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The {\it matrix-chain multiplication} problem is a classic problem that is widely taught to illustrate dynamic programming. The textbook solution runs in $\theta(n^3)$ time. However, there is a complex $O(n \log n)$-time method \cite{HU82},…
We develop deterministic algorithms for the problems of consensus, gossiping and checkpointing with nodes prone to failing. Distributed systems are modeled as synchronous complete networks. Failures are represented either as crashes or…
Some iterative calculations can be carried out by parallel communicating processors, and yield the same results whether or not the processors are synchronized. We show that this is the case if and only if the iteration is a contraction that…
We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform…
Continuous-time, event-native spiking neural networks (SNNs) operate strictly on spike events, treating spike timing and ordering as the representation rather than an artifact of time discretization. This viewpoint aligns with biological…
Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently proved mathematically that memcomputing…
Identifying causal order from restricted projective data is generally nontrivial. When two quantum players interact only through an unobserved environment, the available local measurement statistics are typically not tomographically…
We consider strongly-connected directed networks of identical synchronous, finite-state processors with in- and out-degree uniformly bounded by a network constant. Via a straightforward extension of Ostrovsky and Wilkerson's Backwards…
The MapReduce framework has firmly established itself as one of the most widely used parallel computing platforms for processing big data on tera- and peta-byte scale. Approaching it from a theoretical standpoint has proved to be…
Neurally-parameterized Structural Causal Models in the Pearlian notion to causality, referred to as NCM, were recently introduced as a step towards next-generation learning systems. However, said NCM are only concerned with the learning…
Sequential deep learning models such as RNN, causal CNN and attention mechanism do not readily consume continuous-time information. Discretizing the temporal data, as we show, causes inconsistency even for simple continuous-time processes.…
Efficiently solving NP-complete problems-such as protein structure prediction, cryptographic decryption, and vulnerability detection-remains a central challenge in computer science. Traditional electronic computers, constrained by the…
Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories -- based on the data structures which…
The imposition of real-time constraints on a parallel computing environment- specifically high-performance, cluster-computing systems- introduces a variety of challenges with respect to the formal verification of the system's timing…
The difficulty of developing reliable parallel software is generating interest in deterministic environments, where a given program and input can yield only one possible result. Languages or type systems can enforce determinism in new code,…
Temporal models based on recurrent neural networks have proven to be quite powerful in a wide variety of applications. However, training these models often relies on back-propagation through time, which entails unfolding the network over…
Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
Classical computability theory tells us that self-modifying code (SMC) on a deterministic universal Turing machine can be simulated by non-SMC code on the same model. That abstraction, however, omits the external timing inputs, concurrency,…
Nested parallelism exists in scientific codes that are searching multi-dimensional spaces. However, implementations of nested parallelism often have overhead and load balance issues. The Orbital Analysis code we present exhibits a sparse…