Fine Hierarchy of Regular ω-Languages
نویسنده
چکیده
By applying descriptive set theory to the Wagner’s fine structure of regular ω-languages we get quite different proofs of his results and obtain new results. We give an automata-free description of the fine structure. We present also a simple property of a deterministic Muller automaton equivalent to the condition that the corresponding regular ω-language belongs to any given level of the fine structure. Our results and proofs demonstrate deep interconnections between descriptive set theory and the theory of ω-languages.
منابع مشابه
ω-Semigroups and the Fine Classification of Borel Subsets of Finite Ranks of the Cantor Space
The algebraic study of formal languages draws the equivalence between ω-regular languages and subsets of finite ω-semigroups. The ω-regular languages being the ones characterised by second order monadic formulas. Within this framework, in [1]we provide a characterisation of the algebraic counterpart of the Wagner hierarchy: a celebrated hierarchy of ω-regular languages. For this, we adopt a hie...
متن کاملDeterministic Fuzzy Automaton on Subclasses of Fuzzy Regular ω-Languages
In formal language theory, we are mainly interested in the natural language computational aspects of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, we introduce two subclasses of fuzzy regular ω-languages called fuzzy n-local ω-languages and Buchi fuzzy n-local ω-languages, and give some closure properties for those subclasses. We define a ...
متن کاملThe Wadge Hierarchy of Petri Nets ω-Languages
We describe the Wadge hierarchy of the ω-languages recognized by deterministic Petri nets. This is an extension of the celebrated Wagner hierarchy which turned out to be the Wadge hierarchy of the ω-regular languages. Petri nets are more powerful devices than finite automata. They may be defined as partially blind multi-counter automata. We show that the whole hierarchy has height ω 2 , and giv...
متن کاملAcceptance conditions for omega-languages and the Borel hierarchy
This paper investigates acceptance conditions for finite automata recognizing ω-regular languages. As a first result, we show that, under any acceptance condition that can be defined in the MSO logic, a finite automaton can recognize at most ω-regular languages. Starting from this, the paper aims at classifying acceptance conditions according to their expressive power and at finding the exact p...
متن کاملTopological Complexity of omega-Powers: Extended Abstract
The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. It produces ω-powers, i.e. ω-languages in the form V , where V is a finitary language. This operation appears in the characterization of the class REGω of ω-regular languages (respectively, of the class CFω of context free ω-languages) as the ω-Kleene closure of the family REG of regular finitary la...
متن کامل