270 research outputs found
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
ATLsc with partial observation
Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful
formalism for expressing properties of multi-agent systems: it extends CTL with
strategy quantifiers, offering a convenient way of expressing both
collaboration and antagonism between several agents. Incomplete observation of
the state space is a desirable feature in such a framework, but it quickly
leads to undecidable verification problems. In this paper, we prove that
uniform incomplete observation (where all players have the same observation)
preserves decidability of the model-checking problem, even for very expressive
logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53
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
Counting LTL
The original publication is available at ieeexplore.ieee.org.International audienceThis paper presents a quantitative extension for the linear-time temporal logic LTL allowing to specify the number of states satisfying certain sub-formulas along paths. We give decision procedures for the satisfiability and model checking of this new temporal logic and study the complexity of the corresponding problems. Furthermore we show that the problems become undecidable when more expressive constraints are considered
Modal Logics for Timed Control
International audienceIn this paper we use the timed modal logic to specify control objectives for timed plants. We show that the control problem for a large class of objectives can be reduced to a model-checking problem for an extension () of the logic Lnu with a new modality. More precisely we define a fragment of , namely , such that any control objective of can be translated into a formula that holds for the plant if and only if there is a controller that can enforce the control objective. We also show that the new modality of strictly increases the expressive power of while model-checking of Lc remains EXPTIME-complete
Counting CTL
The original publication is available at www.springerlink.com.International audienceThis paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations of Boolean and arithmetic operations allowed in constraints, one obtains several distinct logics generalizing CTL. We provide a thorough analysis of their expressiveness and of the complexity of their model-checking problem (ranging from P-complete to undecidable)
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