A Note on Negative Tagging for Least Fixed-Point Formulae

Dilian Gurov; Bruce Kapron

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 33, Issue: 4-5, page 383-392
  • ISSN: 0988-3754

Abstract

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Proof systems with sequents of the form U ⊢ Φ for proving validity of a propositional modal μ-calculus formula Φ over a set U of states in a given model usually handle fixed-point formulae through unfolding, thus allowing such formulae to reappear in a proof. Tagging is a technique originated by Winskel for annotating fixed-point formulae with information about the proof states at which these are unfolded. This information is used later in the proof to avoid unnecessary unfolding, without having to investigate the history of the proof. Depending on whether tags are used for acceptance or for rejection of a branch in the proof tree, we refer to “positive” or “negative” tagging, respectively. In their simplest form, tags consist of the sets U at which fixed-point formulae are unfolded. In this paper, we generalise results of earlier work by Andersen et al. which, in the case of least fixed-point formulae, are applicable to singleton U sets only.

How to cite

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Gurov, Dilian, and Kapron, Bruce. "A Note on Negative Tagging for Least Fixed-Point Formulae." RAIRO - Theoretical Informatics and Applications 33.4-5 (2010): 383-392. <http://eudml.org/doc/222092>.

@article{Gurov2010,
abstract = { Proof systems with sequents of the form U ⊢ Φ for proving validity of a propositional modal μ-calculus formula Φ over a set U of states in a given model usually handle fixed-point formulae through unfolding, thus allowing such formulae to reappear in a proof. Tagging is a technique originated by Winskel for annotating fixed-point formulae with information about the proof states at which these are unfolded. This information is used later in the proof to avoid unnecessary unfolding, without having to investigate the history of the proof. Depending on whether tags are used for acceptance or for rejection of a branch in the proof tree, we refer to “positive” or “negative” tagging, respectively. In their simplest form, tags consist of the sets U at which fixed-point formulae are unfolded. In this paper, we generalise results of earlier work by Andersen et al. which, in the case of least fixed-point formulae, are applicable to singleton U sets only. },
author = {Gurov, Dilian, Kapron, Bruce},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {propositional modal -calculus; branching-time properties; proof systems; unfolding; proof tree; tagging; least fixed-point formulae},
language = {eng},
month = {3},
number = {4-5},
pages = {383-392},
publisher = {EDP Sciences},
title = {A Note on Negative Tagging for Least Fixed-Point Formulae},
url = {http://eudml.org/doc/222092},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Gurov, Dilian
AU - Kapron, Bruce
TI - A Note on Negative Tagging for Least Fixed-Point Formulae
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 4-5
SP - 383
EP - 392
AB - Proof systems with sequents of the form U ⊢ Φ for proving validity of a propositional modal μ-calculus formula Φ over a set U of states in a given model usually handle fixed-point formulae through unfolding, thus allowing such formulae to reappear in a proof. Tagging is a technique originated by Winskel for annotating fixed-point formulae with information about the proof states at which these are unfolded. This information is used later in the proof to avoid unnecessary unfolding, without having to investigate the history of the proof. Depending on whether tags are used for acceptance or for rejection of a branch in the proof tree, we refer to “positive” or “negative” tagging, respectively. In their simplest form, tags consist of the sets U at which fixed-point formulae are unfolded. In this paper, we generalise results of earlier work by Andersen et al. which, in the case of least fixed-point formulae, are applicable to singleton U sets only.
LA - eng
KW - propositional modal -calculus; branching-time properties; proof systems; unfolding; proof tree; tagging; least fixed-point formulae
UR - http://eudml.org/doc/222092
ER -

References

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  1. H.R. Andersen, Verification of Temporal Properties of Concurrent Systems. Ph.D. Thesis, Computer Science Department, Aarhus University, Denmark (1993).  
  2. H.R. Andersen, C. Stirling and G. Winskel, A compositional proof system for the modal mu-calculus, in Proc. of LICS'94 (1994).  
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  7. D. Gurov, S. Berezin and B. Kapron, A modal µ-calculus and a proof system for value passing processes. Electron. Notes Theoret. Comput. Sci.5 (1996).  
  8. D. Kozen, Results on the propositional µ-calculus. Theoret. Comput. Sci.27 (1983) 333-354.  
  9. C. Stirling and D. Walker, Local model checking in the modal mu-calculus. Theoret. Comput. Sci.89 (1991) 161-177.  
  10. R.S. Streett and E.A. Emerson, An automata theoretic decision procedure for the propositional mu-calculus. Inform. and Comput.81 (1989) 249-264.  
  11. G. Winskel, A note on model checking the modal nu-calculus. Theoret. Comput. Sci.83 (1991) 157-167.  

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