Clément Aubert

Characterizing co-NL by a group action

In a recent paper, Girard ( 2012 ) proposed to use his recent construction of a geometry of interaction in the hyperfinite factor (Girard 2011 ) in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girards definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce the non-deterministic pointer machine as a technical tool, a concrete model to compute algorithms.

Logarithmic space and permutations

In a recent work, Girard proposed a new and innovative approach to computational complexity based on the proofs-as-programs correspondence. In a previous paper, the authors showed how Girards proposal succeeds in obtaining a new characterization of co-NL languages as a set of operators acting on a Hilbert Space. In this paper, we extend this work by showing that it is also possible to define a set of operators characterizing the class L of logarithmic space languages.

Logic Programming and Logarithmic Space

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a syntactic restriction, using an encoding of words that derives from proof theory.

Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction.

Unary Resolution: Characterizing Ptime

We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms. This construction stems from an interactive interpretation of the cut-elimination procedure of linear logic known as the geometry of interaction.

Reversible Barbed Congruence on Configuration Structures

A standard contextual equivalence for process algebras is strong barbed congruence. Configuration structures are a denotational semantics for processes in which one can define equivalences that are more discriminating, i.e. that distinguish the denotation of terms equated by barbed congruence. Hereditary history preserving bisimulation (HHPB) is such a relation. We define a strong back and forth barbed congruence using a reversible process algebra and show that the relation induced by the back and forth congruence is equivalent to HHPB, providing a contextual characterization of HHPB.

Sublogarithmic uniform Boolean proof nets

Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al. gave a logspace translation allowing us to compare their computational power as uniform complexity classes. This paper presents a novel translation in AC0 and focuses on a simpler restricted notion of uniform Boolean proof nets. We can then encode constant-depth circuits and compare complexity classes below logspace, which were out of reach with the previous translations.

Performing pull-ups with small climbing holds influences grip and biomechanical arm action

ABSTRACT Pull-ups are often used by sport-climbers and other athletes to train their arm and back muscle capabilities. Sport-climbers use different types of holds to reinforce finger strength concomitantly. However, the effect of grip types on pull-up performance had not previously been investigated. A vertical force platform sensor measured the force exerted by climbers when performing pull-ups under six different grip conditions (gym-bar, large climbing hold, and four small climbing holds: 22mm, 18mm, 14mm, and 10mm). The electromyography of finger flexors and extensor muscles were recorded simultaneously. The maximal arm power and summed mechanical work were computed. The results revealed that the number of pull-ups, maximal power, and summed mechanical work decreased significantly with the size of the climbing hold used, even if no differences were found between a large climbing hold and a gym-bar. Electromyography of the forearm muscles revealed that the use of a climbing hold generated finger flexor fatigue and that the level of cocontraction was impacted by the different segment coordination strategies generated during the pull-ups. These findings are likely to be useful for quantifying training loads more accurately and designing training exercises and programs.