Heuristic search of (semi-)bent functions based on cellular automata

An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter

Exhaustive Generation of Linear Orthogonal Cellular Automata

We consider the problem of exhaustively visiting all pairs of linear cellular automata which give rise to orthogonal Latin squares, i.e., linear Orthogonal Cellular Automata (OCA). The problem is equivalent to enumerating all pairs of coprime polynomials over a finite field having the same degree and a nonzero constant term. While previous research showed how to count all such pairs for a given degree and order of the finite field, no practical enumeration algorithms have been proposed so far. Here, we start closing this gap by addressing the case of polynomials defined over the field \F_2, which corresponds to binary CA. In particular, we exploit Benjamin and Bennett's bijection between coprime and non-coprime pairs of polynomials, which enables us to organize our study along three subproblems, namely the enumeration and count of: (1) sequences of constant terms, (2) sequences of degrees, and (3) sequences of intermediate terms. In the course of this investigation, we unveil interesting connections with algebraic language theory and combinatorics, obtaining an enumeration algorithm and an alternative derivation of the counting formula for this problem.Comment: 9 pages, 1 figure. Submitted to the exploratory track of AUTOMATA 2023. arXiv admin note: text overlap with arXiv:2207.0040

On the impact of treewidth in the computational complexity of freezing dynamics

An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states such that the state evolution of any node is non-decreasing in any orbit. They are commonly used to model epidemic propagation, diffusion phenomena like bootstrap percolation or cristal growth. In this paper we establish how treewidth and maximum degree of the underlying graph are key parameters which influence the overall computational complexity of finite freezing automata networks. First, we define a general model checking formalism that captures many classical decision problems: prediction, nilpotency, predecessor, asynchronous reachability. Then, on one hand, we present an efficient parallel algorithm that solves the general model checking problem in NC for any graph with bounded degree and bounded treewidth. On the other hand, we show that these problems are hard in their respective classes when restricted to families of graph with polynomially growing treewidth. For prediction, predecessor and asynchronous reachability, we establish the hardness result with a fixed set-defiend update rule that is universally hard on any input graph of such families

Decomposition and factorisation of transients in Functional Graphs

Functional graphs (FGs) model the graph structures used to analyze the behavior of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be quite large, it is interesting to decompose and factorize them into several subgraphs acting together. Polynomial equations over functional graphs provide a formal way to represent this decomposition and factorization mechanism, and solving them validates or invalidates hypotheses on their decomposability. The current solution method breaks down a single equation into a series of \emph{basic} equations of the form $A\times X=B$ (with $A$, $X$, and $B$ being FGs) to identify the possible solutions. However, it is able to consider just FGs made of cycles only. This work proposes an algorithm for solving these basic equations for general connected FGs. By exploiting a connection with the cancellation problem, we prove that the upper bound to the number of solutions is closely related to the size of the cycle in the coefficient $A$ of the equation. The cancellation problem is also involved in the main algorithms provided by the paper. We introduce a polynomial-time semi-decision algorithm able to provide constraints that a potential solution will have to satisfy if it exists. Then, exploiting the ideas introduced in the first algorithm, we introduce a second exponential-time algorithm capable of finding all solutions by integrating several `hacks' that try to keep the exponential as tight as possible

Invisible Reconstruction: Cross-disciplinary responses to natural, biological and man-made disasters

What does it really mean to reconstruct a city after a natural, biological or man-made disaster? Is the repair and reinstatement of buildings and infrastructure sufficient without the mending of social fabric? The authors of this volume believe that the true measure of success should be societal. After all, a city without people is no city at all. Invisible Reconstruction takes the view that effective disaster mitigation and recovery require interdisciplinary tactics. Historian Lucia Patrizio Gunning and urbanist Paola Rizzi expand beyond the confines of individual disciplines or disaster studies to bring together academics and practitioners from a wide variety of disciplines, comparing strategies and outcomes in different scenarios and cultures from South America, Europe and Asia. From cultural heritage and public space to education and participation, contributors reflect on the interconnection of people, culture and environment and on constructive approaches to strengthening the intangible ties to increase resilience and reduce vulnerability. By bringing practical examples of how communities and individuals have reacted to or prepared for disaster, the publication proposes a shift in public policy to ensure that essential physical reinforcement and rebuilding are matched by attention to societal needs. Invisible Reconstruction is essential reading for policymakers, academics and practitioners working to reduce the impact of natural, biological and man-made disaster or to improve post-disaster recovery

Invisible Reconstruction

What does it really mean to reconstruct a city after a natural, biological or man-made disaster? Is the repair and reinstatement of buildings and infrastructure sufficient without the mending of social fabric? The authors of this volume believe that the true measure of success should be societal. After all, a city without people is no city at all. Invisible Reconstruction takes the view that effective disaster mitigation and recovery require interdisciplinary tactics. Historian Lucia Patrizio Gunning and urbanist Paola Rizzi expand beyond the confines of individual disciplines or disaster studies to bring together academics and practitioners from a wide variety of disciplines, comparing strategies and outcomes in different scenarios and cultures from South America, Europe and Asia. From cultural heritage and public space to education and participation, contributors reflect on the interconnection of people, culture and environment and on constructive approaches to strengthening the intangible ties to increase resilience and reduce vulnerability. By bringing practical examples of how communities and individuals have reacted to or prepared for disaster, the publication proposes a shift in public policy to ensure that essential physical reinforcement and rebuilding are matched by attention to societal needs. Invisible Reconstruction is essential reading for policymakers, academics and practitioners working to reduce the impact of natural, biological and man-made disaster or to improve post-disaster recovery

Invisible Reconstruction

What does it really mean to reconstruct a city after a natural, biological or man-made disaster? Is the repair and reinstatement of buildings and infrastructure sufficient without the mending of social fabric? The authors of this volume believe that the true measure of success should be societal. After all, a city without people is no city at all. Invisible Reconstruction takes the view that effective disaster mitigation and recovery require interdisciplinary tactics. Historian Lucia Patrizio Gunning and urbanist Paola Rizzi expand beyond the confines of individual disciplines or disaster studies to bring together academics and practitioners from a wide variety of disciplines, comparing strategies and outcomes in different scenarios and cultures from South America, Europe and Asia. From cultural heritage and public space to education and participation, contributors reflect on the interconnection of people, culture and environment and on constructive approaches to strengthening the intangible ties to increase resilience and reduce vulnerability. By bringing practical examples of how communities and individuals have reacted to or prepared for disaster, the publication proposes a shift in public policy to ensure that essential physical reinforcement and rebuilding are matched by attention to societal needs. Invisible Reconstruction is essential reading for policymakers, academics and practitioners working to reduce the impact of natural, biological and man-made disaster or to improve post-disaster recovery