194 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
Model Checking One-clock Priced Timed Automata
We consider the model of priced (a.k.a. weighted) timed automata, an
extension of timed automata with cost information on both locations and
transitions, and we study various model-checking problems for that model based
on extensions of classical temporal logics with cost constraints on modalities.
We prove that, under the assumption that the model has only one clock,
model-checking this class of models against the logic WCTL, CTL with
cost-constrained modalities, is PSPACE-complete (while it has been shown
undecidable as soon as the model has three clocks). We also prove that
model-checking WMTL, LTL with cost-constrained modalities, is decidable only if
there is a single clock in the model and a single stopwatch cost variable
(i.e., whose slopes lie in {0,1}).Comment: 28 page
Pure Nash Equilibria in Concurrent Deterministic Games
We study pure-strategy Nash equilibria in multi-player concurrent
deterministic games, for a variety of preference relations. We provide a novel
construction, called the suspect game, which transforms a multi-player
concurrent game into a two-player turn-based game which turns Nash equilibria
into winning strategies (for some objective that depends on the preference
relations of the players in the original game). We use that transformation to
design algorithms for computing Nash equilibria in finite games, which in most
cases have optimal worst-case complexity, for large classes of preference
relations. This includes the purely qualitative framework, where each player
has a single omega-regular objective that she wants to satisfy, but also the
larger class of semi-quantitative objectives, where each player has several
omega-regular objectives equipped with a preorder (for instance, a player may
want to satisfy all her objectives, or to maximise the number of objectives
that she achieves.)Comment: 72 page
Game-based Synthesis of Distributed Controllers for Sampled Switched Systems
Switched systems are a convenient formalism for modeling physical processes interacting with a digital controller. Unfortunately, the formalism does not capture the distributed nature encountered e.g. in cyber-physical systems, which are organized as networks of elements interacting with local controllers. Most current methods for control synthesis can only produce a centralized controller, which is assumed to have complete knowledge of all the component states and can interact with all of them. In this paper, we consider a centralized-controller synthesis technique based on state-space decomposition, and use a game-based approach to extend it to a distributed framework
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)
On Termination for Faulty Channel Machines
A channel machine consists of a finite controller together with several fifo
channels; the controller can read messages from the head of a channel and write
messages to the tail of a channel. In this paper, we focus on channel machines
with insertion errors, i.e., machines in whose channels messages can
spontaneously appear. Such devices have been previously introduced in the study
of Metric Temporal Logic. We consider the termination problem: are all the
computations of a given insertion channel machine finite? We show that this
problem has non-elementary, yet primitive recursive complexity
Logical Forms of Chronicles
A chronicle is a temporal model introduced by Dousson et al. for situation recognition. In short, a chronicle consists of a set of events and a set of real-valued temporal constraints on the delays between pairs of events. This work investigates the relationship between chronicles and classical temporal-model formalisms, namely TPTL and MTL. More specifically, we answer the following question: is it possible to find an equivalent formula in such formalisms for any chronicle? This question arises from the observation that a single chronicle captures complex temporal behaviours, without imposing a particular order of the events in time.
For our purpose, we introduce the subclass of linear chronicles, which set the order of occurrence of the events to be recognized in a temporal sequence. Our first result is that any chronicle can be expressed as a disjunction of linear chronicles. Our second result is that any linear chronicle has an equivalent TPTL formula. Using existing expressiveness results between TPTL and MTL, we show that some chronicles have no equivalent in MTL. This confirms that the model of chronicle has interesting properties for situation recognition
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