10,622 research outputs found
The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)
We introduce a geometry of interaction model for Mazza's multiport
interaction combinators, a graph-theoretic formalism which is able to
faithfully capture concurrent computation as embodied by process algebras like
the -calculus. The introduced model is based on token machines in which
not one but multiple tokens are allowed to traverse the underlying net at the
same time. We prove soundness and adequacy of the introduced model. The former
is proved as a simulation result between the token machines one obtains along
any reduction sequence. The latter is obtained by a fine analysis of
convergence, both in nets and in token machines
The Geometry of Synchronization (Long Version)
We graft synchronization onto Girard's Geometry of Interaction in its most
concrete form, namely token machines. This is realized by introducing
proof-nets for SMLL, an extension of multiplicative linear logic with a
specific construct modeling synchronization points, and of a multi-token
abstract machine model for it. Interestingly, the correctness criterion ensures
the absence of deadlocks along reduction and in the underlying machine, this
way linking logical and operational properties.Comment: 26 page
Relational type-checking for MELL proof-structures. Part 1: Multiplicatives
Relational semantics for linear logic is a form of non-idempotent
intersection type system, from which several informations on the execution of a
proof-structure can be recovered. An element of the relational interpretation
of a proof-structure R with conclusion acts thus as a type (refining
) having R as an inhabitant. We are interested in the following
type-checking question: given a proof-structure R, a list of formulae ,
and a point x in the relational interpretation of , is x in the
interpretation of R? This question is decidable. We present here an algorithm
that decides it in time linear in the size of R, if R is a proof-structure in
the multiplicative fragment of linear logic. This algorithm can be extended to
larger fragments of multiplicative-exponential linear logic containing
-calculus
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.
We show how unification can be used to build a model of computation by means
of specific subalgebras associated to finite permutations groups. We then prove
that whether an observation (the algebraic counterpart of a program) accepts a
word can be decided within logarithmic space. We also show that the
construction can naturally represent pointer machines, an intuitive way of
understanding logarithmic space computing
Physical Primitive Decomposition
Objects are made of parts, each with distinct geometry, physics,
functionality, and affordances. Developing such a distributed, physical,
interpretable representation of objects will facilitate intelligent agents to
better explore and interact with the world. In this paper, we study physical
primitive decomposition---understanding an object through its components, each
with physical and geometric attributes. As annotated data for object parts and
physics are rare, we propose a novel formulation that learns physical
primitives by explaining both an object's appearance and its behaviors in
physical events. Our model performs well on block towers and tools in both
synthetic and real scenarios; we also demonstrate that visual and physical
observations often provide complementary signals. We further present ablation
and behavioral studies to better understand our model and contrast it with
human performance.Comment: ECCV 2018. Project page: http://ppd.csail.mit.edu
The Geometry of Interaction of Differential Interaction Nets
The Geometry of Interaction purpose is to give a semantic of proofs or
programs accounting for their dynamics. The initial presentation, translated as
an algebraic weighting of paths in proofnets, led to a better characterization
of the lambda-calculus optimal reduction. Recently Ehrhard and Regnier have
introduced an extension of the Multiplicative Exponential fragment of Linear
Logic (MELL) that is able to express non-deterministic behaviour of programs
and a proofnet-like calculus: Differential Interaction Nets. This paper
constructs a proper Geometry of Interaction (GoI) for this extension. We
consider it both as an algebraic theory and as a concrete reversible
computation. We draw links between this GoI and the one of MELL. As a
by-product we give for the first time an equational theory suitable for the GoI
of the Multiplicative Additive fragment of Linear Logic.Comment: 20 pagee, to be published in the proceedings of LICS0
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