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An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…
The busy beaver is a well-known specific example of a non-computable function. Whilst many aspect of this problem have been investigated, it is not always easy to find thorough and convincing evidence for the claims made about the…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
This note introduces a generalization to the setting of infinite-time computation of the busy beaver problem from classical computability theory, and proves some results concerning the growth rate of an associated function. In our view,…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
In this paper, we introduce complexity-aware planning for finite-horizon deterministic finite automata with rewards as outputs, based on Kolmogorov complexity. Kolmogorov complexity is considered since it can detect computational…
We argue that the halting problem for quantum computers which was first raised by Myers, is by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties that arise in a quantum computer when different…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…
We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
This work presents an empirical analysis of exact algorithms for the unbounded knapsack problem, which includes seven algorithms from the literature, two commercial solvers, and more than ten thousand instances. The terminating step-off, a…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations.…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to decidable as one can expect them to be: there exist sound…