3,820 research outputs found
Action Type Geometrical Equivalence of Representations of Groups
For every variety of algebras and every algebras in these variety we can
consider an algebraic geometry. Algebras may be many sorted (not necessarily
one sorted) algebras. A set of sorts is fixed for each variety. This theory can
be applied to the variety of representations of groups over fixed commutative
ring with unit. We consider a representation as two sorted algebra. We
concentrate on the case of the action type algebraic geometry of
representations of groups. In this case algebraic sets are defined by systems
of action type equations and equations in the acting group are not considered.
This is the special case, which cannot be deduced from the general theory. In
this paper the following basic notions are introduced: action type geometrical
equivalence of two representations, action type quasi-identity in
representations, action type quasi-variety of representations, action type
Noetherian variety of representations, action type geometrically Noetherian
representation, action type logically Noetherian representation.Comment: 35 page
A Model of Cooperative Threads
We develop a model of concurrent imperative programming with threads. We
focus on a small imperative language with cooperative threads which execute
without interruption until they terminate or explicitly yield control. We
define and study a trace-based denotational semantics for this language; this
semantics is fully abstract but mathematically elementary. We also give an
equational theory for the computational effects that underlie the language,
including thread spawning. We then analyze threads in terms of the free algebra
monad for this theory.Comment: 39 pages, 5 figure
Hilbert-Post completeness for the state and the exception effects
In this paper, we present a novel framework for studying the syntactic
completeness of computational effects and we apply it to the exception effect.
When applied to the states effect, our framework can be seen as a
generalization of Pretnar's work on this subject. We first introduce a relative
notion of Hilbert-Post completeness, well-suited to the composition of effects.
Then we prove that the exception effect is relatively Hilbert-Post complete, as
well as the "core" language which may be used for implementing it; these proofs
have been formalized and checked with the proof assistant Coq.Comment: Siegfried Rump (Hamburg University of Technology), Chee Yap (Courant
Institute, NYU). Sixth International Conference on Mathematical Aspects of
Computer and Information Sciences , Nov 2015, Berlin, Germany. 2015, LNC
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