Related papers: Sleptsov Nets are Turing-complete
Spiking neural networks (SNN) are a biologically inspired model of neural networks with certain brain-like properties. In the past few decades, this model has received increasing attention in computer science community, owing also to the…
We give strengthened provable guarantees on the performance of widely employed and empirically successful {\sl top-down decision tree learning heuristics}. While prior works have focused on the realizable setting, we consider the more…
Spiking neural networks (SNNs) communicate via discrete spikes in time rather than continuous activations. Their event-driven nature offers advantages for temporal processing and energy efficiency on resource-constrained hardware, but…
It is shown that the toy Turing Tumble, suitably extended with an infinitely long game board and unlimited supply of pieces, is Turing-Complete. This is achieved via direct simulation of a Turing machine. Unlike previously informally…
A Petri net is structurally cyclic if every configuration is reachable from itself in one or more steps. We show that structural cyclicity is decidable in deterministic polynomial time. For this, we adapt the Kosaraju's approach for the…
Synthesis consists in deciding whether a given labeled transition system (TS) $A$ can be implemented by a net $N$ of type $\tau$. In case of a negative decision, it may be possible to convert $A$ into an implementable TS $B$ by applying…
Recent advancements in legged robots using deep reinforcement learning have led to significant progress. Quadruped robots can perform complex tasks in challenging environments, while bipedal and humanoid robots have also achieved…
Spiking neural network (SNN) is interesting both theoretically and practically because of its strong bio-inspiration nature and potentially outstanding energy efficiency. Unfortunately, its development has fallen far behind the conventional…
The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input…
Spiking neural networks (SNNs) with adaptive synapses reflect core properties of biological neural networks. Speech recognition, as an application involving audio coding and dynamic learning, provides a good test problem to study SNN…
The spiking neural network, known as the third generation neural network, is an important network paradigm. Due to its mode of information propagation that follows biological rationality, the spiking neural network has strong energy…
We study the capacity of \emph{sign} perceptrons neural networks (SPNN) and particularly focus on 1-hidden layer \emph{treelike committee machine} (TCM) architectures. Similarly to what happens in the case of a single perceptron neuron, it…
In this paper we study Hornets extended with firing probabilities. Hornets are a Nets-within-Nets formalism, i.e., a Petri net formalism where the tokens are Petri nets again. Each of these net-tokens has its own firing rate, independent…
For a fixed type of Petri nets $\tau$, \textsc{$\tau$-Synthesis} is the task of finding for a given transition system $A$ a Petri net $N$ of type $\tau$ ($\tau$-net, for short) whose reachability graph is isomorphic to $A$ if there is one.…
The energy-efficient and brain-like information processing abilities of Spiking Neural Networks (SNNs) have attracted considerable attention, establishing them as a crucial element of brain-inspired computing. One prevalent challenge…
We present a novel neural network algorithm, the Tensor Switching (TS) network, which generalizes the Rectified Linear Unit (ReLU) nonlinearity to tensor-valued hidden units. The TS network copies its entire input vector to different…
Spiking-neural-networks (SNNs) are promising at edge devices since the event-driven operations of SNNs provides significantly lower power compared to analog-neural-networks (ANNs). Although it is difficult to efficiently train SNNs, many…
Spiking neural networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…
In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…