A Calculus of Looping Sequences with Local Rules

TL;DR

This paper introduces an extended version of the Calculus of Looping Sequences with local rules that are compartment-specific and dynamic, along with a parallel semantics and a type system to ensure rule consistency, demonstrated through cellular interaction modeling.

Contribution

It presents a novel variant of CLS with local, dynamic rules and a parallel semantics, along with a type system to enforce compartment-specific rule properties.

Findings

Local rules can be added, moved, and erased dynamically.

Parallel semantics allow multiple rules to be applied simultaneously.

Modeling cellular interactions demonstrates the calculus's applicability.

Abstract

In this paper we present a variant of the Calculus of Looping Sequences (CLS for short) with global and local rewrite rules. While global rules, as in CLS, are applied anywhere in a given term, local rules can only be applied in the compartment on which they are defined. Local rules are dynamic: they can be added, moved and erased. We enrich the new calculus with a parallel semantics where a reduction step is lead by any number of global and local rules that could be performed in parallel. A type system is developed to enforce the property that a compartment must contain only local rules with specific features. As a running example we model some interactions happening in a cell starting from its nucleus and moving towards its mitochondria.