Leaf Language Classes

Wagner, Klaus W.

doi:10.1007/978-3-540-31834-7_5

Cited by 12 publications

(15 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [175] a notion of reducibility (called ptt-reducibility) was introduced which is related to the unbalanced leaf language definability in exactly the same way as in Theorem 8.3. In [14,136,145] exact characterizations of NP in terms of regular leaf languages were obtained.…”

Section: Relation To Complexity Theorymentioning

confidence: 99%

“…Less obvious is the close relation of this section to complexity theory which we briefly discuss here. For a comprehensive survey see [175].…”

Section: Relation To Complexity Theorymentioning

confidence: 99%

“…Now, relate to any language L ⊆ A + (called in this situation a leaf language) the language M −1 (L) ⊆ B * . Denote by Leaf b (L) the set of languages M −1 (L), for all machines M specified above which have balanced (in some natural sense, see [175] for details) computation trees, and denote by Leaf u (L) the set of languages M −1 (L), for all machines M specified above (which may have unbalanced computation trees). Obviously, we have Leaf b (L) ⊆ Leaf u (L) for every language L, and there exist languages L where Leaf b (L) = Leaf u (L) is unlikely.…”

Section: Relation To Complexity Theorymentioning

confidence: 99%

“…The classes of regular aperiodic and quasi-aperiodic languages may be characterized in the complexity-theoretic terms [175,136] as follows: a regular language…”

Section: Relation To Complexity Theorymentioning

confidence: 99%

See 3 more Smart Citations

Fine hierarchies and m-reducibilities in theoretical computer science

Selivanov

2008

Theoretical Computer Science

View full text Add to dashboard Cite

a b s t r a c tThis is a survey of results about versions of fine hierarchies and many-one reducibilities that appear in different parts of theoretical computer science. These notions and related techniques play a crucial role in understanding complexity of finite and infinite computations. We try not only to present the corresponding notions and facts from the particular fields but also to identify the unifying notions, techniques and ideas.

show abstract

Section: Relation To Complexity Theorymentioning

confidence: 99%

“…Less obvious is the close relation of this section to complexity theory which we briefly discuss here. For a comprehensive survey see [175].…”

Section: Relation To Complexity Theorymentioning

confidence: 99%

Section: Relation To Complexity Theorymentioning

confidence: 99%

“…The classes of regular aperiodic and quasi-aperiodic languages may be characterized in the complexity-theoretic terms [175,136] as follows: a regular language…”

Section: Relation To Complexity Theorymentioning

confidence: 99%

See 2 more Smart Citations

Fine hierarchies and m-reducibilities in theoretical computer science

Selivanov

2008

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…Another surprising connection between language hierarchies and the structure of complexity classes is offered by the theory of leaf languages [16,17,18,19,23,36,37,92,93,116].…”

Section: Connection With Complexity Classesmentioning

confidence: 99%

The Dot-Depth Hierarchy, 45 Years Later

2017

The Role of Theory in Computer Science

View full text Add to dashboard Cite

In 1970, R. S. Cohen and Janusz A. Brzozowski introduced a hierarchy of star-free languages called the dot-depth hierarchy. This hierarchy and its generalisations, together with the problems attached to them, had a long-lasting influence on the development of automata theory. This survey article reports on the numerous results and conjectures attached to this hierarchy.This paper is a follow-up of the survey article Open problems about regular languages, 35 years later [57]. The dot-depth hierarchy, also known as Brzozowski hierarchy, is a hierarchy of star-free languages first introduced by Cohen and Brzozowski [25] in 1971. It immediately gave rise to many interesting questions and an account of the early results can be found in Brzozowski's survey [20] from 1976. Terminology, notation and backgroundMost of the terminology used in this paper was introduced in [57]. We just complete these definitions by giving the ordered versions of the notions of syntactic monoid and variety of finite monoids. Syntactic order and positive varietiesAn ordered monoid is a monoid equipped with an order compatible with the multiplication: x y implies zx zy and xz yz.The syntactic preorder 1 of a language L of A * is the relation L defined on A * by u L v if and only if, for every x, y ∈ A * , xuy ∈ L ⇒ xvy ∈ L. * The author was funded from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 670624).1 Unfortunately, the author used the opposite order in earlier papers (from 1995 to 2011). 1The syntactic congruence of L is the associated equivalence relation ∼ L , defined by u ∼ L v if and only if u L v and v L u.The syntactic monoid of L is the quotient M (L) of A * by ∼ L and the natural morphism η : A * → A * /∼ L is called the syntactic morphism of L. The syntactic preorder L induces an order on the quotient monoid M (L). The resulting ordered monoid is called the syntactic ordered monoid of L.For instance, the syntactic monoid of the language {a, aba} is the monoid M = {1, a, b, ab, ba, aba, 0} presented by the relations a 2 = b 2 = bab = 0. Its syntactic order is given by the relations 0 < ab < 1, 0 < ba < 1, 0 < aba < a, 0 < b.The syntactic ordered monoid of a language was first introduced by Schützenberger [86] in 1956, but thereafter, he apparently only used the syntactic monoid.A positive variety of languages is a class of languages closed under finite unions, finite intersections, left and right quotients and inverses of morphisms. A variety of languages is a positive variety closed under complementation.Similarly, a variety of finite ordered monoids is a class of finite ordered monoids closed under taking ordered submonoids, quotients and finite products. Varieties of finite (ordered) semigroups are defined analogously. If V is a variety of ordered monoids, let V d denote the dual variety, consisting of all ordered monoids (M, ) such that (M, ) ∈ V. We refer the reader to the books [2, 28, 62] for more details.Eilenberg's variety theor...

show abstract

Some Reducibilities on Regular Sets

Selivanov

2005

New Computational Paradigms

View full text Add to dashboard Cite

Leaf Language Classes

Cited by 12 publications

References 35 publications

Fine hierarchies and m-reducibilities in theoretical computer science

Fine hierarchies and m-reducibilities in theoretical computer science

The Dot-Depth Hierarchy, 45 Years Later

Some Reducibilities on Regular Sets

Contact Info

Product

Resources

About