Related papers: Probabilities to accept languages by quantum finit…
Unambiguous non-deterministic finite automata have intermediate expressive power and succinctness between deterministic and non-deterministic automata. It has been conjectured that every unambiguous non-deterministic one-way finite…
Let $\mathcal{P}(\Sigma^*)$ be the semiring of languages, and consider its subset $\mathcal{P}(\Sigma)$. In this paper we define the language recognized by a weighted automaton over $\mathcal{P}(\Sigma)$ and a one-letter alphabet.…
We investigate the accepting state complexity of deterministic finite automata for regular languages obtained by applying one of the following operations to languages accepted by permutation automata: union, quotient, complement,…
Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs (LNCS, Vol. 4588, Springer, Berlin, 2007, pp. 60-71), and they showed that multi-letter QFAs can accept with…
In this paper, different variants of reversible finite automata are compared, and their hierarchy by the expressive power is established. It is shown that one-way reversible automata with multiple initial states (MRFA) recognize strictly…
There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three…
The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
Deep probabilistic programming languages try to combine the advantages of deep learning with those of probabilistic programming languages. If successful, this would be a big step forward in machine learning and programming languages.…
A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…
Several methods are discussed that construct a finite automaton given a context-free grammar, including both methods that lead to subsets and those that lead to supersets of the original context-free language. Some of these methods of…
Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…
We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite…
Weighted finite automata (WFA) are often used to represent probabilistic models, such as $n$-gram language models, since they are efficient for recognition tasks in time and space. The probabilistic source to be represented as a WFA,…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…
This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of…