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Abstract: We introduce a geometry of interaction model given by an algebra of clauses equipped with resolution (following [Gir95]) into which proofs of Elementary Linear Logic can be interpreted. In order to extend geometry of interaction computation (the so called execution formula) to a wider class of programs in the algebra than just those coming from proofs, we define a variant of execution (called weak execution). Its application to any program of clauses is shown to terminate with a bound on the... (Update)
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.... studied by [DJ99] and [KL98] Notably, several interesting semantics have recently been proposed for these logics ( KOS00] [BP99], Bai00] MO00] which may shed new light on the nature of the polytime (and the elementary) functions on a semantic basis. In this paper, to...
.... estimates for # than the one above were given by Max Kanovich in [10] in sequent calculus, and by Patrick Baillot and Marco Pedicini in [2], in the geometry of interaction framework. 7 2.2 ILL and IELL as typed lambda calculi We now attach to each ill proof typed term of #...
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3: Ramified Recurrence and Computational Complexity I: Word recurrence and poly-tim.. (context) - Leivant - 1995
2: Information and Computation (context) - Girard, Logic - 1998
2: Sub-recursion: functions and hierarchy (context) - Rose - 1984
BibTeX entry: (Update)
P. Baillot and M. Pedicini. Elementary complexity and the geometry of interaction (extended abstract). In Proceedings of TLCA'99. Springer-Verlag, LNCS, 1999. http://citeseer.ist.psu.edu/baillot00elementary.html More
@inproceedings{ baillot99elementary,
author = "Patrick Baillot and Marco Pedicini",
title = "Elementary Complexity and Geometry of Interaction",
booktitle = "Typed Lambda Calculus and Applications",
pages = "25-39",
year = "1999",
url = "citeseer.ist.psu.edu/baillot00elementary.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
69 Geometry of interaction I: an interpretation of system F (context) - Girard - 1988
68 Towards a geometry of interaction (context) - Girard
40 Proof-nets: the parallel syntax for proof theory (context) - Girard
31 Lambda-Calcul et reseaux (context) - Regnier - 1992
31 Information and Computation (context) - Girard, logic - 1998
24 Geometry of interaction II: Deadlock free algorithms (context) - Girard - 1988
21 Proof nets and the Hilbert space - Danos, Regnier
13 Phase semantics for light linear logic - Kanovich, Okada et al.
11 La Logique Lineaire appliquee a l'etude de divers processus .. (context) - Danos - 1990
5 Quantifiers in linear logic II (context) - Girard
2 Stratified coherent spaces: a denotational semantics for lig.. - Baillot - 2000
2 Remarks on elementary linear logic - Pedicini - 1996
2 Geometry of interaction 3: the general case (context) - Girard
1 Elementary recursive functions and linear logic (context) - Danos, Joinet - 1999
1 Some results on the interpretation of #-calculus in operator.. (context) - Malacaria, Regnier - 1991
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Stratified coherent spaces: a denotational semantics for Light.. - Baillot (2000) (Correct)
Unknown - (Correct)
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