ترغب بنشر مسار تعليمي؟ اضغط هنا

On the word problem for SP-categories, and the properties of two-way communication

174   0   0.0 ( 0 )
 نشر من قبل Luigi Santocanale
 تاريخ النشر 2009
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

The word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly interpreted as processes which communicate by two-way channels. The maps of an SP-category may also be viewed as a proof theory for a simple logic with a game theoretic intepretation. The cut-elimination procedure for this logic determines equality only up to certain permuting



قيم البحث

اقرأ أيضاً

We develop a denotational semantics of Linear Logic with least and greatest fixed points in coherence spaces (where both fixed points are interpreted in the same way) and in coherence spaces with totality (where they have different interpretations). These constructions can be carried out in many different denotational models of LL (hypercoherences, Scott semantics, finiteness spaces etc). We also present a natural embedding of G{o}del System T in LL with fixed points thus enforcing the expressive power of this system as a programming language featuring both normalization and a huge expressive power in terms of data types.
209 - Bas Spitters 2016
Coquands cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. This paper contributes to the understand ing of this model. We make three contributions: 1. Johnstones topological topos was created to present the geometric realization of simplicial sets as a geometric morphism between toposes. Johnstone shows that simplicial sets classify strict linear orders with disjoint endpoints and that (classically) the unit interval is such an order. Here we show that it can also be a target for cubical realization by showing that Coquands cubical sets classify the geometric theory of flat distributive lattices. As a side result, we obtain a simplicial realization of a cubical set. 2. Using the internal `interval in the topos of cubical sets, we construct a Moore path model of identity types. 3. We construct a premodel structure internally in the cubical type theory and hence on the fibrant objects in cubical sets.
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differentia l categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.
Lovasz (1967) showed that two finite relational structures A and B are isomorphic if, and only if, the number of homomorphisms from C to A is the same as the number of homomorphisms from C to B for any finite structure C. Soon after, Pultr (1973) pro ved a categorical generalisation of this fact. We propose a new categorical formulation, which applies to any locally finite category with pushouts and a proper factorisation system. As special cases of this general theorem, we obtain two variants of Lovasz theorem: the result by Dvov{r}ak (2010) that characterises equivalence of graphs in the k-dimensional Weisfeiler-Leman equivalence by homomorphism counts from graphs of tree-width at most k, and the result of Grohe (2020) characterising equivalence with respect to first-order logic with counting and quantifier depth k in terms of homomorphism counts from graphs of tree-depth at most k. The connection of our categorical formulation with these results is obtained by means of the game comonads of Abramsky et al. We also present a novel application to homomorphism counts in modal logic.
It is well known that univalence is incompatible with uniqueness of identity proofs (UIP), the axiom that all types are h-sets. This is due to finite h-sets having non-trivial automorphisms as soon as they are not h-propositions. A natural question is then whether univalence restricted to h-propositions is compatible with UIP. We answer this affirmatively by constructing a model where types are elements of a closed universe defined as a higher inductive type in homotopy type theory. This universe has a path constructor for simultaneous partial univalent completion, i.e., restricted to h-propositions. More generally, we show that univalence restricted to $(n-1)$-types is consistent with the assumption that all types are $n$-truncated. Moreover we parametrize our construction by a suitably well-behaved container, to abstract from a concrete choice of type formers for the universe.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا