# Questions tagged [linear-temporal-logic]

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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### Validity of □(P→ Q) → (◊P → ◊Q) in linear temporal logic

How can I prove that $\Box(P\rightarrow Q)\rightarrow (\Diamond P\rightarrow\Diamond Q)$ is valid in linear temporal logic (LTL)?
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### distinguishing between CTL* formulas $A[FG p]$ and $AFAG p$ using transition system

It is to show, using a transition system, that the two formulas $A[FG p]$ and $AFAG p$ are not equivalent. For me, it seems strange that they are not equivalent. As the first one says that any ...
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### Linear Temporal Logic (LTL) Syntax Infinitely Often

I'm a little confused about some LTL syntax. When the Global and Future operator (GFx) or []<>x is used, what does it mean. In the lecture slides it is given as infinitely often. But I don't ...
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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 ...
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### Writing LTL formula for sequencing with coordination

Suppose there are 2 workers w1 and w2 who can cool a hot iron. So if iron is hot (denoted by atomic proposition ...
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### How to graph search a LTL-generated Buchi automaton to generate valid execution paths

I have a set of tasks, and a LTL specification that describes which orders of the tasks are legal. I want to find a way to enumerate all permutations of the tasks that meet the specification. For ...
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### Proving the equivalence of an LTL and a CTL formula

For a lecture I am attending, we have to prove that $$\forall \big(a \textsf{U} (b \land \forall \square a)\big) \equiv \big(a \textsf{U} (b \land \square a)\big).$$ That is, we need to prove that ...
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### What is this operator in “The Temporal Logic of Programs” Pnueli 1977?

In The Temporal Logic of Programs there is an operator first appearing on page 3 (48) under "Partial Correctness" that looks like an elongated super set symbol. What is it?
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### Show the formula is a law of LTL

Show that the following formula is a law of LTL, i. e. the formula is satisfied on all paths in all models G(p → X q) ∧ G(q → F p) ∧ p → G F p I dont know how ...
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### Unable to have an equivalent of A(FG p) and AG(EF p)

It states in my lecture notes that there is no CTL formula that is equivalent to A(FG p) in LTL and likewise, there is no LTL formula that is equivalent to CTL formula AG(EF p). I am just starting to ...
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### LTL to GBA versus LTL to BA

Let's assume that I have an LTL formula and I want to convert it to a Buchi automaton. For which fragment of LTL, GBA is more succinct and for which fragment BA has the same size as GBA.
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### Linear Temporal Logic with non-Boolean propositions (e.g. Integers)?

LTL works with Boolean propositions. People probably studied extensions to non-Boolean propositions... Do you know a good starting reference? (I am aware of STL, but it also seems to talk about ...
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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 assertions below 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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### 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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### 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:...