Related papers: Real-Time Vector Automata
We introduce and investigate forgetting 1-limited automata, which are single-tape Turing machines that, when visiting a cell for the first time, replace the input symbol in it by a fixed symbol, so forgetting the original contents. These…
During the last decades, classical models in language theory have been extended by control mechanisms defined by monoids. We study which monoids cause the extensions of context-free grammars, finite automata, or finite state transducers to…
We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
We study multi-task reinforcement learning (RL), a setting in which an agent learns a single, universal policy capable of generalising to arbitrary, possibly unseen tasks. We consider tasks specified as linear temporal logic (LTL) formulae,…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Regular languages are closed under a wealth of formal language operators. Incorporating such operators in regular expressions leads to concise language specifications, but the transformation of such enhanced regular expressions to finite…
Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time,…
It is well-known that one-tape Turing machines working in linear time are no more powerful than finite automata, namely they recognize exactly the class of regular languages. We prove that it is not decidable if a one-tape machine works in…
Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…
The paper addresses the problem of computing maximal expected time to termination of probabilistic timed automata (PTA) models, under the condition that the system will, eventually, terminate. This problem can exhibit high computational…
1-way quantum finite automata are deterministic and reversible in nature, which greatly reduces its accepting property. In fact the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. In this…
We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (over 0.98), then the power of 1-way QFAs…
We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a…
After the first treatments of quantum finite state automata by Moore and Crutchfield and by Kondacs and Watrous, a number of papers study the power of quantum finite state automata and their variants. This paper introduces a model of…
Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable…
An automaton is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis…
We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…