1,061 research outputs found
Model-checking Quantitative Alternating-time Temporal Logic on One-counter Game Models
We consider quantitative extensions of the alternating-time temporal logics
ATL/ATLs called quantitative alternating-time temporal logics (QATL/QATLs) in
which the value of a counter can be compared to constants using equality,
inequality and modulo constraints. We interpret these logics in one-counter
game models which are infinite duration games played on finite control graphs
where each transition can increase or decrease the value of an unbounded
counter. That is, the state-space of these games are, generally, infinite. We
consider the model-checking problem of the logics QATL and QATLs on one-counter
game models with VASS semantics for which we develop algorithms and provide
matching lower bounds. Our algorithms are based on reductions of the
model-checking problems to model-checking games. This approach makes it quite
simple for us to deal with extensions of the logical languages as well as the
infinite state spaces. The framework generalizes on one hand qualitative
problems such as ATL/ATLs model-checking of finite-state systems,
model-checking of the branching-time temporal logics CTL and CTLs on
one-counter processes and the realizability problem of LTL specifications. On
the other hand the model-checking problem for QATL/QATLs generalizes
quantitative problems such as the fixed-initial credit problem for energy games
(in the case of QATL) and energy parity games (in the case of QATLs). Our
results are positive as we show that the generalizations are not too costly
with respect to complexity. As a byproduct we obtain new results on the
complexity of model-checking CTLs in one-counter processes and show that
deciding the winner in one-counter games with LTL objectives is
2ExpSpace-complete.Comment: 22 pages, 12 figure
On the Complexity of ATL and ATL* Module Checking
Module checking has been introduced in late 1990s to verify open systems,
i.e., systems whose behavior depends on the continuous interaction with the
environment. Classically, module checking has been investigated with respect to
specifications given as CTL and CTL* formulas. Recently, it has been shown that
CTL (resp., CTL*) module checking offers a distinctly different perspective
from the better-known problem of ATL (resp., ATL*) model checking. In
particular, ATL (resp., ATL*) module checking strictly enhances the
expressiveness of both CTL (resp., CTL*) module checking and ATL (resp. ATL*)
model checking. In this paper, we provide asymptotically optimal bounds on the
computational cost of module checking against ATL and ATL*, whose upper bounds
are based on an automata-theoretic approach. We show that module-checking for
ATL is EXPTIME-complete, which is the same complexity of module checking
against CTL. On the other hand, ATL* module checking turns out to be
3EXPTIME-complete, hence exponentially harder than CTL* module checking.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
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)
On the complexity of resource-bounded logics
We revisit decidability results for resource-bounded logics and use decision problems for vector addition systems with states (VASS) to characterise the complexity of (decidable) model-checking problems.
We show that the model-checking problem for the logic RB+-ATL is 2EXPTIME-complete by using recent results on alternating VASS.
In addition, we establish that the model-checking problem for RBTL is decidable and has the same complexity as for RBTL* (the extension of RBTL with arbitrary path formulae), namely EXPSPACE-complete, proving a new decidability result as a by-product of the approach. Finally, we establish that the model-checking problem for RB+-ATL* is decidable by a reduction to parity games, and show how to synthesise values for resource parameters
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
Satisfiability Games for Branching-Time Logics
The satisfiability problem for branching-time temporal logics like CTL*, CTL
and CTL+ has important applications in program specification and verification.
Their computational complexities are known: CTL* and CTL+ are complete for
doubly exponential time, CTL is complete for single exponential time. Some
decision procedures for these logics are known; they use tree automata,
tableaux or axiom systems. In this paper we present a uniform game-theoretic
framework for the satisfiability problem of these branching-time temporal
logics. We define satisfiability games for the full branching-time temporal
logic CTL* using a high-level definition of winning condition that captures the
essence of well-foundedness of least fixpoint unfoldings. These winning
conditions form formal languages of \omega-words. We analyse which kinds of
deterministic {\omega}-automata are needed in which case in order to recognise
these languages. We then obtain a reduction to the problem of solving parity or
B\"uchi games. The worst-case complexity of the obtained algorithms matches the
known lower bounds for these logics. This approach provides a uniform, yet
complexity-theoretically optimal treatment of satisfiability for branching-time
temporal logics. It separates the use of temporal logic machinery from the use
of automata thus preserving a syntactical relationship between the input
formula and the object that represents satisfiability, i.e. a winning strategy
in a parity or B\"uchi game. The games presented here work on a Fischer-Ladner
closure of the input formula only. Last but not least, the games presented here
come with an attempt at providing tool support for the satisfiability problem
of complex branching-time logics like CTL* and CTL+
Results on Alternating-Time Temporal Logics with Linear Past
We investigate the succinctness gap between two known equally-expressive and different linear-past extensions of standard CTL^* (resp., ATL^*). We establish by formal non-trivial arguments that the "memoryful" linear-past extension (the history leading to the current state is taken into account) can be exponentially more succinct than the standard "local" linear-past extension (the history leading to the current state is forgotten). As a second contribution, we consider the ATL-like fragment, denoted ATL_{lp}, of the known "memoryful" linear-past extension of ATL^{*}. We show that ATL_{lp} is strictly more expressive than ATL, and interestingly, it can be exponentially more succinct than the more expressive logic ATL^{*}. Moreover, we prove that both satisfiability and model-checking for the logic ATL_{lp} are Exptime-complete
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