Related papers: A Calculus of Looping Sequences with Local Rules
The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite…
We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in…
A version of the situation calculus in which situations are represented as first-order terms is presented. Fluents can be computed from the term structure, and actions on the situations correspond to rewrite rules on the terms. Actions that…
This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations…
In this paper we describe COLIN, a forward-chaining heuristic search planner, capable of reasoning with COntinuous LINear numeric change, in addition to the full temporal semantics of PDDL. Through this work we make two advances to the…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
Living organisms interact with their surroundings in a closed-loop fashion, where sensory inputs dictate the initiation and termination of behaviours. Even simple animals are able to develop and execute complex plans, which has not yet been…
This paper establishes several convergence results about flows of the dynamical system LCA (Locally Competitive Algorithm) to the mixed $\ell_2$-$\ell_1$ minimization problem LASSO and the constrained version, called CLASSO here, where the…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
For input $x$, let $F(x)$ denote the set of outputs that are the "legal" answers for a computational problem $F$. Suppose $x$ and members of $F(x)$ are so large that there is not time to read them in their entirety. We propose a model of…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
The explainability of machine learning algorithms is crucial, and numerous methods have emerged recently. Local, post-hoc methods assign an attribution score to each feature, indicating its importance for the prediction. However, these…
Modularity is a compelling solution to continual learning (CL), the problem of modeling sequences of related tasks. Learning and then composing modules to solve different tasks provides an abstraction to address the principal challenges of…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
A locally iterative learning (LIL) rule is adapted to a model of the associative memory based on the evolving recurrent-type neural networks composed of growing neurons. There exist extremely different scale parameters of time, the…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…