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Abstract: Linear logic is a resource-aware logic that is based on an analysis of the classical proof rules of contraction (copying) and weakening (throwing away). In this paper we study the decision problem for the multiplicative fragment of linear logic without quantifiers or propositions: the constant-only case. We show that this fragment is np-complete. Earlier work by Max Kanovich showed that propositional multiplicative linear logic is np-complete. With Natarajan Shankar, the first author developed... (Update)
Context of citations to this paper: More
.... that multiplicative linear logic is np complete [8] Lincoln and Winkler demonstrated np completeness of MLL using only the constants [13]. Lincoln and Scedrov had previously shown this fragment of linear logic to be nexptime hard [11] By extending this proof search paradigm,...
Cited by: More
System BV is NP-complete - Kahramanogullari (2005) (Correct)
Decision Problems for Second-Order Linear Logic - Lincoln, Scedrov, Shankar (1995) (Correct)
First Order Linear Logic without Modalities is NEXPTIME-Hard - Lincoln, Scedrov (1994) (Correct)
Active bibliography (related documents): More All
0.7: Constant-Only Multiplicative Linear Logic is NP-Complete - Lincoln, Winkler (1992) (Correct)
0.4: A Brief Guide to Linear Logic - Scedrov (1993) (Correct)
0.3: Deciding Provability of Linear Logic Formulas - Lincoln (1994) (Correct)
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23: Theoretical Computer Science (context) - Girard - 1987
19: Decision problems for propositional linear logic - Lincoln, Mitchell et al. - 1992
14: First order linear logic without modalities is NEXPTIME-hard - Lincoln, Scedrov - 1994
BibTeX entry: (Update)
P. Lincoln and T. Winkler. Constant-Only Multiplicative Linear Logic is NP-Complete. Manuscript, September 1992. Available using anonymous ftp from host ftp.csl.sri.com and the file pub/lincoln/comultnpc. dvi. http://citeseer.ist.psu.edu/lincoln92constantonly.html More
@article{ lincoln94constantonly,
author = "Patrick Lincoln and Timothy Winkler",
title = "Constant-only multiplicative linear logic is {NP}-complete",
journal = "Theoretical Computer Science",
volume = "135",
number = "1",
pages = "155--169",
year = "1994",
url = "citeseer.ist.psu.edu/lincoln92constantonly.html" }
Citations (may not include all citations):4212 Computers and Intractability: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
982 Theoretical Computer Science (context) - Girard - 1987
257 Logic programming in a fragment of intuitionistic linear log.. - Hodas, Miller - 1991
233 Computational interpretations of linear logic - Abramsky - 1991
223 Linear objects: Logical processes with built-in inheritance - Andreoli, Pareschi - 1990
96 Decision problems for propositional linear logic - Lincoln, Mitchell et al. - 1992
51 Operational aspects of linear lambda calculus - Lincoln, Mitchell - 1992
39 Horn programming in linear logic is np-complete (context) - Kanovich - 1992
30 Permutability of inferences in Gentzen's calculi LK and LJ (context) - Kleene - 1952
28 autonomous categories (context) - Barr - 1979
17 and cofree coalgebras (context) - Seely, -autonomous - 1989
16 Computational Aspects of Linear Logic - Lincoln - 1992
16 Mechanizing Proof Theory: Resource-Aware Logics and Proof-Tr.. (context) - Bellin - 1990
16 The multiplicative fragment of linear logic is np-complete (context) - Kanovich - 1991
16 The multiplicative fragment of linear logic is np-complete (context) - Kanovich - 1991
6 Some properties of linear logic proved by semantic methods - Avron - 1992
1 Personal communication (context) - Girard - 1990
The graph only includes citing articles where the year of publication is known.
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The Formal Verification of an Algorithm for Interactive.. - Lincoln, Rushby (1993) (Correct)
First Order Linear Logic without Modalities is NEXPTIME-Hard - Lincoln, Scedrov (1994) (Correct)
Algorithmic Aspects of Type Inference With Subtypes - Lincoln, Mitchell (1992) (Correct)
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