# A Note on Negative Tagging for Least Fixed-Point Formulae

RAIRO - Theoretical Informatics and Applications (2010)

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

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topGurov, 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

top- H.R. Andersen, Verification of Temporal Properties of Concurrent Systems. Ph.D. Thesis, Computer Science Department, Aarhus University, Denmark (1993).
- H.R. Andersen, C. Stirling and G. Winskel, A compositional proof system for the modal mu-calculus, in Proc. of LICS'94 (1994).
- J. Bradfield, Verifying Temporal Properties of Systems. Birkhauser (1992). Zbl0753.68065
- M. Dam, CTL* and ECTL* as fragments of the modal µ-calculus. Theoret. Comput. Sci.126 (1994) 77-96.
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- M. Dam, L. Fredlund and D. Gurov, Toward parametric verification of open distributed systems, H. Langmaack, A. Pnueli and W.-P. De Roever, Eds., Compositionality: The Significant Difference. Springer, Lecture Notes in Comput. Sci.1536 (1998) 150-158.
- 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).
- D. Kozen, Results on the propositional µ-calculus. Theoret. Comput. Sci.27 (1983) 333-354. Zbl0553.03007
- C. Stirling and D. Walker, Local model checking in the modal mu-calculus. Theoret. Comput. Sci.89 (1991) 161-177. Zbl0745.03027
- R.S. Streett and E.A. Emerson, An automata theoretic decision procedure for the propositional mu-calculus. Inform. and Comput.81 (1989) 249-264. Zbl0671.03023
- G. Winskel, A note on model checking the modal nu-calculus. Theoret. Comput. Sci.83 (1991) 157-167. Zbl0745.68083

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