Related papers: Towards Completely Characterizing the Complexity o…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
A probabilistic Boolean network (PBN) is a discrete-time system composed of a collection of Boolean networks between which the PBN switches in a stochastic manner. This paper focuses on the study of quotients of PBNs. Given a PBN and an…
In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown…
Reactive computer systems bear inherent complexity due to continuous interactions with their environment. While this environment often proves to be uncontrollable, we still want to ensure that critical computer systems will not fail, no…
We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains $N$ Boolean elements each with $K$ inputs. A directed state space network (SSN) is constructed by linking each dynamical state,…
A Boolean network (BN) with $n$ components is a discrete dynamical system described by the successive iterations of a function $f:\{0,1\}^n\to\{0,1\}^n$. In most applications, the main parameter is the interaction graph of $f$: the digraph…
Given a Boolean specification between a set of inputs and outputs, the problem of Boolean functional synthesis is to synthesise each output as a function of inputs such that the specification is met. Although the past few years have…
In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function $f$ is…
Four terminal switching network is an alternative structure to realize the logic functions in electronic circuit modeling. This network can be used to implement a Boolean function with less number of switches than the two terminal based…
A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often…
Boolean circuits form the foundational computational substrate of symmetric cryptography, yet the exploration of their architectural design space has remained largely confined to a handful of canonical paradigms - SPN, Feistel networks, and…
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that…
The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this paper, we propose a unified approach to determine all the four types of observability of BCNs in the…
We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes…
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
A Petri net is choice-free if any place has at most one transition in its postset (consuming its tokens) and it is (extended) free-choice (EFC) if the postsets of any two places are either equal or disjoint. Asymmetric choice (AC) extends…
In the noisy query model, the (binary) return value of every query (possibly repeated) is independently flipped with some fixed probability $p \in (0, 1/2)$. In this paper, we obtain tight bounds on the noisy query complexity of several…
It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning.…
We present an exact synthesis approach for computing Exclusive-or Sum-of-Products (ESOP) forms with a minimum number of product terms using Boolean satisfiability. Our approach finds one or more ESOP forms for a given Boolean function. The…