Related papers: On the Computational Complexity of MapReduce
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
Many physical systems have underlying safety considerations that require that the policy employed ensures the satisfaction of a set of constraints. The analytical formulation usually takes the form of a Constrained Markov Decision Process…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
In this paper, we study CTP maps, that is, marked rational maps with constant Thurston pullback mapping. We prove that all the regular or mixing CTP polynomials satisfy McMullen's condition. Additionally, we construct a new class of…
We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
The integration of Model Predictive Control (MPC) and Reinforcement Learning (RL) has emerged as a promising paradigm for constrained decision-making and adaptive control. MPC offers structured optimization, explicit constraint handling,…
We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…
Miller and Reif's FOCS'85 classic and fundamental tree contraction algorithm is a broadly applicable technique for the parallel solution of a large number of tree problems. Additionally it is also used as an algorithmic design technique for…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read…
Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…
This work applies Matrix Completion (MC) -- a class of machine-learning methods commonly used in the context of recommendation systems -- to analyse economic complexity. MC is applied to reconstruct the Revealed Comparative Advantage (RCA)…
In this work we treat a famous topic in Ergodic Theory and Dynamical Systems: uniformly expanding maps. We relate regularity of expanding maps and conjugacies with Lyapunov exponents, metric and topological entropies for expanding maps of…
Contextual Markov decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. While CMDPs serve…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…