3 research outputs found
A Metric for Linear Temporal Logic
We propose a measure and a metric on the sets of infinite traces generated by
a set of atomic propositions. To compute these quantities, we first map
properties to subsets of the real numbers and then take the Lebesgue measure of
the resulting sets. We analyze how this measure is computed for Linear Temporal
Logic (LTL) formulas. An implementation for computing the measure of bounded
LTL properties is provided and explained. This implementation leverages SAT
model counting and effects independence checks on subexpressions to compute the
measure and metric compositionally
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