# Tagged Questions

LTL (linear temporal logic or linear-time temporal logic) is a temporal logic that can encode assertions about the future of traces.

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### Size of parity automata and Buchi automata from linear time mu-calculus?

Given a linear time mu-calculus formula, there are many works on transforming the formula to Buchi or Parity automaton. Using the best algorithm, what is the size of the resulting Buchi automaton and ...
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### The difference between dynamic logic and temporal logic

To find the difference, I'd just encountered with below assertions about temporal logic in Wikipedia: another variant of modal logic sharing many common features with dynamic logic, differs from ...
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### How to prove LTL-formulas true for all paths?

I'm quoting a question from my homework which I don't understand its wording. Also, I'm not looking for an answer for my problem, I just want to be pointed at some articles/tutorials/reading/tips to ...
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### NuSMV : simple game modeling

I'm new to NuSMV and try to model this simple turn-based game. There are 10 bricks in a pile, each player can take 1-3 brick per turn, whoever take the last brick wins the game. Assume player A go ...
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### How BDI agent can select next step (action)?

I am reading now about BDI (Belief-Desire-Intention) agents. I guess that this type of agents is the most popular model of cognitive agents and agents of multi-agent systems. Of course I am reading ...
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### Counterexample for LTL - CTL equivalence [closed]

I have to find an example of a model where the LTL-formula $F G p \wedge F q$ is valid and the CTL-formula $EF AG p \wedge AF q$ is not valid. I found this example, but I'm not completely sure whether ...
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### BDI logic or KARO framework solver - are there solvers for any new logic?

I am reading about agent logics and especially affective agents. There are BDI logics and combination of logics called KARO framework that considers those questions. All those logics seem to be ...
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### Help understaning LTL formulae [closed]

I am studying Software Engineering and I have different LTL formulas for which I have to determine if they are valid, unsatisfiable or neither. Here are the formulas : (<>[]p ∧ <>[]q) → <>[...
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### How to express r-bounded waiting for $r=0,1,2$ in LTL and Promela?

How to express $r$-bounded waiting for $r=0,1,2$ in LTL? I'm having trouble expressing the above in LTL and translating it to Promela. I've already expressed starvation-free and mutual exclusion. ...
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### LTL properties in bounded model checking via assertions

Is there a way to check LTL properties in a bounded model checker? As an example, consider a liveness property ($G F p$ - always eventually $p$)? Suppose we have the following trivial program ...
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### Find equivalent LTL formula, without Y (Yesterday) operator. How can I handle first state?

The task is to find an equivalent LTL formula for $G(a \Rightarrow Yb)$, which doesn't contain the Y operator. My idea is to search for invalid path patterns with 2 $a$'s in a row, e.g. bbbbaab. ...
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### Given a set of LTL formulas, on which states does the Kripke structure hold? [closed]

I'm currently learning about LTL and CTL formulas and to get a better understanding I try to manually interpret the formulas over a given Kripke structure. Since I'm not 100% sure if my results are ...
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### A linear temporal property that represents this (basic) execution?

A question gives me a set of atomic propositions AP = {a, b, c}and asks me to give a linear temporal property that represents all executions over AP such that: (1) ...
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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:...
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### Given this transition system, for which states are these (very basic) LTL formulas fulfilled?

I missed a lot of lectures for this module due to surgery so I'm trying to teach it to myself now. This is the question I've been working on: First of all, would I be correct in saying that the LTL ...
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### Spot the formalism (some kind of process logic)

Consider the following specification technique. A specification consists of a finite set of triples $\langle C, A, C' \rangle$, where $A$ is the name of an action and $C, C'$ are conditions, that is, ...
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### Why is GFp -> GFq false in LTL, even though GFp and GFq are false?

Consider the Kripke structure:  \begin{array}{ccccccc} \to & (p, \neg q) & \to & (\neg p, \neg q) & \to & (\neg p, q) \\ & \circlearrowright & & \circlearrowright ...
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### Time to construct a GNBA for LTL formula

I have a problem with the proof for constructing a GNBA (generalized nondeterministic Büchi automaton) for a LTL formula: Theorem: For any LTL formula $\varphi$ there exists a GNBA $G_{\varphi}$ ...
### Equivalence of Büchi automata and linear $\mu$-calculus
It's a known fact that every LTL formula can be expressed by a Büchi $\omega$-automaton. But, apparently, Büchi automata are a more powerful, expressive model. I've heard somewhere that Büchi automata ...
Linear temporal logic and deterministic Büchi automata are incomparable: DBA cannot express $FGa$, and LTL cannot express "at least each odd letter is 'a'". But sometimes it is interesting to know ...