Axiomatizing the equational theory of regular tree languages
نویسندگان
چکیده
منابع مشابه
Duality and Equational Theory of Regular Languages
In their more general form, our equations are of the form u → v, where u and v are profinite words. The first result not only subsumes Eilenberg-Reiterman’s theory of varieties and their subsequent extensions, but it shows for instance that any class of regular languages defined by a fragment of logic closed under conjunctions and disjunctions (first order, monadic second order, temporal, etc.)...
متن کاملDuality and the equational theory of regular languages
On one hand, the Eilenberg variety theorem establishes a bijective correspondence between varieties of formal languages and varieties of finite monoids. On the other hand, the Reiterman theorem states that varieties of finite monoids are exactly the classes of finite monoids definable by profinite equations. Together these two theorems give a structural insight in the algebraic theory of finite...
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Algebraic reasoning about programming language constructs has been a popular research topic for many years. At the propositional level, the theory of flowchart programs and linear recursion are well handled by such systems as Kleene algebra and iteration theories, systems that characterize the equational theory of the regular sets. To handle more general forms of recursion including procedures ...
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We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic Σ-algebra or minimal tree automaton, but adds new expressivity to it. The main result in this paper is a variety theorem à la Eilenberg, but we also discuss importa...
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We present a general framework to define an application–dependent weight measure on terms that subsumes e.g. total simplification orderings, and an O(n · log n) algorithm for the simultaneous computation of the minimal weight of a term in the language of each nonterminal of a regular tree grammar, based on Barzdins’ liquid–flow technique.
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ژورنال
عنوان ژورنال: The Journal of Logic and Algebraic Programming
سال: 2010
ISSN: 1567-8326
DOI: 10.1016/j.jlap.2009.10.001