# Questions tagged [mu-calculus]

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### First-order linear mu-calculus?

There is linear $\mu$-calculus (see e.g. ) and first-order $\mu$-calculus (see e.g. here). Has anybody studied first-order linear $\mu$-calculus? : Christian Dax, Martin Hofmann, Martin Lange: A ...
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### Generalization of computability to continuous for loops? [closed]

A computable function, formulated in the sense of mu recursion, can compute a for or do loop over some (possibly infinite) integer range. I was wondering if a suitable generalization exists that ...
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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 ...
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### 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 $T_1$, $T_2$ ...
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### 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: ...
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### 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 $\mu$-...
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### 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 ...
### 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 ...