Membership and Finiteness Problems for Rational Sets of Regular Languages

2005 ◽  
pp. 88-99
Author(s):  
Sergey Afonin ◽  
Elena Hazova
Keyword(s):  
Regular Languages ◽  
Rational Sets

MEMBERSHIP AND FINITENESS PROBLEMS FOR RATIONAL SETS OF REGULAR LANGUAGES

2006 ◽  
Vol 17 (03) ◽  
pp. 493-506 ◽  
Author(s):  
SERGEY AFONIN ◽  
ELENA KHAZOVA
Keyword(s):  
Query Processing ◽  
Regular Language ◽  
Regular Languages ◽  
Finite Alphabet ◽  
Finitely Generated ◽  
Semistructured Databases ◽  
Rational Subset ◽  
Finite Set ◽  
Rational Sets

Let Σ be a finite alphabet. A set [Formula: see text] of regular languages over Σ is called rational if there exists a finite set [Formula: see text] of regular languages over Σ such that [Formula: see text] is a rational subset of the finitely generated semigroup [Formula: see text] with [Formula: see text] as the set of generators and language concatenation as a product. We prove that for any rational set [Formula: see text] and any regular language R ⊆ Σ* it is decidable (1) whether [Formula: see text] or not, and (2) whether [Formula: see text] is finite or not. Possible applications to semistructured databases query processing are discussed.

scholarly journals Closure properties and complexity of rational sets of regular languages

2015 ◽  
Vol 605 ◽  
pp. 62-79
Author(s):  
Andreas Holzer ◽  
Christian Schallhart ◽  
Michael Tautschnig ◽  
Helmut Veith
Keyword(s):  
Regular Languages ◽  
Closure Properties ◽  
Rational Sets

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 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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