14 research outputs found
On the Expressiveness of QCTL
QCTL extends the temporal logic CTL with quantification over atomic propositions. While the algorithmic questions for QCTL and its fragments with limited quantification depth are well-understood (e.g. satisfiability of QkCTL, with at most k nested blocks of quantifiers, is (k+1)-EXPTIME-complete), very few results are known about the expressiveness of this logic.
We address such expressiveness questions in this paper. We first consider the distinguishing power of these logics (i.e., their ability to separate models), their relationship with behavioural equivalences, and their ability to capture the behaviours of finite Kripke structures with so-called characteristic formulas. We then consider their expressive power (i.e., their ability to express a property), showing that in terms of expressiveness the hierarchy QkCTL collapses at level 2 (in other terms, any QCTL formula can be expressed using at most two nested blocks of quantifiers)
Is your Model Checker on Time? On the Complexity of Model Checking for Timed Modal Logics
This paper studies the structural complexity of model checkingfor (variations on) the specification formalisms used in the tools CMCand Uppaal, and fragments of a timed alternation-free mu-calculus. Foreach of the logics we study, we characterize the computational complexityof model checking, as well as its specification and program complexity,using timed automata as our system model
From Timed Automata to Logic - and Back
One of the most successful techniques for automatic verification is thatof model checking. For finite automata there exist since long extremelyefficient model-checking algorithms, and in the last few years these algorithms have been made applicable to the verification of real-time automata using the region-techniques of Alur and Dill.In this paper, we continue this transfer of existing techniques from thesetting of finite (untimed) automata to that of timed automata. In particular, a timed logic L is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic L formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for L with respect to given bounds on the number of clocks and constants of the timed automata to be constructed. None of these results have as yet been succesfully accounted for in the presence of time
The Power of Proofs: New Algorithms for Timed Automata Model Checking (with Appendix)
This paper presents the first model-checking algorithm for an expressive
modal mu-calculus over timed automata, , and reports performance results for an implementation.
This mu-calculus contains extended time-modality operators and can express all
of TCTL. Our algorithmic approach uses an "on-the-fly" strategy based on proof
search as a means of ensuring high performance for both positive and negative
answers to model-checking questions. In particular, a set of proof rules for
solving model-checking problems are given and proved sound and complete; we
encode our algorithm in these proof rules and model-check a property by
constructing a proof (or showing none exists) using these rules. One noteworthy
aspect of our technique is that we show that verification performance can be
improved with \emph{derived rules}, whose correctness can be inferred from the
more primitive rules on which they are based. In this paper, we give the basic
proof rules underlying our method, describe derived proof rules to improve
performance, and compare our implementation of this model checker to the UPPAAL
tool.Comment: This is the preprint of the FORMATS 2014 paper, but this is the full
version, containing the Appendix. The final publication is published from
Springer, and is available at
http://link.springer.com/chapter/10.1007%2F978-3-319-10512-3_9 on the
Springer webpag
On the Expressiveness and Complexity of ATL
ATL is a temporal logic geared towards the specification and verification of
properties in multi-agents systems. It allows to reason on the existence of
strategies for coalitions of agents in order to enforce a given property. In
this paper, we first precisely characterize the complexity of ATL
model-checking over Alternating Transition Systems and Concurrent Game
Structures when the number of agents is not fixed. We prove that it is
\Delta^P_2 - and \Delta^P_?_3-complete, depending on the underlying multi-agent
model (ATS and CGS resp.). We also consider the same problems for some
extensions of ATL. We then consider expressiveness issues. We show how ATS and
CGS are related and provide translations between these models w.r.t.
alternating bisimulation. We also prove that the standard definition of ATL
(built on modalities "Next", "Always" and "Until") cannot express the duals of
its modalities: it is necessary to explicitely add the modality "Release"
The Twentieth Century
Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic model-checking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one-clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that, for one-clock probabilistic timed automata, the model-checking problem for the probabilistic timed temporal logic PTCTL is EXPTIME-complete. However, the model-checking problem for the subclass of PTCTL which does not permit both punctual timing bounds, which require the occurrence of an event at an exact time point, and comparisons with probability bounds other than 0 or 1, is PTIME-complete for one-clock probabilistic timed automata
Model Checking Probabilistic Timed Automata with One or Two Clocks
Probabilistic timed automata are an extension of timed automata with discrete
probability distributions. We consider model-checking algorithms for the
subclasses of probabilistic timed automata which have one or two clocks.
Firstly, we show that PCTL probabilistic model-checking problems (such as
determining whether a set of target states can be reached with probability at
least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for
one-clock probabilistic timed automata, and are EXPTIME-complete for
probabilistic timed automata with two clocks. Secondly, we show that, for
one-clock probabilistic timed automata, the model-checking problem for the
probabilistic timed temporal logic PCTL is EXPTIME-complete. However, the
model-checking problem for the subclass of PCTL which does not permit both
punctual timing bounds, which require the occurrence of an event at an exact
time point, and comparisons with probability bounds other than 0 or 1, is
PTIME-complete for one-clock probabilistic timed automata
Temporal Logic with Forgettable Past
We investigate NLTL, a linear-time temporal logic with forgettable past. NLTL can be exponentially more succinct than LTL Past (which in turn can be more succinct than LTL). We study satisfiability and model checking for NLTL and provide optimal automata-theoretic algorithms for these EXPSPACE-complete problems
Modd checking probabilistic timed automata with one or two clocks
Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider model-checking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic model-checking problems (such as determining whether it set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIME-complete for one clock probabilistic timed automata, and are EXPTIME-complete for probabilistic timed automata with two clocks. Secondly, we show that the model-checking problem for the probabilistic timed temporal logic PTCTL is EXPTIME-complete for one clock probabilistic timed automata. However, the corresponding model-checking problem for the subclass of PTCTL which does not permit both (1) punctual timing bounds, which require the occurrence of an event at an exact time point, and (2) comparisons with probability bounds other than 0 or 1, is PTIME-complete