Related papers: Regular Expressions, au point
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
A recent trend in probabilistic inference emphasizes the codification of models in a formal syntax, with suitable high-level features such as individuals, relations, and connectives, enabling descriptive clarity, succinctness and…
Handling and digesting a huge amount of information in an efficient manner has been a long-term demand in modern society. Some solutions to map key points (short textual summaries capturing essential information and filtering redundancies)…
Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
This paper establishes logical and expression-based characterizations for the class of languages recognized by nondeterministic register automata with guessing (NRA) over infinite alphabets. We introduce Scoped MSO, a logic featuring a…
This article proposes a convenient tool for decoding the output of neural networks trained by Connectionist Temporal Classification (CTC) for handwritten text recognition. We use regular expressions to describe the complex structures…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way…
Multi-tildes are regular operators that were introduced to enhance the factorization power of regular expressions, allowing us to add the empty word in several factors of a catenation product of languages. In addition to multi-bars, which…
We provide syntactic derivative-like operations, defined by recursion on regular expressions, in the styles of both Brzozowski and Antimirov, for trace closures of regular languages. Just as the Brzozowski and Antimirov derivative…
We extend Antimirov's partial derivatives from regular expressions to $\mu$-regular expressions that describe context-free languages. We prove the correctness of partial derivatives as well as the finiteness of the set of iterated partial…
Presentations of Kan extensions of category actions provide a natural framework for expressing induced actions, and therefore a range of different combinatorial problems. Rewrite systems for Kan extensions have been defined and a variation…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…
Many programming languages and tools, ranging from grep to the Java String library, contain regular expression matchers. Rather than first translating a regular expression into a deterministic finite automaton, such implementations…
In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the…