159,575 Hits in 3.5 sec

From Proof-Nets to Linear Logic Type Systems for Polynomial Time Computing [chapter]

Patrick Baillot
2007 Lecture Notes in Computer Science  
We stress the importance of proof-nets from Light linear logic for the design of this type system and for a result establishing that typable lambda-terms can be evaluated efficiently with optimal reduction  ...  In this presentation we give an overview of Dual Light Affine Logic (DLAL), a polymorphic type system for lambda calculus ensuring that typable lambda terms are executable in polynomial time.  ...  Linear logic. Here we focus our attention on the linear logic (LL) approach to ICC, which is based on the proofs-as-programs correspondence.  ... 
doi:10.1007/978-3-540-73228-0_2 fatcat:7axovijfpfbbxhxe5umqljqnku

A Lightweight ISA Extension for AES and SM4 [article]

Markku-Juhani O. Saarinen
2020 arXiv   pre-print
The implementation contains depth- and size-optimized joint AES and SM4 S-Box logic based on the Boyar-Peralta construction with a shared non-linear middle layer, demonstrating additional avenues for logic  ...  Sixteen instructions (and a subkey load) is required to implement an AES round with the extension, instead of 80 without.  ...  The instructions require logic only for a single S-Box, which is combined with additional linear layers for increased code density and performance.  ... 
arXiv:2002.07041v5 fatcat:k5pkyohy35dmbmsw67fkvxwkri

Taming Modal Impredicativity: Superlazy Reduction [chapter]

Ugo Dal Lago, Luca Roversi, Luca Vercelli
2008 Lecture Notes in Computer Science  
Linear logic, implicit computational complexity, proof theory.  ...  Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation.  ...  Linear Logic with superlazy reduction can be seen as a generalization of the principles of Soft Linear Logic. Every time a box is replicated, that box is opened.  ... 
doi:10.1007/978-3-540-92687-0_10 fatcat:choxyganlbehtgzjlzv2ipr5ui

Encoding of Planning Problems and Their Optimizations in Linear Logic [chapter]

Lukáš Chrpa, Pavel Surynek, Jiří Vyskočil
2009 Lecture Notes in Computer Science  
This fact motivates us to provide a possible encoding of planning problems in linear logic.  ...  This paper shows how planning problems can be encoded in Linear Logic and how some optimizations of planning problems can be encoded.  ...  Example In this example we will use a predicate extension of Linear Logic. Imagine a version of "Block World", where we have slots and boxes, and every slot may contain at most one box.  ... 
doi:10.1007/978-3-642-00675-3_4 fatcat:yykw6lzx6jajrppkmhrw6e7rbm

On the linear decoration of intuitionistic derivations

Vincent Danos, Jean-Baptiste Joinet, Harold Schellinx
1995 Archive for Mathematical Logic  
We de ne an optimal proof-by-proof embedding of intuitionistic sequent calculus into linear logic and analyse the (purely logical) linearity information thus obtained. ; ) A ; ?  ...  (By linearity no boxes in are contained in 1 .) 1. Consider the following situation: In all other cases one can perform the reduction without e ecting the adequate chain.  ...  ) A is derivable in linear logic.  ... 
doi:10.1007/bf02390456 fatcat:cpjegmb4ovdaveybvpvn3oh7da

Linear logic

Jean-Yves Girard
1987 Theoretical Computer Science  
Following this basic discovery, a completely new approach to the whole area between constructive logics and programmation is initiated.  ...  The familiar connective of negation is broken into two operations: linear negation which is the purely negative part of negation and the modality "of course" which has the meaning of a reaffirmation.  ...  Acknowledgment The author is indebted to Jean-Louis Krivine, whose simultaneous work on lambda-calculus and its execution had some crucial influence on earlier versions of linear logic.  ... 
doi:10.1016/0304-3975(87)90045-4 fatcat:2pz66b65i5fzjaggrqhwyeimki

Size-Change Termination and Satisfiability for Linear-Time Temporal Logics [chapter]

Martin Lange
2011 Lecture Notes in Computer Science  
Linear-time temporal logics like LTL, PSL and the linear-time µ-calculus have relatively simple translations into alternating parity automata, and this automaton model is closed under all Boolean operations  ...  Thus, the typical decision problems for such linear-time temporal logics reduce relatively simply to the emptiness problem for alternating parity automata.  ...  LTL One of the simplest and most well-known linear-time temporal logics is LTL.  ... 
doi:10.1007/978-3-642-24364-6_3 fatcat:qktjgpig2rc4tl6mvcvkhs2pvm

Elementary Linear Logic Revisited for Polynomial Time and an Exponential Time Hierarchy [chapter]

