The search session has expired. Please query the service again.
Coalgebras for an endofunctor provide a category theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra...
Given a groupoid , and , we say that is antiassociative if an only if for all , and are never equal. Generalizing this, is -antiassociative if and only if for all , any two distinct expressions made by putting parentheses in are never equal. We prove that for every , there exist finite groupoids that are -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.
Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification of the algorithm...
Natural algorithms to compute rational expressions for recognizable
languages, even those which work well in practice, may produce very long
expressions. So, aiming towards the computation of the commutative image of a
recognizable language, one should avoid passing through an expression
produced this way.
We modify here one of those algorithms in
order to compute directly a semilinear expression for the commutative image
of a recognizable language. We also give a second
modification of the algorithm...
Formalization of a part of [11]. Unfortunately, not all is possible to be formalized. Namely, in the paper there is a mistake in the proof of Lemma 3. It states that there exists x ∈ M1 such that M1(x) > N1(x) and (∀y ∈ N1)x ⊀ y. It should be M1(x) ⩾ N1(x). Nevertheless we do not know whether x ∈ N1 or not and cannot prove the contradiction. In the article we referred to [8], [9] and [10].
We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are established and applied to the one-way two-party communication complexity of symmetric Boolean functions. It is shown that the number of required communication bits does not depend on the communication direction, provided that neither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient...
We study deterministic one-way communication complexity
of functions with Hankel communication matrices.
Some structural properties of such matrices are established
and applied to the one-way two-party communication complexity
of symmetric Boolean functions.
It is shown that the number of required communication bits
does not depend on the communication direction, provided that
neither direction needs maximum complexity.
Moreover, in order to obtain an optimal protocol, it is
in any case sufficient...
Currently displaying 1 –
20 of
24