Questions tagged [mu-calculus]

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Is every countable, finite-branching LTS bisimilar to a tree?

Let $L$ be a finite set of labels, and let $\mathcal{C}$ be the set of finitely-branching transition systems labeled by $L$ and with a countable set of states. Let $\sim$ denote the bisimulation ...
2
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1answer
138 views

Is modal $\mu$-calculus “equivalent” to bisimulation?

I know that propositional modal $\mu$-calculus $L\mu$ is bisimulation-invariant. However, I'm curious to what degree it captures bisimulation. Q1: Given two labeled transition systems $T_1$, $T_2$ ...
1
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2answers
2k views

LTL property - safety or liveness?

How can I check if an LTL (Linear Temporal Logic) property is safety or liveness? Is it right to say that a property is safety OR liveness (or neither)? How can I evaluate this: ...
9
votes
1answer
1k views

CTL* and mu-calculus

it is well known that the modal $\mu$-calculus is one of the most expressive temporal logics for expressing properties of trees/graphs, and that CTL* is strictly less expressive than the $\mu$-...
6
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2answers
218 views

Fragments of the mu calculus

I would like to know if somebody has studied the following very simple fragment of the modal mu-calculus: $$F::= X \;| \; p \; | \; F \wedge G \; | \; [a]F \; | \; \nu X.F$$ where p ranges over ...
3
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2answers
2k views

What are “$\mu$-recursive functions” and $\mu$-calculus?

I saw in this question a reference to $\mu$-recursive functions or $\mu$-calculus as some computation model equivalent to Turing machines and $\lambda$-calculus. I know about these two but never heard ...
6
votes
1answer
499 views

Books on Mu-Calculus

I need a book on Mu-Calculus with lots of examples that can be used for self-study and preparation for exams.