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# Tag Info

Accepted

### Do past time LTL and future time LTL have the same expressiveness?

The quick summary is that LTL with only past and no future modalities defines properties expressed over finite-words and these are the star-free subset of the regular languages. Standard LTL when ...
• 12.3k
Accepted

### CTL and LTL logic difference

There are already some rather good related answers regarding LTL versus CTL. In a nutshell, LTL is first and foremost a logic of traces, and an LTL formula is true for a transition system $S$ if and ...
• 2,470

### Do past time LTL and future time LTL have the same expressiveness?

The logics are expressively the same, though past operators make LTL exponentially more succinct. You can start here, from which there are references.
• 5,261

### LTL property - safety or liveness?

Your first question is answered in this paper: https://www.cs.cornell.edu/fbs/publications/RecSafeLive.pdf Given an LTL formula, translate it into a Büchi automaton, and remove states that have ...
• 1,175
Accepted

### Calculating least fixed points in equations

In general, we look at fixed-points of monotone functions over lattices, i.e. with some partial ordering over your elements. If your lattice is complete (it has a least and greatest element, called a ...
• 2,724
Accepted

### Are both safety and liveness properties closed under finite intersection?

Safety properties are closed under finite intersection. This can be seen by following Alpern and Schneider's characterisation which showed that safety properties are limit-closed when viewed ...
• 800
Accepted

### Is every countable, finite-branching LTS bisimilar to a tree?

Q1: Yes, every LTS is bisimilar to its unfolding, which is a tree. Q2: No, by a cardinality argument. For instance take infinite binary trees with $L=\{a,b\}$. Each tree has countable set of states ...
• 7,643

• 3,314

### Equivalent formula for LTL with and without past operators

The "equally expressive" statement means that if a formula of PLTL is a statement about the future, i.e. if it's evaluated at the first instant $0$ of the time domain $\mathbb N$, then there exists an ...
• 7,643

### resolution based theorem prover for temporal logic

Your translation goes into Presburger arithmetic, which is decidable. You could take your translated formula, do quantifier elimination on it, and then hand it over to a proof-producing SMT solver. ...
• 31.6k
1 vote
Accepted

### Linear temporal logic in computational trees

This question should (and will) probably be migrated to cs.se. In the meantime, consider the computation tree of the depicted structure: in almost all paths, $p$ is seen only finitely often, making ...
• 5,261
1 vote

### Algorithms to synthesize optimal plans satisfying temporal logic constraints

Maybe take a look at http://www.syntcomp.org/ This is a competition of tools solving the LTL synthesis problem (and some related problems).
• 366
1 vote

### Are there temporal logics linear time properties that only have counterexamples that are more complex than a lasso?

I think it depends on what you mean by linear-time temporal logics. If you mean temporal logics that have linear time semantics (i.e. cannot distinguish more than trace equivalence, a la van Glabbeek) ...
• 366
1 vote

### Reference for CTL* logic

See Venema, Yde. Temporal Logic. The blackwell guide to Philosophical Logic.
1 vote
Accepted

### LTL property - safety or liveness?

To answer your second question: there is one property that is both safety and liveness: True. With this exception, however, it is fair to say that a property is either safety or liveness or neither. "...
• 366

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