Three notes on the complexity of model checking fixpoint logic with chop

Martin Lange

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 41, Issue: 2, page 177-190
  • ISSN: 0988-3754

Abstract

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This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations to derive the following results: the combined model checking complexity as well as the data complexity of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression complexity of FLC is trivially P-hard and limited from above by the complexity of solving a parity game, i.e. in UP ∩ co-UP. For any fragment of fixed alternation depth, in particular alternation- free formulas it is P-complete.

How to cite

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Lange, Martin. "Three notes on the complexity of model checking fixpoint logic with chop." RAIRO - Theoretical Informatics and Applications 41.2 (2007): 177-190. <http://eudml.org/doc/250076>.

@article{Lange2007,
abstract = { This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations to derive the following results: the combined model checking complexity as well as the data complexity of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression complexity of FLC is trivially P-hard and limited from above by the complexity of solving a parity game, i.e. in UP ∩ co-UP. For any fragment of fixed alternation depth, in particular alternation- free formulas it is P-complete. },
author = {Lange, Martin},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Model checking; games; EXPTIME-complete; model checking; mu-calculus; fixpoint calculus with Chop; complexity},
language = {eng},
month = {7},
number = {2},
pages = {177-190},
publisher = {EDP Sciences},
title = {Three notes on the complexity of model checking fixpoint logic with chop},
url = {http://eudml.org/doc/250076},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Lange, Martin
TI - Three notes on the complexity of model checking fixpoint logic with chop
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/7//
PB - EDP Sciences
VL - 41
IS - 2
SP - 177
EP - 190
AB - This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations to derive the following results: the combined model checking complexity as well as the data complexity of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression complexity of FLC is trivially P-hard and limited from above by the complexity of solving a parity game, i.e. in UP ∩ co-UP. For any fragment of fixed alternation depth, in particular alternation- free formulas it is P-complete.
LA - eng
KW - Model checking; games; EXPTIME-complete; model checking; mu-calculus; fixpoint calculus with Chop; complexity
UR - http://eudml.org/doc/250076
ER -

References

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