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Spiking neural networks (SNNs) have received significant attention for their biological plausibility. SNNs theoretically have at least the same computational power as traditional artificial neural networks (ANNs). They possess potential of…

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of…

Strongly Turing determinacy, or $\mathrm{sTD}$, says that for any set $A$ of reals, if $\forall x\exists y\geq_T x (y\in A)$, then there is a pointed set $P\subseteq A$. We prove the following consequences of Turing determinacy…

We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy on places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also…

Neuromorphic computing has recently gained momentum with the emergence of various neuromorphic processors. As the field advances, there is an increasing focus on developing training methods that can effectively leverage the unique…

Due to the policy-rich BGP, multiple stable forwarding states might exist for the same network topology and configuration, rendering the network convergence non-deterministic. This paper proves that any network with multiple converged…

Neuromorphic computing and, in particular, spiking neural networks (SNNs) have become an attractive alternative to deep neural networks for a broad range of signal processing applications, processing static and/or temporal inputs from…

Spiking Neural Networks (SNNs) represent the latest generation of neural computation, offering a brain-inspired alternative to conventional Artificial Neural Networks (ANNs). Unlike ANNs, which depend on continuous-valued signals, SNNs…

We study reductions that limit the extreme adaptivity of Turing reductions. In particular, we study reductions that make a rapid, structured progression through the set to which they are reducing: Each query is strictly longer (shorter)…

We prove that $\omega$-languages of (non-deterministic) Petri nets and $\omega$-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of $\omega$-languages of…

Neuromorphic hardware as a non-Von Neumann architecture has better energy efficiency and parallelism than the conventional computer. Here, with numerical modeling spin-orbit torque (SOT) device using current-induced SOT and Joule heating…

Van der Aalst's theorem is an important result for the analysis and synthesis of process models. The paper proves the theorem by exhausting perpetual free-choice Petri nets by CP-subnets. The resulting T-systems are investigated by…

The well-quasi-ordering (i.e., a well-founded quasi-ordering such that all antichains are finite) that defines well-structured transition systems (WSTS) is shown not to be the weakest hypothesis that implies decidability of the coverability…

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a…

Spiking Neural Networks (SNNs) claim to present many advantages in terms of biological plausibility and energy efficiency compared to standard Deep Neural Networks (DNNs). Recent works have shown that DNNs are vulnerable to adversarial…

Spiking Neural Networks (SNNs) are increasingly studied as energy-efficient alternatives to Convolutional Neural Networks (CNNs), particularly for edge intelligence. However, prior work has largely emphasized large-scale models, leaving the…

Larger Spiking Neural Network (SNN) models are typically favorable as they can offer higher accuracy. However, employing such models on the resource- and energy-constrained embedded platforms is inefficient. Towards this, we present a…

The spiking neural networks (SNNs) are considered as one of the most promising artificial neural networks due to their energy efficient computing capability. Recently, conversion of a trained deep neural network to an SNN has improved the…

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…

Spiking Neural Networks (SNNs) are highly energy-efficient due to event-driven, sparse computation, but their training is challenged by spike non-differentiability and trade-offs among performance, efficiency, and biological plausibility.…