The Uniform Measure of Simple Regular Sets of Infinite Trees

Nonterminal complexity of some families of infinite regular languages

Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different families of regular languages. In this paper we study nonterminal complexity of some families of infinite regular languages.

Morphisms on infinite alphabets, countable states automata and regular sequences

In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by countable states automata. Moreover, we prove that the regularity of some regular sequences is invariant under some codings.

On the Uniform Distribution of Regular Expressions

Although regular expressions do not correspond univocally to regular languages, it is still worthwhile to study their properties and algorithms. For the average case analysis one often relies on the uniform random generation using a specific grammar for regular expressions, that can represent regular languages with more or less redundancy. Generators that are uniform on the set of expressions are not necessarily uniform on the set of regular languages. Nevertheless, it is not straightforward that asymptotic estimates obtained by considering the whole set of regular expressions are different fr…

Deterministic and game separability for regular languages of infinite trees

We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the separator is fixed, or not. In each case, we show that separability can be decided in EXPTIME, and that separating automata of exponential size suffice. We obtain our results by reducing to infinite duration games with ω-regular winning conditions and applying the finite-memory determinacy theorem of Büchi and Landweber.

无限字母表上语言的名义正则表达式。扩展抽象

Nominal Regular Expressions for Languages over Infinite Alphabets. Extended Abstract

我们提出正则表达式来抽象模型，并研究资源感知计算的性质。受名义技术（如进程演算中流行的技术）的启发，我们用名称（对计算资源建模）和合适的运算符（用于资源的分配、解分配、范围和新鲜度条件）扩展了经典正则表达式。我们讨论类这样的名义正则表达式，显示如何这样的表达式有自然的解释，在无限的字母表的语言，并给出Kleene定理来证明他们的形式语言的名义自动机。

一个由逐类有限代数可识别的无限树非正则语言

A non-regular language of infinite trees that is recognizable by a sort-wise finite algebra

本文证明存在一个逐类有限且有限生成的ω-克隆可识别无限树的非正则语言，表明无限树的正则性与有限代数识别之间并非简单等价。