论文标题
卷积和并发
Convolution and Concurrency
论文作者
论文摘要
我们展示了并发的量子和同时的Kleene代数如何作为卷积代数$ q^x $ Q^x $ from thustures $ x $的函数以及两个三元关系，将关系互换法律满足并发量化的量子量或kleene代数$ q $。 $ Q $的元素可以理解为重量； case $ q = \ bool $对应于powerset提升。我们在$ x $中的关系属性与$ q $中的代数属性与$ q $的代数属性与$ q^x $的代数属性之间开发了对应理论，并在模态和子结构逻辑方面以及与操作员的布尔代数。作为示例，我们构建了$ q $加权单词，挖掘，posets，同构类别的同时定量和kleene代数的有限挖掘和pomsets。
We show how concurrent quantales and concurrent Kleene algebras arise as convolution algebras $Q^X$ of functions from structures $X$ with two ternary relations that satisfy relational interchange laws into concurrent quantales or Kleene algebras $Q$. The elements of $Q$ can be understood as weights; the case $Q=\bool$ corresponds to a powerset lifting. We develop a correspondence theory between relational properties in $X$ and algebraic properties in $Q$ and $Q^X$ in the sense of modal and substructural logics, and boolean algebras with operators. As examples, we construct the concurrent quantales and Kleene algebras of $Q$-weighted words, digraphs, posets, isomorphism classes of finite digraphs and pomsets.
