Comparing the succinctness of monadic query languages over finite trees

Martin Grohe; Nicole Schweikardt

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 38, Issue: 4, page 343-373
  • ISSN: 0988-3754

Abstract

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We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog.
Succinctness of the languages is closely related to the combined and parameterised complexity of query evaluation for these languages.

How to cite

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Grohe, Martin, and Schweikardt, Nicole. "Comparing the succinctness of monadic query languages over finite trees." RAIRO - Theoretical Informatics and Applications 38.4 (2010): 343-373. <http://eudml.org/doc/92747>.

@article{Grohe2010,
abstract = { We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog.
Succinctness of the languages is closely related to the combined and parameterised complexity of query evaluation for these languages. },
author = {Grohe, Martin, Schweikardt, Nicole},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {monadic second-order logic; monadic least fixed point logic; full modal mu-calculus; stratified monadic datalog; monadic datalog; finite automata on labelled finite trees},
language = {eng},
month = {3},
number = {4},
pages = {343-373},
publisher = {EDP Sciences},
title = {Comparing the succinctness of monadic query languages over finite trees},
url = {http://eudml.org/doc/92747},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Grohe, Martin
AU - Schweikardt, Nicole
TI - Comparing the succinctness of monadic query languages over finite trees
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 4
SP - 343
EP - 373
AB - We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog.
Succinctness of the languages is closely related to the combined and parameterised complexity of query evaluation for these languages.
LA - eng
KW - monadic second-order logic; monadic least fixed point logic; full modal mu-calculus; stratified monadic datalog; monadic datalog; finite automata on labelled finite trees
UR - http://eudml.org/doc/92747
ER -

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