Related papers: Towards Completely Characterizing the Complexity o…
We propose a Dynamical Boolean Network (DBN), which is a Virtual Boolean Network (VBN) whose set of states is fixed but whose transition matrix can change from one discrete time step to another. The transition matrix $T_{k}$ of our DBN for…
Boolean Skolem function synthesis concerns synthesizing outputs as Boolean functions of inputs such that a relational specification between inputs and outputs is satisfied. This problem, also known as Boolean functional synthesis, has…
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
In a previous paper we introduced immediate observation (IO) Petri nets, a class of interest in the study of population protocols and enzymatic chemical networks. In the first part of this paper we show that IO nets are globally flat, and…
Petri Net is a formalism to describe changes between 2 or more states across discrete time and has been used to model many systems. We present PNet - a pure Python library for Petri Net modeling and simulation in Python programming…
This paper proposes a new parameter for studying Boolean networks: the independence number. We establish that a Boolean network is $k$-independent if, for any set of $k$ variables and any combination of binary values assigned to them, there…
The list of knots with up to 10 crossings is commonly referred to as the Rolfsen Table. This paper presents a way to generate the Rolfsen table in a simple, clear, and reproducible manner. The methods we use are similar to those used by J.…
We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed…
In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Safe Rust guarantees memory safety through strict compile-time constraints: ownership can be transferred, borrowing can temporarily guarantee either shared read-only or exclusive write access, and ownership and borrowing are scoped by…
Using a graph-theoretic approach, we derive a new sufficient condition for observability of a Boolean control network (BCN). Based on this condition, we describe two algorithms: the first selects a set of nodes so that observing this set…
A universal deterministic inhibitor Petri net with 14 places, 29 transitions and 138 arcs was constructed via simulation of Neary and Woods' weakly universal Turing machine with 2 states and 4 symbols; the total time complexity is…
Boolean Satisfiability problems are vital components in Electronic Design Automation, particularly within the Logic Equivalence Checking process. Currently, SAT solvers are employed for these problems and neural network is tried as…
AND-OR networks are Boolean networks where each coordinate function is either the AND or OR logical operator. We study the number of fixed points of these Boolean networks in the case that they have a wiring diagram with chain topology. We…
Boolean networks are dynamical models of disease development in which the activation levels of genes are represented by binary variables. Given a Boolean network, controls represent mutations or medical treatments that fix the activation…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the…
A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an…
Petri nets provide accurate analogues to chemical reaction networks, with places representing individual molecules (the resources of the system) and transitions representing chemical reactions which convert educt molecules into product…