Sergio Ramírez

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set $\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. In particular, we show for $\mathbf{M}_n$, the discrete order of $n$ elements extended with top and bottom, $| \mathcal{E}(\mathbf{M}_n) | =n!\m...

Let $L$ be a distributive lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of finding $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ given $L$ and $f,g\in \mathcal{E}(L)$ as inputs. (1) We show that it can be solved in time $O(n)$ where $n=| L |$. The previous upper bound was $O(n^2)$. (2) We characterize t...

Let L be a distributive lattice and E(L) be the set of join endomorphisms of L. We consider the problem of finding f⊓E(L)g given L and f,g∈E(L) as inputs. (1) We show that it can be solved in time O(n) where n=|L|. The previous upper bound was O(n2). (2) We characterize the standard notion of distributed knowledge of a group as the greatest lower b...

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-pr...

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-pr...

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set \({\mathcal {E}}(L)\) of all join-endomorphisms of a given finite lattice \(L\). In particular, we show that when \(L\) is \(\mathbf {M}_n\), the discrete order of n elements extended with top and bottom, \(| {\mathcal...

This paper addresses the issue of specifying, simulating, and verifying reactive systems in rewriting logic. It presents an executable semantics for probabilistic, timed, and spatial concurrent constraint programming ---here called stochastic and spatial concurrent constraint systems (SSCC)--- in the rewriting logic semantic framework. The approach...

Process calculi provide a language in which the structure of terms represents the structure of processes together with an operational semantics to represent computational steps. This paper uses rewriting logic for specifying and analyzing a process calculus for concurrent constraint programming (\(\textsf {ccp}\)), combining spatial and real-time b...

This paper presents a case study on the formal specification of a cache coherence protocol and the verification of some of its safety properties. Cache coherence refers to the consistency between the contents of a memory resource shared by many processes, that can have read and write access, and each local copy of the memory contents. The protocol...