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Questions tagged [computation-tree-logic]

39 questions
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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.) Could you please explain/point me to papers/books…
Dimiter
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How can I decide manually whether two CTL formulae are equivalent?

Assume I have two formulae $\Phi$ and $\Psi$ (over the same set of atomic propositions $AP$) in CTL. We have that $\Phi \equiv \Psi$ iff $Sat_{TS}(\Phi) = Sat_{TS}(\Psi)$ for all transition systems $TS$ over $AP$. Given that there are infinitely…
bitmask
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Least fix point of CTL formula

In the book Logic in Computer Science on page 244, there is a proof that $[[E(\phi U\psi)]]$ is the least fixed point of $G(X)=[[\psi]] \cup ([[\phi]]\cap\mathop{\textrm{pre}}_\exists(X))$. I don't get the idea of point 2. I tried to understand why…
nrofis
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1 answer

CTL* query evaluation order

I'm currently trying to evaluate a CTL* expression and am not sure how to stepwisely evaluate the queries. For example I have EFG p. This means something like 'there is a path where eventually there exists a state s where from there on, globally p…
hubsi
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3
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1 answer

What does "AF AX p" mean in CTL?

Both Logic in Computer Science (Huth and Ryan, 2004) and Branching vs. Linear Time: Final Showdown (Vardi, 2002), state something to this effect (paraphrased): In LTL, X F p and F X p are equivalent, meaning "p is eventually true in some state that…
Lee Sleek
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3
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1 answer

CTL trouble translating text into formula

I have an excercise where I have to translate verbally formulated statements into CTL formulas. I have particularly trouble with this one: On every path q is true at least once and p was true sometime before, after no longer. My attempt is the…
Iwan5050
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How do you correctly write this sentence as a CTL formula?

Sentence: From every reachable state it is possible to reach a state where $p$ is true. How do you write this sentence as a CTL formula? So far I only dealt with CTL syntax and trees but maybe it will also be asked in a test how you convert a…
tenepolis
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How to express the existence of winning strategy of the starter of a game in temporal logic?

Consider a two-player game. A winning strategy of a player is a strategy following which the player can always beat his opponent, no matter how his opponent responds. A game can be unfolded to a state space consisting of the possible ways of both…
hengxin
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Convert CTL* formula to CTL

I have a CTL* formula: $\mathsf{EF}[p\land \mathsf{AX}[q\ \mathsf{U}\ r]]$ but in my application, I am limited to CTL. To my understanding, this formula is no valid CTL and I wonder whether I can transform it (preserving semantic, of course). The…
user13397
2
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1 answer

Why is $AF \phi \lor \varphi$ not equivalent to $AF \phi \lor AF \varphi$?

Can someone explain to me (perhaps with an example) why $AF (\phi \lor \varphi)$ is not equivalent to $AF \phi \lor AF \varphi$. This seems counter-intuitive, because in any path where $\phi$ (or $\varphi$) is true, $\phi \lor \varphi$ is true as…
Robin Haveneers
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Intuition behind straight-line programs

Wikipedia defines straight-line programs in the following manner: In mathematics, more specifically in computational algebra[disambiguation needed], a straight-line program (SLP) for a finite group G = 〈S〉 is a finite sequence L of elements of G…
Mike Battaglia
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CTL vs LTL - when a formula satisfy a model

I'm trying to understand the difference between LTL and CTL. In particular, i'm trying to understand when a model (a transition system eg. Kripke structure) satisfy a formula. This is my point of view: a model satisfy an LTL formula if an only if…
Fabrizio Duroni
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Transition systems that satisfy LTL but not CTL, and vice versa

I am learning about temporal logic and model checking systems. One conceptual exercise that I am struggling with is how to create a transition system which satisfies only one of two given properties, when one is in LTL and one is in CTL. For…
KJ50
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Is there any open-source tools for verifying TCTL formulae over timed automata can be imported into my project?

In my project, there is one important step to automatically verify a timed automata with TCTL formulae. I briefly surveyed the tool UPPAAL that provides a GUI to construct a timed automata and to specify CTL formulae. However, I didn't find the api…
Yiling Yang
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Can CTL* express every model's behaviour

CTL* as in https://en.wikipedia.org/wiki/CTL*, is a logic that combines CTL and LTL. I know that CTL* can express everything expressible in these two languages and more. My question is whether we can model the computation tree of each LTS with CTL*
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