstract and experimental claims assert correct implementation of the ADF semantics via the BN equivalence, yet the paper supplies no verification details (e.g., cross-checks against known small ADF instances, data-exclusion rules, or timeout handling). Without these, it is impossible to confirm that the reported equivalence is faithfully realized in the BDD encoding.

Authors: We acknowledge that the current manuscript omits explicit verification procedures. In the revised version we will insert a new subsection 'Implementation Verification' in §3. It will report: (i) systematic cross-checks on all ADF instances with ≤20 variables from the literature, comparing BAss outputs against adf-bdd and a SAT-based reference solver (exact match on admissible, complete, preferred, and stable semantics); (ii) the timeout policy (3600 s wall-clock limit per instance; timeouts are recorded separately and excluded from 'solved' counts); and (iii) data-exclusion rules (none applied beyond parse failures, of which there were zero in the collected benchmark set). These details will confirm that the BN–ADF equivalence is correctly realized in the BDD encoding. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation relies on external equivalence and independent benchmarks

full rationale

The paper presents BAss as a BDD-based symbolic solver for ADFs that extends prior tools (bioLQM, AEON, adf-bdd) by leveraging the BN-ADF equivalence cited from Heyninck et al. (2024) and Azpeitia et al. (2024). These citations are external to the present authors and are not self-citations. All performance claims rest on experiments over a collection of real-world models rather than any fitted parameters, self-definitional reductions, or predictions that collapse to inputs by construction. No uniqueness theorems, ansatzes, or renamings are smuggled in via self-citation chains. The central method (symbolic computation of interpretations and models) is therefore self-contained against external benchmarks and does not reduce to its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the correctness of the BDD implementation for ADF semantics and the validity of the BN-ADFs equivalence from prior work. No new free parameters or invented entities are introduced.

axioms (2)

domain assumption The equivalence between Boolean Networks and Abstract Dialectical Frameworks as established by Heyninck et al. (2024) and Azpeitia et al. (2024)
The approach is inspired by and extends this equivalence for symbolic computation.
standard math BDDs can efficiently represent and manipulate the boolean functions corresponding to ADF interpretations and models
Core assumption underlying the symbolic solver design.

pith-pipeline@v0.9.0 · 5515 in / 1397 out tokens · 64707 ms · 2026-05-07T08:09:12.546243+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

57 extracted references · 4 canonical work pages · 1 internal anchor

[1]

Trevor J. M. Bench-Capon and Paul E. Dunne. Argumentation in artificial intelligence.Artif. Intell., 171(10- 15):619–641, 2007

2007
[2]

Towards artificial argumentation.AI Mag., 38(3):25–36, 2017

Katie Atkinson, Pietro Baroni, Massimiliano Giacomin, Anthony Hunter, Henry Prakken, Chris Reed, Guillermo Ricardo Simari, Matthias Thimm, and Serena Villata. Towards artificial argumentation.AI Mag., 38(3):25–36, 2017

2017
[3]

On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games.Artif

Phan Minh Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games.Artif. Intell., 77(2):321–358, 1995

1995
[4]

Methods for solving reasoning problems in abstract argumentation - A survey.Artif

Günther Charwat, Wolfgang Dvorák, Sarah Alice Gaggl, Johannes Peter Wallner, and Stefan Woltran. Methods for solving reasoning problems in abstract argumentation - A survey.Artif. Intell., 220:28–63, 2015

2015
[5]

The first international competition on computational models of argumentation: Results and analysis.Artif

Matthias Thimm and Serena Villata. The first international competition on computational models of argumentation: Results and analysis.Artif. Intell., 252:267–294, 2017

2017
[6]

µ-toksia: An efficient abstract argumentation reasoner

Andreas Niskanen and Matti Järvisalo. µ-toksia: An efficient abstract argumentation reasoner. InKR, pages 800–804, 2020

2020
[7]

Approximating operators and semantics for abstract dialectical frameworks.Artif

Hannes Strass. Approximating operators and semantics for abstract dialectical frameworks.Artif. Intell., 205:39– 70, 2013

2013
[8]

Abstract dialectical frameworks

Gerhard Brewka and Stefan Woltran. Abstract dialectical frameworks. InKR, pages 102–111. AAAI Press, 2010

2010
[9]

Abstract dialectical frameworks revisited

Gerhard Brewka, Hannes Strass, Stefan Ellmauthaler, Johannes Peter Wallner, and Stefan Woltran. Abstract dialectical frameworks revisited. InIJCAI, pages 803–809. IJCAI/AAAI, 2013

2013
[10]

The stable model semantics for logic programming

Michael Gelfond and Vladimir Lifschitz. The stable model semantics for logic programming. InICLP, pages 1070–1080. MIT Press, 1988

