2 research outputs found
Stellar Resolution: Multiplicatives
We present a new asynchronous model of computation named Stellar Resolution
based on first-order unification. This model of computation is obtained as a
formalisation of Girard's transcendental syntax programme, sketched in a series
of three articles. As such, it is the first step towards a proper formal
treatment of Girard's proposal to tackle first-order logic in a
proofs-as-program approach. After establishing formal definitions and basic
properties of stellar resolution, we explain how it generalises traditional
models of computation, such as logic programming and combinatorial models such
as Wang tilings. We then explain how it can represent multiplicative
proof-structures, their cut-elimination and the correctness criterion of Danos
and Regnier. Further use of realisability techniques lead to dynamic semantics
for Multiplicative Linear Logic, following previous Geometry of Interaction
models
Probabilistic Complexity Classes through Semantics
In a recent paper, the author has shown how Interaction Graphs models for linear logic can be used to obtain implicit characterisations of non-deterministic complexity classes. In this paper, we show how this semantic approach to Implicit Complexity Theory (ICC) can be used to characterise deterministic and probabilistic models of computation. In doing so, we obtain correspondences between group actions and both deterministic and probabilistic hierarchies of complexity classes. As a particular case, we provide the first implicit characterisations of the classes PLogspace (un-bounded error probabilistic logarithmic space) and PPtime (unbounded error probabilistic polynomial time