Advances in Boolean Functions and Dynamical Systems

The field of Boolean functions and dynamical systems is witnessing significant developments, with a focus on innovative representations, efficient counting methods, and approximate axiomatizations. Researchers are exploring new ways to study Boolean functions through binary sequences, leading to a deeper understanding of their properties and connections to other areas of mathematics. Meanwhile, the analysis of dynamical systems, such as Boolean networks, is being advanced through the development of scalable counting methods and approximate answer set counting techniques. These advancements have the potential to impact various domains, including systems biology, computational logic, and artificial intelligence. Noteworthy papers in this area include: A New Representation of Binary Sequences by means of Boolean Functions, which introduces a new bijection between Boolean functions and binary sequences, and Scalable Counting of Minimal Trap Spaces and Fixed Points in Boolean Networks, which proposes novel methods for efficiently counting minimal trap spaces and fixed points in Boolean networks.

Sources

A New Representation of Binary Sequences by means of Boolean Functions

Differential Spectrum and Boomerang Spectrum of Some Power Mapping

Towards an Analysis of Proofs in Arithmetic

Scalable Counting of Minimal Trap Spaces and Fixed Points in Boolean Networks

Approximate Axiomatization for Differentially-Defined Functions

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions

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