Log In Sign Up

"Most of" leads to undecidability: Failure of adding frequencies to LTL

by   Bartosz Bednarczyk, et al.

Linear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not yet fully explored. The main goal of this work is to study the effect of adding weak forms of percentage constraints (e.g. that most of the positions in the past satisfy a given condition, or that sigma is the most-frequent letter occurring in the past) to fragments of LTL. Such extensions could potentially be used for the verification of influence networks or statistical reasoning. Unfortunately, as we prove in the paper, it turns out that percentage extensions of even tiny fragments of LTL have undecidable satisfiability and model-checking problems. Our undecidability proofs not only sharpen most of the undecidability results on logics with arithmetics interpreted on words known from the literature, but also are fairly simple. We also show that the undecidability can be avoided by restricting the allowed usage of the negation, and briefly discuss how the undecidability results transfer to first-order logic on words.


page 1

page 2

page 3

page 4


First-order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications

Formalisms based on temporal logics interpreted over finite strict linea...

On Classical Decidable Logics extended with Percentage Quantifiers and Arithmetics

During the last decades, a lot of effort was put into identifying decida...

Two-variable logics with some betweenness relations: Expressiveness, satisfiability and membership

We study two extensions of FO2[<], first-order logic interpreted in fini...

Expressiveness and Decidability of Temporal Logics for Asynchronous Hyperproperties

Hyperproperties are properties of systems that relate different executio...

Model checking and model synthesisfrom partial models: a logic-based perspective

I consider the following generic scenario: an abstract model M of some '...

A first-order logic characterization of safety and co-safety languages

Linear Temporal Logic (LTL) is one of the most popular temporal logics, ...

Flow Logic

Flow networks have attracted a lot of research in computer science. Inde...