4,589 research outputs found
Strategy Logic with Imperfect Information
We introduce an extension of Strategy Logic for the imperfect-information
setting, called SLii, and study its model-checking problem. As this logic
naturally captures multi-player games with imperfect information, the problem
turns out to be undecidable. We introduce a syntactical class of "hierarchical
instances" for which, intuitively, as one goes down the syntactic tree of the
formula, strategy quantifications are concerned with finer observations of the
model. We prove that model-checking SLii restricted to hierarchical instances
is decidable. This result, because it allows for complex patterns of
existential and universal quantification on strategies, greatly generalises
previous ones, such as decidability of multi-player games with imperfect
information and hierarchical observations, and decidability of distributed
synthesis for hierarchical systems. To establish the decidability result, we
introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL*
with second-order quantification over atomic propositions) by parameterising
its quantifiers with observations. The simple syntax of QCTL* ii allows us to
provide a conceptually neat reduction of SLii to QCTL*ii that separates
concerns, allowing one to forget about strategies and players and focus solely
on second-order quantification. While the model-checking problem of QCTL*ii is,
in general, undecidable, we identify a syntactic fragment of hierarchical
formulas and prove, using an automata-theoretic approach, that it is decidable.
The decidability result for SLii follows since the reduction maps hierarchical
instances of SLii to hierarchical formulas of QCTL*ii
Reasoning about Knowledge and Strategies under Hierarchical Information
Two distinct semantics have been considered for knowledge in the context of
strategic reasoning, depending on whether players know each other's strategy or
not. The problem of distributed synthesis for epistemic temporal specifications
is known to be undecidable for the latter semantics, already on systems with
hierarchical information. However, for the other, uninformed semantics, the
problem is decidable on such systems. In this work we generalise this result by
introducing an epistemic extension of Strategy Logic with imperfect
information. The semantics of knowledge operators is uninformed, and captures
agents that can change observation power when they change strategies. We solve
the model-checking problem on a class of "hierarchical instances", which
provides a solution to a vast class of strategic problems with epistemic
temporal specifications on hierarchical systems, such as distributed synthesis
or rational synthesis
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
We show that Branching-time temporal logics CTL and CTL*, as well as
Alternating-time temporal logics ATL and ATL*, are as semantically expressive
in the language with a single propositional variable as they are in the full
language, i.e., with an unlimited supply of propositional variables. It follows
that satisfiability for CTL, as well as for ATL, with a single variable is
EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a
single variable is 2EXPTIME-complete,--i.e., for these logics, the
satisfiability for formulas with only one variable is as hard as satisfiability
for arbitrary formulas.Comment: Prefinal version of the published pape
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
MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications
We introduce MCMAS-SLK, a BDD-based model checker for the verification of
systems against specifications expressed in a novel, epistemic variant of
strategy logic. We give syntax and semantics of the specification language and
introduce a labelling algorithm for epistemic and strategy logic modalities. We
provide details of the checker which can also be used for synthesising agents'
strategies so that a specification is satisfied by the system. We evaluate the
efficiency of the implementation by discussing the results obtained for the
dining cryptographers protocol and a variant of the cake-cutting problem
Refining and Delegating Strategic Ability in ATL
We propose extending Alternating-time Temporal Logic (ATL) by an operator <i
refines-to G> F to express that agent i can distribute its powers to a set of
sub-agents G in a way which satisfies ATL condition f on the strategic ability
of the coalitions they may form, possibly together with others agents. We prove
the decidability of model-checking of formulas whose subformulas with this
operator as the main connective have the form ...<i_m
refines-to G_m> f, with no further occurrences of this operator in f.Comment: In Proceedings SR 2014, arXiv:1404.041
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