arXiv subjects

Thomas Seiller

Publications and source records attributed to Thomas Seiller.

39 records · Page 3Linked to original sources

arXiv2014

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 synctactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation.

cs.LO↗

arXiv2013

Fully-abstract concurrent games for pi

We define a semantics for Milner's pi-calculus, with three main novelties. First, it provides a fully-abstract model for fair testing equivalence, whereas previous semantics covered variants of bisimilarity and the may and must testing equivalences. Second, it is based on reduction semantics, whereas previous semantics were based on labelled transition systems. Finally, it has a strong game semantical flavor in the sense of Hyland-Ong and Nickau. Indeed, our model may both be viewed as an innocent presheaf semantics and as a concurrent game semantics.

cs.LO↗

arXiv2012

Interaction Graphs: Multiplicatives

We introduce a graph-theoretical representation of proofs of multiplicative linear logic which yields both a denotational semantics and a notion of truth. For this, we use a locative approach (in the sense of ludics) related to game semantics and the Danos-Regnier interpretation of GoI operators as paths in proof nets. We show how we can retrieve from this locative framework both a categorical semantics for MLL with distinct units and a notion of truth. Moreover, we show how a restricted version of our model can be reformulated in the exact same terms as Girard's latest geometry of interaction. This shows that this restriction of our framework gives a combinatorial approach to J.-Y. Girard's geometry of interaction in the hyperfinite factor, while using only graph-theoretical notions.

cs.LO↗