1988
[11]

Abstract dialectical frameworks

Gerhard Brewka, Stefan Ellmauthaler, Hannes Strass, Johannes Peter Wallner, and Stefan Woltran. Abstract dialectical frameworks. an overview.FLAP, 4(8), 2017

2017
[12]

Latifa Al-Abdulkarim, Katie Atkinson, and Trevor J. M. Bench-Capon. A methodology for designing systems to reason with legal cases using abstract dialectical frameworks.Artif. Intell. Law, 24(1):1–49, 2016

2016
[13]

Generating defeasible knowledge bases from real-world argumentations using D-BAS

Daniel Neugebauer. Generating defeasible knowledge bases from real-world argumentations using D-BAS. In AI3@AI*IA, pages 105–110. CEUR-WS.org, 2017

2017
[14]

Abstract dialectical frameworks for text exploration

Elena Cabrio and Serena Villata. Abstract dialectical frameworks for text exploration. InICAART, pages 85–95. SciTePress, 2016. 12 APREPRINT- MAY5, 2026

2016
[15]

Implementing instantiation of knowledge bases in argumentation frameworks

Hannes Strass. Implementing instantiation of knowledge bases in argumentation frameworks. InCOMMA, pages 475–476. IOS Press, 2014

2014
[16]

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory.Artif

Hannes Strass and Johannes Peter Wallner. Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory.Artif. Intell., 226:34–74, 2015

2015
[17]

Advanced algorithms for abstract dialectical frameworks based on complexity analysis of subclasses and SAT solving.Artif

Thomas Linsbichler, Marco Maratea, Andreas Niskanen, Johannes Peter Wallner, and Stefan Woltran. Advanced algorithms for abstract dialectical frameworks based on complexity analysis of subclasses and SAT solving.Artif. Intell., 307:103697, 2022

2022
[18]

Representing abstract dialectical frameworks with binary decision diagrams

Stefan Ellmauthaler, Sarah Alice Gaggl, Dominik Rusovac, and Johannes Peter Wallner. Representing abstract dialectical frameworks with binary decision diagrams. InLPNMR, pages 177–189. Springer, 2022

2022
[19]

Abstract dialectical frameworks are Boolean networks

Jesse Heyninck, Matthias Knorr, and João Leite. Abstract dialectical frameworks are Boolean networks. In LPNMR, pages 98–111. Springer, 2024

2024
[20]

Rosenblueth, and Octavio Zapata

Eugenio Azpeitia, Stan Muñoz Gutiérrez, David A. Rosenblueth, and Octavio Zapata. Bridging abstract dialectical argumentation and Boolean gene regulation.CoRR, abs/2407.06106, 2024

work page arXiv 2024
[21]

Boolean formalisation of genetic control circuits.J

René Thomas. Boolean formalisation of genetic control circuits.J. Theor. Biol., 42:565–583, 1973

1973
[22]

Boolean networks as predictive models of emergent biological behaviors

Jordan C Rozum, Colin Campbell, Eli Newby, Fatemeh Sadat Fatemi Nasrollahi, and Réka Albert. Boolean networks as predictive models of emergent biological behaviors. 2023. https://doi.org/10.48550/arXiv.2310.12901

work page doi:10.48550/arxiv.2310.12901 2023
[23]

Boolean modeling in systems biology: an overview of methodology and applications.Phys

Rui-Sheng Wang, Assieh Saadatpour, and Reka Albert. Boolean modeling in systems biology: an overview of methodology and applications.Phys. Biol., 9(5):055001, 2012

2012
[24]

Computing maximal and minimal trap spaces of Boolean networks.Nat

Hannes Klarner, Alexander Bockmayr, and Heike Siebert. Computing maximal and minimal trap spaces of Boolean networks.Nat. Comput., 14(4):535–544, 2015

2015
[25]

Scalable enumeration of trap spaces in Boolean networks via answer set programming

Van-Giang Trinh, Belaid Benhamou, Samuel Pastva, and Sylvain Soliman. Scalable enumeration of trap spaces in Boolean networks via answer set programming. InAAAI, pages 10714–10722. AAAI Press, 2024

2024
[26]

Mapping the attractor landscape of Boolean networks with biobalm.Bioinform., 41(5):btaf280, 2025

Van-Giang Trinh, Kyu Hyong Park, Samuel Pastva, and Jordan C Rozum. Mapping the attractor landscape of Boolean networks with biobalm.Bioinform., 41(5):btaf280, 2025

2025
[27]

ADF-BDD.DEV: insights to undecided statements in abstract dialectical frameworks

Stefan Ellmauthaler and Lukas Gerlach. ADF-BDD.DEV: insights to undecided statements in abstract dialectical frameworks. InAIˆ3. CEUR-WS.org, 2023

