2019
[GBM19] Patrick Gardy, Patricia Bouyer, and Nicolas Markey. Dependences in Strategy Logic. Theory of Computing Systems. Springer-Verlag, 2019.
Abstract

Strategy Logic (SL) is a very expressive temporal logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express LTL properties of the resulting plays. Such a powerful framework has two drawbacks: first, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not correspond to what is expected. In this paper, we focus on strategy dependences in SL, by tracking how existentially-quantified strategies in a formula may (or may not) depend on other strategies selected in the formula, revisiting the approach of [Mogavero et al., Reasoning about strategies: On the model-checking problem, 2014]. We explain why elementary dependences, as defined by Mogavero et al., do not exactly capture the intended concept of behavioral strategies. We address this discrepancy by introducing timeline dependences, and exhibit a large fragment of SL for which model checking can be performed in 2EXPTIME under this new semantics.

@article{tocsys2019-GBM,
  author =              {Gardy, Patrick and Bouyer, Patricia and Markey,
                         Nicolas},
  title =               {Dependences in Strategy Logic},
  publisher =           {Springer-Verlag},
  journal =             {Theory of Computing Systems},
  year =                {2019},
  doi =                 {10.1007/s00224-019-09926-y},
  abstract =            {Strategy Logic~(\textsf{SL}) is a very expressive
                         temporal logic for specifying and verifying
                         properties of multi-agent systems: in~\textsf{SL},
                         one can quantify over strategies, assign them to
                         agents, and express \textsf{LTL} properties of the
                         resulting plays. Such a powerful framework has two
                         drawbacks: first, model checking \textsf{SL} has
                         non-elementary complexity; second, the exact
                         semantics of \textsf{SL} is rather intricate, and
                         may not correspond to what is expected. In~this
                         paper, we~focus on \emph{strategy dependences}
                         in~\textsf{SL}, by tracking how
                         existentially-quantified strategies in a formula may
                         (or~may~not) depend on other strategies selected in
                         the formula, revisiting the approach of~[Mogavero
                         \emph{et~al.}, Reasoning about strategies: On~the
                         model-checking problem,~2014]. We~explain why
                         \emph{elementary} dependences, as defined by
                         Mogavero~\emph{et~al.}, do not exactly capture the
                         intended concept of behavioral strategies.
                         We~address this discrepancy by introducing
                         \emph{timeline} dependences, and exhibit a large
                         fragment of \textsf{SL} for which model checking can
                         be performed in \textsf{2EXPTIME} under this new
                         semantics.},
}
[BKM+19] Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, and Giuseppe Perelli. Reasoning about Quality and Fuzziness of Strategic Behaviours. In IJCAI'19, pages 1588-1594. IJCAI organization, August 2019.
Abstract

We introduce and study SL[F]–-mdash;a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviours. The satisfaction value of an SL[F] formula is a real value in [0,1], reflecting "how much" or "how well" the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of SL[F] in quantitative reasoning about multi-agent systems, by showing how it can express concepts of stability in multi-agent systems, and how it generalises some fuzzy temporal logics. We also provide a model-checking algorithm for our logic, based on a quantitative extension of Quantified CTL.

