相关论文: Numeration-automatic sequences

We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…

Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…

We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language…

In this paper we propose the first machine teaching algorithm for multiple inverse reinforcement learners. Specifically, our contributions are: (i) we formally introduce the problem of teaching a sequential task to a heterogeneous group of…

In probabilistic programming, the inference problem asks to determine a program's posterior distribution conditioned on its "observe" instructions. Inference is challenging, especially when exact rather than approximate results are…

In this paper, we define the class of hourglass automata, which are timed automata with bounded clocks that can be made to progress backwards as well as forwards at a constant rate. We then introduce a new clock update for timed automata…

These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…

In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error…

We characterize those $k$-automatic sets $S$ of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest $j$ such…

We continue studying essential inputs of trees and automata. Strongly essential inputs of trees are introduced and studied. Various examples for application in Computer Science are shown.

Sequences of numbers (either natural integers, or integers or rational) of level $k \in \mathbb{N}$ have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level $k$. This…

Recent work (Xu et al., 2020) has suggested that numeral systems in different languages are shaped by a functional need for efficient communication in an information-theoretic sense. Here we take a learning-theoretic approach and show how…

We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…

This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…

In this paper we take a look at Automatic Differentiation through the eyes of Tensor and Operational Calculus. This work is best consumed as supplementary material for learning tensor and operational calculus by those already familiar with…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

Intelligent systems capable of automatically understanding natural language text are important for many artificial intelligence applications including mobile phone voice assistants, computer vision, and robotics. Understanding language…

Machine translation systems require semantic knowledge and grammatical understanding. Neural machine translation (NMT) systems often assume this information is captured by an attention mechanism and a decoder that ensures fluency. Recent…