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. AVAILABILITY AND IMPLEMENTATION: All software and data are freely available as a reproducible artefact at https://doi.org/10.5281/zenodo.7688740.

SUMMARY: AEON.py is a Python library for the analysis of the long-term behaviour in very large asynchronous Boolean networks. It provides significant computational improvements over the state-of-the-art methods for attractor detection. Furthermore, it admits the analysis of partially specified Boolean networks with uncertain update functions. It also includes techniques for identifying viable source-target control strategies and the assessment of their robustness with respect to parameter perturbations. AVAILABILITY AND IMPLEMENTATION: All relevant results are available in Supplementary Materials. The tool is accessible through https://github.com/sybila/biodivine-aeon-py. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Boolean networks (BNs) provide an effective modelling formalism for various complex biochemical phenomena. Their long term behaviour is represented by attractors-subsets of the state space towards which the BN eventually converges. These are then typically linked to different biological phenotypes. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a methodology for analysing bifurcations in asynchronous parametrised Boolean networks. RESULTS: In this paper, we propose a computational framework employing advanced symbolic graph algorithms that enable the analysis of large networks with hundreds of Boolean variables. To visualise the results of this analysis, we developed a novel interactive presentation technique based on decision trees, allowing us to quickly uncover parameters crucial to the changes in the attractor landscape. As a whole, the methodology is implemented in our tool AEON. We evaluate the method's applicability on a complex human cell signalling network describing the activity of type-1 interferons and related molecules interacting with SARS-COV-2 virion. In particular, the analysis focuses on explaining the potential suppressive role of the recently proposed drug molecule GRL0617 on replication of the virus. CONCLUSIONS: The proposed method creates a working analogy to the concept of bifurcation analysis widely used in kinetic modelling to reveal the impact of parameters on the system's stability. The important feature of our tool is its unique capability to work fast with large-scale networks with a relatively large extent of unknown information. The results obtained in the case study are in agreement with the recent biological findings.

Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours. The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach. However, the large number of colours also renders existing symbolic SCC detection algorithms impractical. This paper proposes a novel algorithm that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot log~n)$ symbolic steps, where $p$ is the number of colours and $n$ is the number of vertices. We evaluate the algorithm using an experimental implementation based on binary decision diagrams (BDDs). Specifically, we use our implementation to explore the SCCs of a large collection of coloured graphs (up to $2^{48}$) obtained from Boolean networks -- a modelling framework commonly appearing in systems biology.

Abstract Detection of bottom strongly connected components (BSCC) in state-transition graphs is an important problem with many applications, such as detecting recurrent states in Markov chains or attractors in dynamical systems. However, these graphs’ size is often entirely out of reach for algorithms using explicit state-space exploration, necessitating alternative approaches such as the symbolic one. Symbolic methods for BSCC detection often show impressive performance, but can sometimes take a long time to converge in large graphs. In this paper, we provide a symbolic state-space reduction method for labelled transition systems, calledinterleaved transition guided reduction(ITGR), which aims to alleviate current problems of BSCC detection by efficiently identifying large portions of the non-BSCC states. We evaluate the suggested heuristic on an extensive collection of 125 real-world biologically motivated systems. We show that ITGR can easily handle all these models while being either the only method to finish, or providing at least an order-of-magnitude speedup over existing state-of-the-art methods. We then use a set of synthetic benchmarks to demonstrate that the technique also consistently scales to graphs with more than $$2^{1000}$$ 21000 vertices, which was not possible using previous methods.

Abstract Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale. We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $$O(p\cdot n\cdot \log n)$$ O ( p · n · log n ) symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to $$2^{48}$$ 2 48 ) coloured graphs produced by models appearing in systems biology.

Boolean networks (BNs) provide an effective modelling tool for various phenomena from science and engineering. Any long-term behaviour of a BN eventually converges to a so-called attractor. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a tool for analysing bifurcations in asynchronous parametrised Boolean networks. To fight the state-space and parameter-space explosion problem the tool uses a parallel semi-symbolic algorithm.

