Bounded Linear Logic: A Modular Approach to Polynomial Time Computability

1990 ◽  
pp. 195-209 ◽  
Author(s):  
Jean-Yves Girard ◽  
Andre Scedrov ◽  
Philip J. Scott
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Modular Approach ◽  
Bounded Linear

scholarly journals Bounded linear logic: a modular approach to polynomial-time computability

1992 ◽  
Vol 97 (1) ◽  
pp. 1-66 ◽  
Author(s):  
Jean-Yves Girard ◽  
Andre Scedrov ◽  
Philip J. Scott
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Modular Approach ◽  
Bounded Linear

scholarly journals Multi-Modular Approach to Polynomial-Time Factorization of Bivariate Integral Polynomials

1994 ◽  
Vol 17 (6) ◽  
pp. 545-563
Author(s):  
Kazuhiro Yokoyama ◽  
Masayuki Noro ◽  
Taku Takeshima
Keyword(s):  
Polynomial Time ◽  
Modular Approach

scholarly journals Mackey-complete spaces and power series – a topological model of differential linear logic

2016 ◽  
Vol 28 (4) ◽  
pp. 472-507 ◽  
Author(s):  
MARIE KERJEAN ◽  
CHRISTINE TASSON
Keyword(s):  
Power Series ◽  
Vector Space ◽  
Topological Vector Space ◽  
Taylor Expansion ◽  
Entire Functions ◽  
Linear Logic ◽  
Quantitative Model ◽  
Linear Functions ◽  
Topological Model ◽  
Bounded Linear

In this paper, we describe a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted as bounded linear functions. So as to interpret non-linear proofs of Linear Logic, we use a notion of power series between Mackey-complete spaces, generalizing entire functions in $\mathbb{C}$. Finally, we get a quantitative model of Intuitionist Differential Linear Logic, with usual syntactic differentiation and where interpretations of proofs decompose as a Taylor expansion.

scholarly journals Generalized Bounded Linear Logic and its Categorical Semantics

2021 ◽  
pp. 226-246
Author(s):  
Yōji Fukihara ◽  
Shin-ya Katsumata
Keyword(s):  
Linear Logic ◽  
Cut Elimination ◽  
Grading System ◽  
Bounded Linear ◽  
The Core ◽  
Categorical Structure ◽  
Categorical Semantics

AbstractWe introduce a generalization of Girard et al.’s called (and its affine variant ). It is designed to capture the core mechanism of dependency in , while it is also able to separate complexity aspects of . The main feature of is to adopt a multi-object pseudo-semiring as a grading system of the !-modality. We analyze the complexity of cut-elimination in , and give a translation from with constraints to with positivity axiom. We then introduce indexed linear exponential comonads (ILEC for short) as a categorical structure for interpreting the $${!}$$ ! -modality of . We give an elementary example of ILEC using folding product, and a technique to modify ILECs with symmetric monoidal comonads. We then consider a semantics of using the folding product on the category of assemblies of a BCI-algebra, and relate the semantics with the realizability category studied by Hofmann, Scott and Dal Lago.

FUNCTIONAL PEARL Linear lambda calculus and PTIME-completeness

2004 ◽  
Vol 14 (6) ◽  
pp. 623-633 ◽  
Author(s):  
HARRY G. MAIRSON
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Lambda Calculus ◽  
Type Inference ◽  
Decision Problems ◽  
Logical Interpretation

We give transparent proofs of the PTIME-completeness of two decision problems for terms in the λ-calculus. The first is a reproof of the theorem that type inference for the simply-typed λ-calculus is PTIME-complete. Our proof is interesting because it uses no more than the standard combinators Church knew of some 70 years ago, in which the terms are linear affine – each bound variable occurs at most once. We then derive a modification of Church's coding of Booleans that is linear, where each bound variable occurs exactly once. A consequence of this construction is that any interpreter for linear λ-calculus requires polynomial time. The logical interpretation of this consequence is that the problem of normalizing proofnets for multiplicative linear logic (MLL) is also PTIME-complete.

scholarly journals Light logics and higher-order processes

2014 ◽  
Vol 26 (6) ◽  
pp. 969-992 ◽  
Author(s):  
UGO DAL LAGO ◽  
SIMONE MARTINI ◽  
DAVIDE SANGIORGI
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Higher Order ◽  
Resource Control ◽  
Process Algebras ◽  
Π Calculus ◽  
Soft Processes

We show that the techniques for resource control that have been developed by the so-calledlight logicscan be fruitfully applied also to process algebras. In particular, we present a restriction of higher-order π-calculus inspired by soft linear logic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.

scholarly journals Soft linear logic and polynomial time

2004 ◽  
Vol 318 (1-2) ◽  
pp. 163-180 ◽  
Author(s):  
Yves Lafont
Keyword(s):  
Polynomial Time ◽  
Linear Logic

scholarly journals Polynomial time in untyped elementary linear logic

2020 ◽  
Vol 813 ◽  
pp. 117-142
Author(s):  
Olivier Laurent
Keyword(s):  
Polynomial Time ◽  
Linear Logic

On session types and polynomial time

2015 ◽  
Vol 26 (8) ◽  
pp. 1433-1458 ◽  
Author(s):  
UGO DAL LAGO ◽  
PAOLO DI GIAMBERARDINO
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Type System ◽  
Session Types ◽  
Intuitionistic Linear Logic

We show how systems of session types can enforce interactions to take bounded time for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as intuitionistic linear logic formulas. Our main result is the existence, for every typable process, of a polynomial bound on the length of reduction sequences starting from it and on the size of its reducts.

Linear logic and polynomial time

2006 ◽  
Vol 16 (06) ◽  
pp. 947 ◽  
Author(s):  
DAMIANO MAZZA
Keyword(s):  
Polynomial Time ◽  
Linear Logic
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