منابع مشابه
Equational descriptions of languages
This paper is a survey on the equational descriptions of languages. The first part is devoted to Birkhoff’s and Reiterman’s theorems on equational descriptions of varieties. Eilenberg’s variety theorem and its successive generalizations form the second part. The more recent results on equational descriptions of lattices of languages are presented in the third part of the paper. Equations have b...
متن کاملSolving Goals in Equational Languages
Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like EQLOG, SLOG and RITE, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditi...
متن کاملDuality 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 کاملInfinitary Axiomatization of the Equational Theory of Context-Free Languages
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 ...
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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ژورنال
عنوان ژورنال: Information and Control
سال: 1972
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(72)90063-0