Formal analysis of non-linear continuous and hybrid systems is a hot topic. A common approach builds on computing a suitable finite discrete abstraction of the continuous system. In this paper, we propose a facetal abstraction which eliminates certain drawbacks of existing abstractions. The states of our abstraction are built primarily from facets of a polytopal partitioning of the system's state space taking thus into account the flow of the continuous dynamics and leading to global over-approximation. The transition system construction is based on queries solved by a δ-decision SMT-solver. The method is evaluated on several case studies.

Digital bifurcation analysis is a new algorithmic method for exploring how the behaviour of a parameter-dependent computer system varies with a change in its parameters and, in particular, for identification of bifurcation points where such variation becomes dramatic. We have developed the method in an analogy with the traditional bifurcation theory and have it successfully applied to models taken from systems biology. In this case study paper, we demonstrate the appropriateness and usefulness of the digital bifurcation analysis as a push-button alternative to the classical approaches as traditionally used for analysing the stability of TCP/IP protocols. We consider two typical examples (congestion control and buffer sizes throughput influence) and show that the method provides the same results as obtained with classical non-automatic analytical and numerical methods.

Version Control Systems (VCS) are frequently used to support development of large-scale software projects. A typical VCS repository of a large project can contain various intertwined branches consisting of a large number of commits. If some kind of unwanted behaviour (e.g. a bug in the code) is found in the project, it is desirable to find the commit that introduced it. Such commit is called a regression point. There are two main issues regarding the regression points. First, detecting whether the project after a certain commit is correct can be very expensive as it may include large-scale testing and/or some other forms of verification. It is thus desirable to minimise the number of such queries. Second, there can be several regression points preceding the actual commit; perhaps a bug was introduced in a certain commit, inadvertently fixed several commits later, and then reintroduced in a yet later commit. In order to fix the actual commit it is usually desirable to find the latest regression point. The currently used distributed VCS contain methods for regression identification, see e.g. the git bisect tool. In this paper, we present a new regression identification algorithm that outperforms the current tools by decreasing the number of validity queries. At the same time, our algorithm tends to find the latest regression points which is a feature that is missing in the state-of-the-art algorithms. The paper provides an experimental evaluation of the proposed algorithm and compares it to the state-of-the-art tool git bisect on a real data set.

In various areas of computer science, the problem of dealing with a set of constraints arises. If the set of constraints is unsatisfiable, one may ask for a minimal description of the reason for this unsatisifiability. Minimal unsatisfiable subsets (MUSes) and maximal satisfiable subsets (MSSes) are two kinds of such minimal descriptions. The goal of this work is the enumeration of MUSes and MSSes for a given constraint system. As such full enumeration may be intractable in general, we focus on building an online algorithm, which produces MUSes/MSSes in an on-the-fly manner as soon as they are discovered. The problem has been studied before even in its online version. However, our algorithm uses a novel approach that is able to outperform the current state-of-the art algorithms for online MUS/MSS enumeration. Moreover, the performance of our algorithm can be adjusted using tunable parameters. We evaluate the algorithm on a set of benchmarks.

Abstract In the last decade it became a common practice to formalise software requirements to improve the clarity of users’ expectations. In this work we build on the fact that functional requirements can be expressed in temporal logic and we propose new sanity checking techniques that automatically detect flaws and suggest improvements of given requirements. Specifically, we describe and experimentally evaluate approaches to consistency and redundancy checking that identify all inconsistencies and pinpoint their exact source (the smallest inconsistent set). We further report on the experience obtained from employing the consistency and redundancy checking in an industrial environment. To complete the sanity checking we also describe a semi-automatic completeness evaluation that can assess the coverage of user requirements and suggest missing properties the user might have wanted to formulate. The usefulness of our completeness evaluation is demonstrated in a case study of an aeroplane control system.