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2answers
42 views

What does least fix point and greatest fix point mean in Safety games

In safety games there are these mathematical notation about greatest fix points and least fix points but I don't get it. How would we describe them plain English without mathematical symbols.
-1
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1answer
68 views

Understanding the reason behind the μ (mu) operator [closed]

What is the purpose of the $\mu$ operator? Is there a real world example? Is it correct that it can create partial functions out of total functions and it makes a function $g$ with k parameters out ...
0
votes
0answers
79 views

Using the μ (mu) operator

Problem I've got this function: $f(x,y)=(6-3\cdot x)\cdot(y+2)$, with $(x,y)\in\mathbb{N}^2$ Now I have to find $g=\mu f$. Proposed solution My solution was to find the smallest $n\in\mathbb{N}$ ...
1
vote
1answer
57 views

Using diagonal argument to prove that $H(x) = \mu y T(x,x,y)$ has no total computable extension

Hello everyone just like the title says I want to prove that $H(x) = \mu y T(x,x,y)$ has no total computable extension such that if we had a function $BIG(x)$ that is both total and agrees with $H(x)$ ...
1
vote
2answers
242 views

The minimization operator is an effective operator

Assume $\{f_i^{(n)}\}_{i=0}^\infty$ is a Gödel enumeration of the $\mu$-recursive functions of $n$ arguments, such that the $S^m_n$ theorem and the universal function theorem hold. Denote the set of ...
0
votes
1answer
98 views

Techniques (tools) to convert temporal logic (CTL,CTL* or LTL) to μ-calculus formulae

Suppose one wants to use a μ-calculus model checker, but specify things in temporal logics, which is easier (more intuitive). Is there a technique (even better, a tool) that automatically translates ...
7
votes
3answers
762 views

Why use $\mu$-calculus and not LTL,CTL,CTL*?

It is known that the temporal logics LTL,CTL,CTL* can be translated/embedded into the $\mu$-calculus. In other words, the (modal) $\mu$-calculus subsumes these logics, (i.e. it is more expressive.) ...
2
votes
1answer
99 views

Have I got the right understanding of the mu operator?

I have a homework problem that says: For $g(x,y)=xy-5$ compute $h(x) = \mu y(g(x,y))$ and determine its domain. I was under the impression that this means the least y such that $g(x,y)=0$, so then ...
1
vote
1answer
233 views

Intuitive meaning of modal $\mu$-calculus formula

I am solving one of the past exams and I am not certain with my solution to one of the exercises. The exercise is asking to give intuitive meaning to modal $\mu$-calculus formula: $$ \phi = \mu Z. ...