Related papers: Program-Size Versus Time Complexity, Speed-Up and …
It is well known that size-based scheduling policies, which take into account job size (i.e., the time it takes to run them), can perform very desirably in terms of both response time and fairness. Unfortunately, the requirement of knowing…
Synthesis of correct by design systems from specification has recently attracted much attention. The theoretical results imply that this problem is highly intractable, e.g., synthesizing a system is 2EXPTIME-complete for an LTL…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
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…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
Algorithm research focuses primarily on how many operations processors need to do (time complexity). But for many problems, both the runtime and energy used are dominated by memory accesses. In this paper, we present the first broad survey…
We present a tractable method for synthesizing arbitrarily large concurrent programs, for a shared memory model with common hardware-available primitives such as atomic registers, compare-and-swap, load-linked/store conditional, etc. The…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
This work explores the relationship between solution space and time complexity in the context of the $\textbf{P}$ vs. $\textbf{NP}$ problem, particularly through the lens of the sliding tile puzzle and root finding algorithms. We focus on…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations,…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called…
The width of a neural network matters since increasing the width will necessarily increase the model capacity. However, the performance of a network does not improve linearly with the width and soon gets saturated. In this case, we argue…
A commonly held view in the turbomachinery community is that finite element methods are not well-suited for very large-scale thermomechanical simulations. We seek to dispel this notion by presenting performance data for a collection of…
When scheduling quantum operations, a shorter overall execution time of the resulting schedule yields a better throughput and higher fidelity output. In this paper, we demonstrate that quantum operation scheduling can be interpreted as a…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
The main way of analyzing the complexity of a program is that of extracting and solving a recurrence that expresses its running time in terms of the size of its input. We develop a method that automatically extracts such recurrences from…