@inproceedings{ijcai2019-BKMMMP,
  author =              {Bouyer, Patricia and Kupferman, Orna and Markey,
                         Nicolas and Maubert, Bastien and Murano, Aniello and
                         Perelli, Giuseppe},
  title =               {Reasoning about Quality and Fuzziness of Strategic
                         Behaviours},
  editor =              {Kraus, Sarit},
  booktitle =           {{P}roceedings of the 28th {I}nternational {J}oint
                         {C}onference on {A}rtificial {I}ntelligence
                         ({IJCAI}'19)},
  acronym =             {{IJCAI}'19},
  publisher =           {IJCAI organization},
  pages =               {1588-1594},
  year =                {2019},
  month =               aug,
  doi =                 {10.24963/ijcai.2019/220},
  abstract =            {We~introduce and study
                         {\(\textsf{SL}[\mathcal{F}]\)}---a~quantitative
                         extension of {\(\textsf{SL}\)} (Strategy Logic),
                         one~of the most natural and expressive logics
                         describing strategic behaviours. The satisfaction
                         value of an {\(\textsf{SL}[\mathcal{F}]\)} formula
                         is a real value in~{\([0,1]\)}, reflecting {"}how
                         much{"} or {"}how well{"} the strategic on-going
                         objectives of the underlying agents are satisfied.
                         We~demonstrate the applications of
                         {\(\textsf{SL}[\mathcal{F}]\)} in quantitative
                         reasoning about multi-agent systems, by showing how
                         it can express concepts of stability in multi-agent
                         systems, and how it generalises some fuzzy temporal
                         logics. We~also provide a model-checking algorithm
                         for our logic, based on a quantitative extension of
                         Quantified~\textsf{CTL}.},
}
[HMR19] Loïc Hélouët, Nicolas Markey, and Ritam Raha. Reachability games with relaxed energy constraints. In GandALF'19, Electronic Proceedings in Theoretical Computer Science. September 2019.
Abstract

We study games with reachability objectives under energy constraints. We first prove that under strict energy constraints (either only lower-bound constraint or interval constraint), those games are LOGSPACE-equivalent to energy games with the same energy constraints but without reachability objective (i.e., for infinite runs). We then consider two kinds of relaxations of the upper-bound constraints (while keeping the lower-bound constraint strict): in the first one, called weak upper bound, the upper bound is absorbing, in the sense that it allows receiving more energy when the upper bound is already reached, but the extra energy will not be stored; in the second one, we allow for temporary violations of the upper bound, imposing limits on the number or on the amount of violations.

We prove that when considering weak upper bound, reachability objectives require memory, but can still be solved in polynomial-time for one-player arenas; we prove that they are in coNP in the two-player setting. Allowing for bounded violations makes the problem PSPACE-complete for one-player arenas and EXPTIME-complete for two players.

@inproceedings{gandalf2019-HMR,
  author =              {H{\'e}lou{\"e}t, Lo{\"\i}c and Markey, Nicolas and
                         Raha, Ritam},
  title =               {Reachability games with relaxed energy constraints},
  editor =              {Leroux, J{\'e}r{\^o}me and Raskin, Jean-Fran{\c
                         c}ois},
  booktitle =           {{P}roceedings of the 10th {I}nternational
                         {S}ymposium on {G}ames, {A}utomata, {L}ogics and
                         {F}ormal {V}erification ({GandALF}'19)},
  acronym =             {{GandALF}'19},
  series =              {Electronic Proceedings in Theoretical Computer
                         Science},
  year =                {2019},
  month =               sep,
  abstract =            {We study games with reachability objectives under
                         energy constraints. We first prove that under strict
                         energy constraints (either only lower-bound
                         constraint or interval constraint), those games are
                         \textsf{LOGSPACE}-equivalent to energy games with
                         the same energy constraints but without reachability
                         objective (i.e., for infinite runs). We then
                         consider two kinds of relaxations of the upper-bound
                         constraints (while keeping the lower-bound
                         constraint strict): in the first one, called
                         \emph{weak upper bound}, the upper bound is
                         \emph{absorbing}, in the sense that it allows
                         receiving more energy when the upper bound is
                         already reached, but the extra energy will not be
                         stored; in~the second~one, we~allow for
                         \emph{temporary violations} of the upper bound,
                         imposing limits on the number or on the amount of
                         violations.\par We prove that when considering weak
                         upper bound, reachability objectives require memory,
                         but can still be solved in polynomial-time for
                         one-player arenas; we prove that they are in
                         \textsf{coNP} in the two-player setting. Allowing
                         for bounded violations makes the problem
                         \textsf{PSPACE}-complete for one-player arenas and
                         \textsf{EXPTIME}-complete for two players.},
}
[RSM19] Victor Roussanaly, Ocan Sankur, and Nicolas Markey. Abstraction Refinement Algorithms for Timed Automata. In CAV'19, Lecture Notes in Computer Science 11561, pages 22-40. Springer-Verlag, July 2019.
Abstract

We present abstraction-refinement algorithms for model checking safety properties of timed automata. The abstraction domain we consider abstracts away zones by restricting the set of clock constraints that can be used to define them, while the refinement procedure computes the set of constraints that must be taken into consideration in the abstraction so as to exclude a given spurious counterexample. We implement this idea in two ways: an enumerative algorithm where a lazy abstraction approach is adopted, meaning that possibly different abstract domains are assigned to each exploration node; and a symbolic algorithm where the abstract transition system is encoded with Boolean formulas.

