63,197 research outputs found
Recursive Session Types Revisited
Session types model structured communication-based programming. In
particular, binary session types for the pi-calculus describe communication
between exactly two participants in a distributed scenario. Adding sessions to
the pi-calculus means augmenting it with type and term constructs. In a
previous paper, we tried to understand to which extent the session constructs
are more complex and expressive than the standard pi-calculus constructs. Thus,
we presented an encoding of binary session pi-calculus to the standard typed
pi-calculus by adopting linear and variant types and the continuation-passing
principle. In the present paper, we focus on recursive session types and we
present an encoding into recursive linear pi-calculus. This encoding is a
conservative extension of the former in that it preserves the results therein
obtained. Most importantly, it adopts a new treatment of the duality relation,
which in the presence of recursive types has been proven to be quite
challenging.Comment: In Proceedings BEAT 2014, arXiv:1408.556
Trees from Functions as Processes
Levy-Longo Trees and Bohm Trees are the best known tree structures on the
{\lambda}-calculus. We give general conditions under which an encoding of the
{\lambda}-calculus into the {\pi}-calculus is sound and complete with respect
to such trees. We apply these conditions to various encodings of the
call-by-name {\lambda}-calculus, showing how the two kinds of tree can be
obtained by varying the behavioural equivalence adopted in the {\pi}-calculus
and/or the encoding
Supplementarity is Necessary for Quantum Diagram Reasoning
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and
quantum information processing. We prove that its \pi/4-fragment is not
complete, in other words the ZX-calculus is not complete for the so called
"Clifford+T quantum mechanics". The completeness of this fragment was one of
the main open problems in categorical quantum mechanics, a programme initiated
by Abramsky and Coecke. The ZX-calculus was known to be incomplete for quantum
mechanics. On the other hand, its \pi/2-fragment is known to be complete, i.e.
the ZX-calculus is complete for the so called "stabilizer quantum mechanics".
Deciding whether its \pi/4-fragment is complete is a crucial step in the
development of the ZX-calculus since this fragment is approximately universal
for quantum mechanics, contrary to the \pi/2-fragment. To establish our
incompleteness result, we consider a fairly simple property of quantum states
called supplementarity. We show that supplementarity can be derived in the
ZX-calculus if and only if the angles involved in this equation are multiples
of \pi/2. In particular, the impossibility to derive supplementarity for \pi/4
implies the incompleteness of the ZX-calculus for Clifford+T quantum mechanics.
As a consequence, we propose to add the supplementarity to the set of rules of
the ZX-calculus. We also show that if a ZX-diagram involves antiphase twins,
they can be merged when the ZX-calculus is augmented with the supplementarity
rule. Merging antiphase twins makes diagrammatic reasoning much easier and
provides a purely graphical meaning to the supplementarity rule.Comment: Generalised proof and graphical interpretation. 16 pages, submitte
Models and termination of proof reduction in the -calculus modulo theory
We define a notion of model for the -calculus modulo theory and
prove a soundness theorem. We then define a notion of super-consistency and
prove that proof reduction terminates in the -calculus modulo any
super-consistent theory. We prove this way the termination of proof reduction
in several theories including Simple type theory and the Calculus of
constructions
A Distribution Law for CCS and a New Congruence Result for the pi-calculus
We give an axiomatisation of strong bisimilarity on a small fragment of CCS
that does not feature the sum operator. This axiomatisation is then used to
derive congruence of strong bisimilarity in the finite pi-calculus in absence
of sum. To our knowledge, this is the only nontrivial subcalculus of the
pi-calculus that includes the full output prefix and for which strong
bisimilarity is a congruence.Comment: 20 page
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