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

2007
*
Lecture Notes in Computer Science
*

We stress the importance of proof-nets from Light

doi:10.1007/978-3-540-73228-0_2
fatcat:7axovijfpfbbxhxe5umqljqnku
*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. ...##
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A Lightweight ISA Extension for AES and SM4
[article]

2020
*
arXiv
*
pre-print

The implementation contains depth- and size-optimized joint AES and SM4 S-

arXiv:2002.07041v5
fatcat:k5pkyohy35dmbmsw67fkvxwkri
*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. ...##
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Taming Modal Impredicativity: Superlazy Reduction
[chapter]

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. ...

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

2009
*
Lecture Notes in Computer Science
*

This fact motivates us to provide a possible encoding of planning problems in

doi:10.1007/978-3-642-00675-3_4
fatcat:yykw6lzx6jajrppkmhrw6e7rbm
*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*. ...##
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On the linear decoration of intuitionistic derivations

1995
*
Archive for Mathematical Logic
*

We de ne an optimal proof-by-proof embedding of intuitionistic sequent calculus into

doi:10.1007/bf02390456
fatcat:cpjegmb4ovdaveybvpvn3oh7da
*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*. ...##
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Linear logic

1987
*
Theoretical Computer Science
*

Following this basic discovery, a completely new approach to the whole area between constructive

doi:10.1016/0304-3975(87)90045-4
fatcat:2pz66b65i5fzjaggrqhwyeimki
*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*. ...##
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Size-Change Termination and Satisfiability for Linear-Time Temporal Logics
[chapter]

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. ...

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

2011
*
Lecture Notes in Computer Science
*

Elementary

doi:10.1007/978-3-642-25318-8_25
fatcat:bomvp25otnfxhnr7ck7udoaxda
*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. ...##
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Sharing Continuations: Proofnets for Languages with Explicit Control
[chapter]

2000
*
Lecture Notes in Computer Science
*

While Lamping's graphs and their variants encode an embedding of intuitionistic

doi:10.1007/3-540-46425-5_16
fatcat:3jevx7qevzahhehomccscbwvum
*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] . ...##
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Soft linear logic and polynomial time

2004
*
Theoretical Computer Science
*

We present a subsystem of second-order

doi:10.1016/s0304-3975(03)00523-1
fatcat:hm25sv3cjfbnhe6kn6jhw3uuru
*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. ...##
###
Soft linear logic and polynomial time

2004
*
Theoretical Computer Science
*

We present a subsystem of second-order

doi:10.1016/j.tcs.2003.10.018
fatcat:xrh6il4cm5duphutvoxjcg6kni
*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. ...##
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Information Theoretic and Security Analysis of a 65-Nanometer DDSLL AES S-Box
[chapter]

2011
*
Lecture Notes in Computer Science
*

In this paper, we complement this work by analyzing an implementation of the AES S-

doi:10.1007/978-3-642-23951-9_15
fatcat:t2xxwhyo4jcbjdis4tkybvzj6m
*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 ...##
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Formalization of Linear Space Theory in the Higher-Order Logic Proving System

2013
*
Journal of Applied Mathematics
*

This paper presents the formalization of the

doi:10.1155/2013/218492
fatcat:4kjrlnyxlfb4zeh3gxe6wlygqy
*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). ...##
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Functorial Boxes in String Diagrams
[chapter]

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. ...

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

2002
*
Lecture Notes in Computer Science
*

Since both the encoding and decoding between a

doi:10.1007/3-540-46093-4_11
fatcat:q5uf5lnvgvdinhr6i4e2ob7kwu
*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. ...
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