2023
[28]

ADF-BDD.DEV: Debug abstract dialectical frameworks with binary decision diagrams

Stefan Ellmauthaler and Lukas Gerlach. ADF-BDD.DEV: Debug abstract dialectical frameworks with binary decision diagrams. InXLoKR 2023, September 2023

2023
[29]

Efficient enumeration of fixed points in complex Boolean networks using answer set programming

Van-Giang Trinh, Belaid Benhamou, and Sylvain Soliman. Efficient enumeration of fixed points in complex Boolean networks using answer set programming. InCP, pages 35:1–35:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023

2023
[30]

BioLQM: a Java toolkit for the manipulation and conversion of logical qualitative models of biological networks.Front

Aurélien Naldi. BioLQM: a Java toolkit for the manipulation and conversion of logical qualitative models of biological networks.Front. Physiol., 9:1605, 2018

2018
[31]

AEON: attractor bifurcation analysis of parametrised Boolean networks

Nikola Benes, Lubos Brim, Jakub Kadlecaj, Samuel Pastva, and David Safránek. AEON: attractor bifurcation analysis of parametrised Boolean networks. InCAV, pages 569–581. Springer, 2020

2020
[32]

Instantiating rule-based defeasible theories in abstract dialectical frameworks and beyond.J

Hannes Strass. Instantiating rule-based defeasible theories in abstract dialectical frameworks and beyond.J. Log. Comput., 28(3):605–627, 2018

2018
[33]

GoDIAMOND 0.6

Hannes Strass and Stefan Ellmauthaler. GoDIAMOND 0.6. 6–ICCMA 2017 system description, 2017.Second International Competition on Computational Models of Argumentation: http://www. dbai. tuwien. ac. at/iccma17, 2017

2017
[34]

Solving advanced argumentation problems with answer set programming.Theory Pract

Gerhard Brewka, Martin Diller, Georg Heissenberger, Thomas Linsbichler, and Stefan Woltran. Solving advanced argumentation problems with answer set programming.Theory Pract. Log. Program., 20(3):391–431, 2020

2020
[35]

PyBoolNet: a python package for the generation, analysis and visualization of Boolean networks.Bioinform., 33(5):770–772, 2017

Hannes Klarner, Adam Streck, and Heike Siebert. PyBoolNet: a python package for the generation, analysis and visualization of Boolean networks.Bioinform., 33(5):770–772, 2017

2017
[36]

Chandra and George Markowsky

Ashok K. Chandra and George Markowsky. On the number of prime implicants.Discret. Math., 24(1):7–11, 1978

1978
[37]

Trap spaces of Boolean networks are conflict-free siphons of their Petri net encoding.Theor

Van-Giang Trinh, Belaid Benhamou, and Sylvain Soliman. Trap spaces of Boolean networks are conflict-free siphons of their Petri net encoding.Theor. Comput. Sci., 971:114073, September 2023

2023
[38]

AEON.py: Python library for attractor analysis in asynchronous Boolean networks.Bioinform., 38(21):4978–4980, 2022

Nikola Benes, Lubos Brim, Ondrej Huvar, Samuel Pastva, David Safránek, and Eva Smijáková. AEON.py: Python library for attractor analysis in asynchronous Boolean networks.Bioinform., 38(21):4978–4980, 2022. 13 APREPRINT- MAY5, 2026

2022
[39]

A SAT-based method for counting all singleton attractors in Boolean networks

Rei Higuchi, Takehide Soh, Daniel Le Berre, Morgan Magnin, Mutsunori Banbara, and Naoyuki Tamura. A SAT-based method for counting all singleton attractors in Boolean networks. InIJCAI, pages 2601–2609. ijcai.org, 2025

2025
[40]

Reconciling qualitative, abstract, and scalable modeling of biological networks.Nat

Loïc Paulevé, Juraj Kolˇcák, Thomas Chatain, and Stefan Haar. Reconciling qualitative, abstract, and scalable modeling of biological networks.Nat. Commun., 11(1):1–7, August 2020

2020
[41]

mpbn: a simple tool for efficient edition and analysis of elementary properties of Boolean networks.CoRR, abs/2403.06255, 2024

Van-Giang Trinh, Belaid Benhamou, and Loïc Paulevé. mpbn: a simple tool for efficient edition and analysis of elementary properties of Boolean networks.CoRR, abs/2403.06255, 2024

work page arXiv 2024
[42]

BAss: Symbolic Reasoning in Abstract Dialectical Frameworks

Samuel Pastva and Van-Giang Trinh. BAss: Symbolic reasoning in abstract dialectical frameworks. 2026. https://arxiv.org/abs/2604.27576

work page internal anchor Pith review Pith/arXiv arXiv 2026
[43]

