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We study the palindrome complexity of infinite sequences on finite alphabets, i.e., the number of palindromic factors (blocks) of given length occurring in a given sequence. We survey the known results and obtain new results for some…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
The paper deals with the interpretability of Graph Neural Networks in the context of Boolean Satisfiability. The goal is to demystify the internal workings of these models and provide insightful perspectives into their decision-making…
Recent works examine the relationship between the communication structure and the performance of a group in a problem solving task. Some conclude that inefficient communication networks with long paths outperform efficient networks on the…
While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established…
The time taken for gene expression varies not least because proteins vary in length considerably. This paper uses an abstract, tuneable Boolean regulatory network model to explore gene expression time variation. In particular, it is shown…
We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be…
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean…
We present a framework for computing with input data specified by intervals, representing uncertainty in the values of the input parameters. To compute a solution, the algorithm can query the input parameters that yield more refined…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
As multi-agent networks grow in size and scale, they become increasingly difficult to synchronize, though agents must work together even when generating and sharing different information at different times. Targeting such cases, this paper…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
Estimating the influence that individual nodes have on one another in a Boolean network is essential to predict and control the system's dynamical behavior, for example, detecting key therapeutic targets to control pathways in models of…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
This paper focuses on proposing a general control framework for large-scale Boolean networks (\texttt{BNs}). Only by the network structure, the concept of structural controllability for \texttt{BNs} is formalized. A necessary and sufficient…
One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is…