@inproceedings{cav2019-RSM,
  author =              {Roussanaly, Victor and Sankur, Ocan and Markey,
                         Nicolas},
  title =               {Abstraction Refinement Algorithms for Timed
                         Automata},
  editor =              {Dillig, I{\c s}il and Ta{\c s}iran, Serdar},
  booktitle =           {{P}roceedings of the 31st {I}nternational
                         {C}onference on {C}omputer {A}ided {V}erification
                         ({CAV}'19)},
  acronym =             {{CAV}'19},
  publisher =           {Springer-Verlag},
  series =              {Lecture Notes in Computer Science},
  volume =              {11561},
  pages =               {22-40},
  year =                {2019},
  month =               jul,
  doi =                 {10.1007/978-3-030-25540-4_2},
  abstract =            {We~present abstraction-refinement algorithms for
                         model checking safety properties of timed automata.
                         The~abstraction domain we consider abstracts away
                         zones by restricting the set of clock constraints
                         that can be used to define them, while the
                         refinement procedure computes the set of constraints
                         that must be taken into consideration in the
                         abstraction so as to exclude a given spurious
                         counterexample. We~implement this idea in two~ways:
                         an~enumerative algorithm where a lazy abstraction
                         approach is adopted, meaning that possibly different
                         abstract domains are assigned to each exploration
                         node; and a symbolic algorithm where the abstract
                         transition system is encoded with Boolean formulas.},
}
[GBL+19] Mauricio González, Patricia Bouyer, Samson Lasaulce, and Nicolas Markey. Optimisation en présence de contraintes en probabilités et processus markoviens contrôlés. In GRETSI'19. August 2019.
Abstract

This article focuses on the existence and synthesis of strategies in double-weighted Markov decision processes, which satisfy both a probability constraint over a weighted reachability condition, and a quantitative constraint on the expected value of a random variable defined using another reachability condition. This work generalizes a scheduling problem for energy consumption (typically the problem of charging electric vehicles). We study the set of values of a parameter (a threshold) for which the problem has a solution, and show how a partial characterization of this set can be obtained via two sequences of optimization problems. We also discuss the completeness and feasibility of the resulting approach.

@inproceedings{gretsi2019-GBLM,
  author =              {Gonz{\'a}lez, Mauricio and Bouyer, Patricia and
                         Lasaulce, Samson and Markey, Nicolas},
  title =               {Optimisation en pr\'esence de contraintes en
                         probabilit\'es et processus markoviens
                         contr\^ol\'es},
  booktitle =           {{A}ctes du 27{\`e}me {C}olloque du {G}roupe
                         d'{\'E}tudes du {T}raitement du {S}ignal et des
                         {I}mages ({GRETSI}'19)},
  acronym =             {{GRETSI}'19},
  year =                {2019},
  month =               aug,
  abstract =            {This article focuses on the existence and synthesis
                         of strategies in double-weighted Markov decision
                         processes, which satisfy both a probability
                         constraint over a weighted reachability condition,
                         and a quantitative constraint on the expected value
                         of a random variable defined using another
                         reachability condition. This work generalizes a
                         scheduling problem for energy consumption (typically
                         the problem of charging electric vehicles). We~study
                         the set of values of a parameter (a~threshold) for
                         which the problem has a solution, and show how a
                         partial characterization of this set can be obtained
                         via two sequences of optimization problems. We~also
                         discuss the completeness and feasibility of the
                         resulting approach.},
}