Related papers: General Computation using Slidable Tiles with Dete…
There is a growing interest in custom spatial accelerators for machine learning applications. These accelerators employ a spatial array of processing elements (PEs) interacting via custom buffer hierarchies and networks-on-chip. The…
A novel MIMO homogeneous Super-Twisting Algorithm is proposed in this paper for nonlinear systems with relative degree one, having a time and state-varying uncertain control matrix. The uncertainty is represented by a constant but unknown…
Suppose $P$ is a symmetric convex polygon in the plane. We give a polynomial time algorithm that decides if $P$ can tile the plane by transations at some level (not necessarily at level one; this is multiple tiling). The main technical…
This work studies the problem of constructing capacity-achieving codes from an algorithmic perspective. Specifically, we prove that there exists a Turing machine which, given a discrete memoryless channel $p_{Y|X}$, a target rate $R$ less…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
Traditionally, computation within self-assembly models is hard to conceal because the self-assembly process generates a crystalline assembly whose computational history is inherently part of the structure itself. With no way to remove…
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
We present a new family of zero-field Ising models over $N$ binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components and subsets of at most three vertices into a tree. The polynomial-time algorithm of…
Motivated by the prospect of nano-robots that assist human physiological functions at the nanoscale, we investigate the coating problem in the three-dimensional model for hybrid programmable matter. In this model, a single agent with…
The recently introduced Thermodynamic Binding Networks (TBN) model was developed with the purpose of studying self-assembling systems by focusing on their thermodynamically favorable final states, and ignoring the kinetic pathways through…
We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…
We define a subclass of quantum Turing machine (QTM) named SR-QTM, which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With the help of QSTD, we…
Finite time analysis of the continuous system is investigated through both stability and stabilization based on Sum of squares programming. A systematic approach is proposed to construct Lyapunov function and Control Lyapunov function for…
This manuscript contains technical results related to a particular approach for the design of Model Predictive Control (MPC) laws. The approach, named "generalized" terminal state constraint, induces the recursive feasibility of the…
Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…
We prove that the abstract Tile Assembly Model (aTAM) of nanoscale self-assembly is intrinsically universal. This means that there is a single tile assembly system U that, with proper initialization, simulates any tile assembly system T.…
We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Active polymers are driven out of equilibrium by internal forces and exhibit conformational properties that differ fundamentally from those of passive chains. Here we study how spatially modulated tangential activity reshapes the…