Randal E. Bryant. Graph-based algorithms for Boolean function manipulation.IEEE Trans. Computers, 35(8):677– 691, 1986

1986
[44]

Springer, 2018

Edmund M Clarke, Thomas A Henzinger, Helmut Veith, Roderick Bloem, et al.Handbook of model checking, volume 10. Springer, 2018

2018
[45]

Henzinger

Samuel Pastva and Thomas A. Henzinger. Binary decision diagrams on modern hardware. InFMCAD, pages 122–131. IEEE, 2023

2023
[46]

Repository of logically consistent real-world Boolean network models.bioRxiv, 2023

Samuel Pastva, David Šafránek, Nikola Beneš, Luboš Brim, and Thomas Henzinger. Repository of logically consistent real-world Boolean network models.bioRxiv, 2023

2023
[47]

Temporal protein expression pattern in intracellular signalling cascade during T-cell activation: A computational study.J

Piyali Ganguli, Saikat Chowdhury, Rupa Bhowmick, and Ram Rup Sarkar. Temporal protein expression pattern in intracellular signalling cascade during T-cell activation: A computational study.J. Biosci., 40:769–789, 2015

2015
[48]

COVID-19 disease map, building a computational repository of SARS-CoV-2 virus-host interaction mechanisms.Sci

Marek Ostaszewski, Alexander Mazein, Marc E Gillespie, Inna Kuperstein, Anna Niarakis, Henning Hermjakob, Alexander R Pico, Egon L Willighagen, Chris T Evelo, Jan Hasenauer, et al. COVID-19 disease map, building a computational repository of SARS-CoV-2 virus-host interaction mechanisms.Sci. Data, 7(1):1–4, 2020

2020
[49]

A network model to explore the effect of the micro-environment on endothelial cell behavior during angiogenesis.Front

Nathan Weinstein, Luis Mendoza, Isidoro Gitler, and Jaime Klapp. A network model to explore the effect of the micro-environment on endothelial cell behavior during angiogenesis.Front. Physiol., 8, November 2017

2017
[50]

Model-based characterization of inflammatory gene expression patterns of activated macrophages.PLoS Comput

Julia Rex, Ute Albrecht, Christian Ehlting, Maria Thomas, Ulrich M Zanger, Oliver Sawodny, Dieter Häussinger, Michael Ederer, Ronny Feuer, and Johannes G Bode. Model-based characterization of inflammatory gene expression patterns of activated macrophages.PLoS Comput. Biol., 12(7):e1005018, 2016

2016
[51]

Basins of attraction, commitment sets, and phenotypes of Boolean networks.IEEE ACM Trans

Hannes Klarner, Frederike Heinitz, Sarah Nee, and Heike Siebert. Basins of attraction, commitment sets, and phenotypes of Boolean networks.IEEE ACM Trans. Comput. Biol. Bioinform., 17(4):1115–1124, 2020

2020
[52]

Phenotype control and elimination of variables in Boolean networks.Peer Community Journal, 4, August 2024

Elisa Tonello and Loïc Paulevé. Phenotype control and elimination of variables in Boolean networks.Peer Community Journal, 4, August 2024

2024
[53]

Control strategy identification via trap spaces in Boolean networks

Laura Cifuentes Fontanals, Elisa Tonello, and Heike Siebert. Control strategy identification via trap spaces in Boolean networks. InCMSB, pages 159–175. Springer, 2020

2020
[54]

Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks

Jordan C Rozum, Jorge Gómez Tejeda Zañudo, Xiao Gan, Dávid Deritei, and Réka Albert. Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks. Sci. Adv., 7(29):eabf8124, 2021

2021
[55]

Reduction of Boolean network models.J

Alan Veliz-Cuba. Reduction of Boolean network models.J. Theor. Biol., 289:167–172, November 2011

2011
[56]

On the decomposition of abstract dialectical frameworks and the complexity of naive-based semantics.J

Sarah Alice Gaggl, Sebastian Rudolph, and Hannes Straß. On the decomposition of abstract dialectical frameworks and the complexity of naive-based semantics.J. Artif. Intell. Res., 70:1–64, 2021

2021
[57]

concurrently

Atefeh Keshavarzi Zafarghandi, Rineke Verbrugge, and Bart Verheij. Semi-stable semantics for abstract dialectical frameworks. InKR, pages 422–431, 2021. A Detailed proofs Proposition 5.The above BDD-based characterizations of ad(D) and co(D) are correct, in the sense that the models off ad(D) (resp.f co(D)) correspond exactly to the admissible (resp. comp...

2021