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Finding Attractors in Synchronous Multiple-Valued Networks Using SAT-based Bounded Model Checking
KTH, School of Information and Communication Technology (ICT), Electronic Systems.ORCID iD: 0000-0001-7382-9408
KTH, School of Information and Communication Technology (ICT), Electronic Systems.
KTH, School of Information and Communication Technology (ICT), Electronic Systems.
2012 (English)In: Journal of Multiple-Valued Logic and Soft Computing, ISSN 1542-3980, E-ISSN 1542-3999, Vol. 19, no 1-3, 109-131 p.Article in journal (Refereed) Published
##### Abstract [en]

Synchronous multiple-valued networks are a discrete-space discrete-time model of the gene regulatory network of living cells. In this model, cell types are represented by the cycles in the state transition graph of a network, called attractors. When the effect of a disease or a mutation on a cell is studied, attractors have to be re-computed each time a fault is injected in the model. This motivates research on algorithms for finding attractors. Existing decision diagram-based approaches have limited capacity due to the excessive memory requirements of decision diagrams. Simulation-based approaches can be applied to larger networks, however, they are incomplete. We present an algorithm for finding attractors which uses a SAT-based bounded model checking. Our model checking approach exploits the deterministic nature of the network model to reduce runtime. Although the idea of applying model checking to the analysis of gene regulatory networks is not new, to our best knowledge, we are the first to use it for computing all attractors in a model. The efficiency of the presented algorithm is evaluated by analyzing 7 networks models of real biological processes as well as 35.000 randomly generated 4-valued networks. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible.

##### Place, publisher, year, edition, pages
Old City Publishing, 2012. Vol. 19, no 1-3, 109-131 p.
##### Keyword [en]
Multiple-Valued Network, SAT, Model Checking, attractor
Natural Sciences
SRA - ICT
##### Identifiers
ISI: 000305440000009ScopusID: 2-s2.0-84864069529OAI: oai:DiVA.org:kth-107495DiVA: diva2:576302
##### Note

QC 20130109

Available from: 2013-01-10 Created: 2012-12-12 Last updated: 2015-11-20Bibliographically approved
##### In thesis
1. Analysis and Synthesis of Boolean Networks
Open this publication in new window or tab >>Analysis and Synthesis of Boolean Networks
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

In this thesis, we present techniques and algorithms for analysis and synthesis of synchronous Boolean and multiple-valued networks.

Synchronous Boolean and multiple-valued networks are a discrete-space discrete-time model of gene regulatory networks. Their cycle of states, called \emph{attractors}, are believed to give a good indication of the possible functional modes of the system. This motivates research on algorithms for finding attractors. Existing decision diagram-based approaches have limited capacity due to the excessive memory requirements of decision diagrams. Simulation-based approaches can be applied to large networks, however, their results are incomplete. In the first part of this thesis, we present an algorithm, which uses a SAT-based bounded model checking approach to find all attractors in a multiple-valued network. The efficiency of the presented algorithm is evaluated by analysing 30 network models of real biological processes as well as \num{35000} randomly generated 4-valued networks. The results show that our algorithm has a potential to handle an order of magnitude larger models than currently possible. One of the characteristic features of genetic regulatory networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random faults. In the second part of this thesis, we focus on the robustness of a special kind of Boolean networks called \emph{Balanced Boolean Networks} (BBNs). We formalize the notion of robustness and introduce a method to construct \emph{BBNs} for $2$-singleton attractors Boolean networks. The experiment results show that \emph{BBNs} are capable of tolerating single stuck-at faults. Our method improves the robustness of random Boolean networks by at least $13\%$ on average, and in some special case, up to $61\%$.

In the third part of this thesis, we focus on a special type of synchronous Boolean networks, namely Feedback Shift Registers (FSRs). FSR-based filter generators are used as a basic building block in many cryptographic systems, e.g. stream ciphers. Filter generators are popular because their well-defined mathematical description enables a detailed formal security analysis. We show how to modify a filter generator into a nonlinear FSR, which is faster, but slightly larger, than the original filter generator. For example, the propagation delay can be reduced 1.54 times at the expense of 1.27\% extra area. The presented method might be important for applications, which require very high data rates, e.g. 5G mobile communication technology.

In the fourth part of this thesis, we present a new method for detecting and correcting transient faults in FSRs based on duplication and parity checking. Periodic fault detection of functional circuits is very important for cryptographic systems because a random hardware fault can compromise their security.

The presented method is more reliable than Triple Modular Redundancy (TMR) for large FSRs, while the area overhead of the two approaches are comparable. The presented approach might be important for cryptographic systems using large FSRs.

##### Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xi, 57 p.
##### Series
, TRITA-ICT, 2015:23
Computer Systems
##### Identifiers
urn:nbn:se:kth:diva-177138 (URN)978-91-7595-770-8 (ISBN)
##### Presentation
2015-12-18, Sla B, Electrum, KTH-ICT, Kista, 09:00 (English)
##### Note

QC 20151120

Available from: 2015-11-20 Created: 2015-11-16 Last updated: 2015-11-20Bibliographically approved

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