Rūsiņš Freivalds

Probabilities to accept languages by quantum finite automata

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.

Trade-off among parameters affecting inductive inference

Abstract This paper is concerned with the algorithmic learning, by example in the limit, of programs that compute recursive functions. The particular focus is on the relationship of three parameters that effect inferribility: the number of experimental trials, the plurality of approaches to the particular learning problem, and the accuracy of the final result. Each of these parameters has been examined extensively before. However, the precise characterization of the three-way interaction between these parameters is still not known. This paper makes significant progress toward a complete solution.

Co-learning of total recursive functions

Sometimes, when people are searching for some consumer item, they have difficult y with describing precisely what they want but profess to be certain that they will know what it is when they find it. It may well be that the shopper themself is trying to learn what it is they want, rejecting bad choices with each new example. Many of us have had the experience of taking an indecisive toddler to an ice cream shop. Would you like vanella? no. chocolate? no. cherry? no. . . . . Of course, the ice cream store will have a small finite number of choices. However, some will have enough choices so that enumerating them all will exceed the patience of all but the most tolerant of us. To consider this type of learning problem in a context that enables us to compare it with other, more traditional, learning problems, we consider situations where there are infinitely many choices. Formally, we consider learning where an algorithmic device inputs data and produces a sequence of programs such that the unique program that is not in the sequence is a correct generator for the input.

On the role of procrastination for machine learning

A needled, non-woven pile fabric comprises a non-woven backing fabric and a non-woven face fabric. The face fabric has its face side printed with an ornamental pattern of pigment color. The backing fabric and the face fabric are needled together so that the fibers of the backing fabric penetrate through the face fabric and mingle with the fibers of the face fabric to form a pile on the face side of the face fabric. The ornamental pattern is thereby imparted with a soft three-dimensional appearance.

A new family of nonstochastic languages

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Quantum Queries on Permutations with a Promise

This paper studies quantum query complexities for deciding (exactly or with probability 1.0) the parity of permutations of n numbers, 0 through n *** 1. Our results show quantum mechanism is quite strong for this non-Boolean problem as it is for several Boolean problems: (i) For n = 3, we need a single query in the quantum case whereas we obviously need two queries deterministically. (ii) For even n , n /2 quantum queries are sufficient whereas we need n *** 1 queries deterministically. (iii) Our third result is for the problem deciding whether the given permutation is the identical one. For this problem, we show that there is a nontrivial promise such that if we impose that promise to the input of size n = 4m , then we need only two quantum queries, while at least 2m + 2 ( = n /2 + 2) deterministic queries are necessary.

Non-constructive methods for finite probabilistic automata

Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artins Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.

Choosing a learning team: a topological approach

Kalvis Apsitis Rtisig5 Freivaldst Carl H. Smith

Ultrametric Finite Automata and Turing Machines

Institute of Mathematics Institute of Mathematics Department of Computer Science and Computer Science and Computer Science University of Maryland University of Latvia University of Latvia College Park, MD 20742 USA Raiqa bulviiris 29 Raiqa bulviiris 29 smith@cs. umd. edu LV-1459, Riga, Latvia LV-1459, Rigs, Latvia apsitistiii. lu.lv rusins@rnii.lu.lv

On the inductive inference of recursive real-valued functions

We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity of ultrametric automata can differ very much.