Patrick Baillot
2011 Lecture Notes in Computer Science  
Elementary linear logic is a simple variant of linear logic, introduced by Girard and which characterizes in the proofs-as-programs approach the class of elementary functions (computable in time bounded  ...  Other systems, like light linear logic have then been defined to capture in a similar way polynomial time functions, but at the price of either a more complicated syntax or of more involved encodings.  ...  The author would like to thank Jean-Yves Girard whose initial question, whether P could be characterized in elementary linear logic, triggered this work.  ... 
doi:10.1007/978-3-642-25318-8_25 fatcat:bomvp25otnfxhnr7ck7udoaxda

Sharing Continuations: Proofnets for Languages with Explicit Control [chapter]

Julia L. Lawall, Harry G. Mairson
2000 Lecture Notes in Computer Science  
While Lamping's graphs and their variants encode an embedding of intuitionistic logic into linear logic, our construction implicitly contains an embedding of classical logic into linear logic.  ...  The technology is founded on proofnets for multiplicative-exponential linear logic, extending the techniques originally proposed by Lamping, where we adapt the continuationpassing style transformation  ...  in linear logic [12, 13] .  ... 
doi:10.1007/3-540-46425-5_16 fatcat:3jevx7qevzahhehomccscbwvum

Soft linear logic and polynomial time

2004 Theoretical Computer Science  
We present a subsystem of second-order linear logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms, and vice versa.  ...  Soft linear logic can be seen as a subsystem of bounded linear logic which is powerful enough to encode polynomial time. It is simpler than bounded linear logic and light linear logic.  ...  . • Light linear logic (see [4] ). The types are essentially those of linear logic, but the rules for exponentials are modiÿed.  ... 
doi:10.1016/s0304-3975(03)00523-1 fatcat:hm25sv3cjfbnhe6kn6jhw3uuru

Soft linear logic and polynomial time

Yves Lafont
2004 Theoretical Computer Science  
We present a subsystem of second-order linear logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms, and vice versa.  ...  Soft linear logic can be seen as a subsystem of bounded linear logic which is powerful enough to encode polynomial time. It is simpler than bounded linear logic and light linear logic.  ...  . • Light linear logic (see [4] ). The types are essentially those of linear logic, but the rules for exponentials are modiÿed.  ... 
doi:10.1016/j.tcs.2003.10.018 fatcat:xrh6il4cm5duphutvoxjcg6kni

Information Theoretic and Security Analysis of a 65-Nanometer DDSLL AES S-Box [chapter]

Mathieu Renauld, Dina Kamel, François-Xavier Standaert, Denis Flandre
2011 Lecture Notes in Computer Science  
In this paper, we complement this work by analyzing an implementation of the AES S-box, in the DDSLL dual-rail logic style, using the same 65-nanometer technology.  ...  We take advantage of state-of-the-art evaluation tools, and discuss the quantity and nature (e.g. linearity) of the physical information they provide.  ...  As illustrated in Figure 1 , the internal clock of the DDSLL logic is driven from gate to gate, without any buffer added, and the block responsible of this derivation is Note that the balanced routing  ... 
doi:10.1007/978-3-642-23951-9_15 fatcat:t2xxwhyo4jcbjdis4tkybvzj6m

Formalization of Linear Space Theory in the Higher-Order Logic Proving System

Jie Zhang, Danwen Mao, Yong Guan
2013 Journal of Applied Mathematics  
This paper presents the formalization of the linear space theory in HOL4. A set of properties is characterized in HOL4.  ...  Higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and stronger semantics. Higher-order logic is more expressive.  ...  Without loss of generality, we show the proof process for Property 1 (i.e., the element "zero" in a linear space is unique).  ... 
doi:10.1155/2013/218492 fatcat:4kjrlnyxlfb4zeh3gxe6wlygqy

Functorial Boxes in String Diagrams [chapter]

Paul-André Melliès
2006 Lecture Notes in Computer Science  
logic; second, we explain how the categorical semantics of linear logic induces that the exponential box of proof-nets decomposes as two enshrined functorial boxes.  ...  : C −→ D transports a trace operator from the category D to the category C, and we then exploit this to construct well-behaved fixpoint operators in cartesian closed categories generated by models of linear  ...  -This short tutorial was stimulated and inspired by discussions with Martin Hyland and Masahito Hasegawa on trace operators in models of linear logic, held during the summer 2005 and onwards.  ... 
doi:10.1007/11874683_1 fatcat:zphjcspjybch7ax6wqx7jox6vy

Linear Approximation of Semi-algebraic Spatial Databases Using Transitive Closure Logic, in Arbitrary Dimension [chapter]

Floris Geerts
2002 Lecture Notes in Computer Science  
Since both the encoding and decoding between a linear spatial database and this finite representation are expressible in FO+TCS, we may conclude the completeness of this logic on linear spatial databases  ...  The completeness of this logic on all linear spatial databases, is then obtained using a finite representation of these databases given by Vandeurzen et al. [20].  ...  It is an interesting question whether there exists natural extensions of FO, which can compute a finite representation of semi-algebraic spatial databases, without the deviation to the linear case.  ... 
doi:10.1007/3-540-46093-4_11 fatcat:q5uf5lnvgvdinhr6i4e2ob7kwu
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