A Logical Descriptor for Regular Languages via Stone Duality

2014 ◽  
pp. 25-42
Author(s):  
Stefano Aguzzoli ◽  
Denisa Diaconescu ◽  
Tommaso Flaminio
Keyword(s):  
Regular Languages ◽  
Stone Duality

Regular languages and stone duality

1997 ◽  
Vol 30 (2) ◽  
pp. 121-134 ◽  
Author(s):  
N. Pippenger
Keyword(s):  
Regular Languages ◽  
Stone Duality

Regular Languages and Stone Duality

1997 ◽  
Vol 30 (2) ◽  
pp. 121-134 ◽  
Author(s):  
N. Pippenger
Keyword(s):  
Regular Languages ◽  
Stone Duality

Learning Regular Languages from Positive Evidence

1998 ◽  
Author(s):  
Laura Firoiu ◽  
Tim Oates ◽  
Paul R. Cohen
Keyword(s):  
Regular Languages ◽  
Positive Evidence

Regular languages under F-gsm mappings

1987 ◽  
Vol 18 (3) ◽  
pp. 41-45
Author(s):  
A J Dos Reis
Keyword(s):  
Regular Languages

On the state complexity of intersection of regular languages

1991 ◽  
Vol 22 (3) ◽  
pp. 52-54 ◽  
Author(s):  
Sheng Yu ◽  
Qingyu Zhuang
Keyword(s):  
The State ◽  
Regular Languages ◽  
State Complexity

On Sub Regular OL Forms

1981 ◽  
Vol 4 (1) ◽  
pp. 135-149
Author(s):  
J. Albert ◽  
H.A. Maurer ◽  
Th. Ottmann
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Regular Languages ◽  
Regularity Problem ◽  
Necessary And Sufficient

We present necessary and sufficient conditions for an OL form F to generate regular languages only. The conditions at issue can be effectively checked, whence the “regularity problem for OL forms” is proven decidable.

scholarly journals CHOICE-FREE STONE DUALITY

2019 ◽  
Vol 85 (1) ◽  
pp. 109-148
Author(s):  
NICK BEZHANISHVILI ◽  
WESLEY H. HOLLIDAY
Keyword(s):  
Boolean Algebra ◽  
Boolean Algebras ◽  
Stone Space ◽  
Spectral Space ◽  
Topological Representation ◽  
Stone Duality ◽  
Closed Sets ◽  
Spectral Spaces ◽  
Basic Facts ◽  
Regular Open

AbstractThe standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras.

scholarly journals Lower bounds for the state complexity of probabilistic languages and the language of prime numbers

2020 ◽  
Vol 30 (1) ◽  
pp. 175-192
Author(s):  
NathanaËl Fijalkow
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Prime Numbers ◽  
Regular Languages ◽  
Automata Theory ◽  
Seminal Paper ◽  
Probabilistic Automata ◽  
State Complexity ◽  
Probabilistic Languages ◽  
Alternating Automata

Abstract This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal paper of Rabin from 1963 introducing probabilistic automata, we study the (deterministic) state complexity of probabilistic languages and prove that probabilistic languages can have arbitrarily high deterministic state complexity. We then look at alternating automata as introduced by Chandra, Kozen and Stockmeyer: such machines run independent computations on the word and gather their answers through boolean combinations. We devise a lower bound technique relying on boundedly generated lattices of languages, and give two applications of this technique. The first is a hierarchy theorem, stating that there are languages of arbitrarily high polynomial alternating state complexity, and the second is a linear lower bound on the alternating state complexity of the prime numbers written in binary. This second result strengthens a result of Hartmanis and Shank from 1968, which implies an exponentially worse lower bound for the same model.

Fuzzy regular languages over finite and infinite words

2006 ◽  
Vol 157 (11) ◽  
pp. 1532-1549 ◽  
Author(s):  
Werner Kuich ◽  
George Rahonis
Keyword(s):  
Regular Languages ◽  
Infinite Words
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