75 research outputs found
A minimalistic look at widening operators
We consider the problem of formalizing the familiar notion of widening in
abstract interpretation in higher-order logic. It turns out that many axioms of
widening (e.g. widening sequences are ascending) are not useful for proving
correctness. After keeping only useful axioms, we give an equivalent
characterization of widening as a lazily constructed well-founded tree. In type
systems supporting dependent products and sums, this tree can be made to
reflect the condition of correct termination of the widening sequence
Fr\'echet Quantum Supergroups
In this paper, we introduce Fr\'echet quantum supergroups and their
representations. By using the universal deformation formula of the abelian
supergroups R^{m|n} we construct various classes of Fr\'echet quantum
supergroups that are deformation of classical ones. For such quantum
supergroups, we find an analog of Kac-Takesaki operators that are superunitary
and satisfy the pentagonal relation.Comment: 21 pages, published versio
MARKETS, SOCIAL NORMS, AND GOVERNMENTS IN THE SERVICE OF ENVIRONMENTALLY SUSTAINABLE ECONOMIC DEVELOPMENT
Environmental Economics and Policy, International Development,
Absoluteness via Resurrection
The resurrection axioms are forcing axioms introduced recently by Hamkins and
Johnstone, developing on ideas of Chalons and Velickovi\'c. We introduce a
stronger form of resurrection axioms (the \emph{iterated} resurrection axioms
for a class of forcings and a given
ordinal ), and show that implies generic
absoluteness for the first-order theory of with respect to
forcings in preserving the axiom, where is a
cardinal which depends on ( if is any
among the classes of countably closed, proper, semiproper, stationary set
preserving forcings).
We also prove that the consistency strength of these axioms is below that of
a Mahlo cardinal for most forcing classes, and below that of a stationary limit
of supercompact cardinals for the class of stationary set preserving posets.
Moreover we outline that simultaneous generic absoluteness for
with respect to and for with respect to
with is in principle
possible, and we present several natural models of the Morse Kelley set theory
where this phenomenon occurs (even for all simultaneously). Finally,
we compare the iterated resurrection axioms (and the generic absoluteness
results we can draw from them) with a variety of other forcing axioms, and also
with the generic absoluteness results by Woodin and the second author.Comment: 34 page
Extensions of SystemC^FL for mixed-signal systems and formal verification
The formal language SystemC^FL is the formalization of SystemC. The language semantics of SystemC^FL was formally defined in a standard structured operational semantics (SOS) style. In this paper, we first provide an overview of the current status of the formal language SystemC^FL and show some practical applications of SystemC^FL.Then, we give an outline for the latest developments of SystemC^FL. These developments include extensions of SystemC^FL for modeling mixed-signal systems and formal verification
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