4 research outputs found
The quotient in preorder theories
Seeking the largest solution to an expression of the form Ax 64 B is a common task in several domains of engineering and computer science. This largest solution is commonly called quotient. Across domains, the meanings of the binary operation and the preorder are quite different, yet the syntax for computing the largest solution is remarkably similar. This paper is about finding a common framework to reason about quotients. We only assume we operate on a preorder endowed with an abstract monotonic multiplication and an involution. We provide a condition, called admissibility, which guarantees the existence of the quotient, and which yields its closed form. We call preordered heaps those structures satisfying the admissibility condition. We show that many existing theories in computer science are preordered heaps, and we are thus able to derive a quotient for them, subsuming existing solutions when available in the literature. We introduce the concept of sieved heaps to deal with structures which are given over multiple domains of definition. We show that sieved heaps also have well-defined quotients
The Quotient in Preorder Theories
Seeking the largest solution to an expression of the form A x <= B is a
common task in several domains of engineering and computer science. This
largest solution is commonly called quotient. Across domains, the meanings of
the binary operation and the preorder are quite different, yet the syntax for
computing the largest solution is remarkably similar. This paper is about
finding a common framework to reason about quotients. We only assume we operate
on a preorder endowed with an abstract monotonic multiplication and an
involution. We provide a condition, called admissibility, which guarantees the
existence of the quotient, and which yields its closed form. We call preordered
heaps those structures satisfying the admissibility condition. We show that
many existing theories in computer science are preordered heaps, and we are
thus able to derive a quotient for them, subsuming existing solutions when
available in the literature. We introduce the concept of sieved heaps to deal
with structures which are given over multiple domains of definition. We show
that sieved heaps also have well-defined quotients.Comment: In Proceedings GandALF 2020, arXiv:2009.0936
Timed Modal Logics for Real-Time Systems - Specification, Verification and Control.
International audienceIn this paper, a timed modal logic Lc is presented for the specification and verification of real-time systems. Several important results for Lc are discussed. First we address the model checking problem and we show that it is an EXPTIME-complete problem. Secondly we consider expressiveness and we explain how to express strong timed bisimilarity and how to build characteristic formulas for timed automata. We also propose a compositional algorithm for Lc model checking. Finally we consider several control problems for which Lc can be used to check controllability