8,486 research outputs found
Operators with smooth functional calculi
We introduce a class of (tuples of commuting) unbounded operators on a Banach
space, admitting smooth functional calculi, that contains all operators of
Helffer-Sj\"ostrand type and is closed under the action of smooth proper
mappings. Moreover, the class is closed under tensor product of commuting
operators. In general an operator in this class has no resolvent in the usual
sense so the spectrum must be defined in terms of the functional calculus. We
also consider invariant subspaces and spectral decompositions
A criterion for separating process calculi
We introduce a new criterion, replacement freeness, to discern the relative
expressiveness of process calculi. Intuitively, a calculus is strongly
replacement free if replacing, within an enclosing context, a process that
cannot perform any visible action by an arbitrary process never inhibits the
capability of the resulting process to perform a visible action. We prove that
there exists no compositional and interaction sensitive encoding of a not
strongly replacement free calculus into any strongly replacement free one. We
then define a weaker version of replacement freeness, by only considering
replacement of closed processes, and prove that, if we additionally require the
encoding to preserve name independence, it is not even possible to encode a non
replacement free calculus into a weakly replacement free one. As a consequence
of our encodability results, we get that many calculi equipped with priority
are not replacement free and hence are not encodable into mainstream calculi
like CCS and pi-calculus, that instead are strongly replacement free. We also
prove that variants of pi-calculus with match among names, pattern matching or
polyadic synchronization are only weakly replacement free, hence they are
separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
Labelled Lambda-calculi with Explicit Copy and Erase
We present two rewriting systems that define labelled explicit substitution
lambda-calculi. Our work is motivated by the close correspondence between
Levy's labelled lambda-calculus and paths in proof-nets, which played an
important role in the understanding of the Geometry of Interaction. The
structure of the labels in Levy's labelled lambda-calculus relates to the
multiplicative information of paths; the novelty of our work is that we design
labelled explicit substitution calculi that also keep track of exponential
information present in call-by-value and call-by-name translations of the
lambda-calculus into linear logic proof-nets
Covering and gluing of algebras and differential algebras
Extending work of Budzynski and Kondracki, we investigate coverings and
gluings of algebras and differential algebras. We describe in detail the gluing
of two quantum discs along their classical subspace, giving a C*-algebra
isomorphic to a certain Podles sphere, as well as the gluing of
U_{\sqrt{q}}(sl_2)-covariant differential calculi on the discs.Comment: latex2e, 27 page
Expressiveness of Generic Process Shape Types
Shape types are a general concept of process types which work for many
process calculi. We extend the previously published Poly* system of shape types
to support name restriction. We evaluate the expressiveness of the extended
system by showing that shape types are more expressive than an implicitly typed
pi-calculus and an explicitly typed Mobile Ambients. We demonstrate that the
extended system makes it easier to enjoy advantages of shape types which
include polymorphism, principal typings, and a type inference implementation.Comment: Submitted to Trustworthy Global Computing (TGC) 2010
On conservativity of concurrent Haskell
The calculus CHF models Concurrent Haskell extended by concurrent, implicit futures. It is a process calculus with concurrent threads, monadic concurrent evaluation, and includes a pure functional lambda-calculus which comprises data constructors, case-expressions, letrec-expressions, and Haskellâs seq. Futures can be implemented in Concurrent Haskell using the primitive unsafeInterleaveIO, which is available in most implementations of Haskell. Our main result is conservativity of CHF, that is, all equivalences of pure functional expressions are also valid in CHF. This implies that compiler optimizations and transformations from pure Haskell remain valid in Concurrent Haskell even if it is extended by futures. We also show that this is no longer valid if Concurrent Haskell is extended by the arbitrary use of unsafeInterleaveIO
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