# On Existentially First-Order Definable Languages and Their Relation to NP

Bernd Borchert; Dietrich Kuske; Frank Stephan

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 33, Issue: 3, page 259-269
- ISSN: 0988-3754

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topBorchert, Bernd, Kuske, Dietrich, and Stephan, Frank. "On Existentially First-Order Definable Languages and Their Relation to NP." RAIRO - Theoretical Informatics and Applications 33.3 (2010): 259-269. <http://eudml.org/doc/222021>.

@article{Borchert2010,

abstract = {
Under the assumption that the Polynomial-Time Hierarchy does not collapse
we show for a regular language L:
the unbalanced polynomial-time leaf language class determined by L
equals iff L is existentially but not
quantifierfree definable in FO[<, min, max, +1, −1].
Furthermore, no such
class lies properly between NP and co-1-NP or NP⊕co-NP.
The proofs rely on a result of Pin and Weil
characterizing
the automata of existentially first-order definable languages.
},

author = {Borchert, Bernd, Kuske, Dietrich, Stephan, Frank},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Leaf languages; NP; first-order definable languages.; polynomial-time hierarchy; first-order logic; existential definability; regular language; automata},

language = {eng},

month = {3},

number = {3},

pages = {259-269},

publisher = {EDP Sciences},

title = {On Existentially First-Order Definable Languages and Their Relation to NP},

url = {http://eudml.org/doc/222021},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Borchert, Bernd

AU - Kuske, Dietrich

AU - Stephan, Frank

TI - On Existentially First-Order Definable Languages and Their Relation to NP

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 3

SP - 259

EP - 269

AB -
Under the assumption that the Polynomial-Time Hierarchy does not collapse
we show for a regular language L:
the unbalanced polynomial-time leaf language class determined by L
equals iff L is existentially but not
quantifierfree definable in FO[<, min, max, +1, −1].
Furthermore, no such
class lies properly between NP and co-1-NP or NP⊕co-NP.
The proofs rely on a result of Pin and Weil
characterizing
the automata of existentially first-order definable languages.

LA - eng

KW - Leaf languages; NP; first-order definable languages.; polynomial-time hierarchy; first-order logic; existential definability; regular language; automata

UR - http://eudml.org/doc/222021

ER -

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## Citations in EuDML Documents

top- Victor L. Selivanov, Relating Automata-theoretic Hierarchies to Complexity-theoretic Hierarchies
- Victor L. Selivanov, Relating automata-theoretic hierarchies to complexity-theoretic hierarchies
- Victor L. Selivanov, Hierarchies and reducibilities on regular languages related to modulo counting
- Victor L. Selivanov, Hierarchies and reducibilities on regular languages related to modulo counting

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